Sound-Producing Dune and Beach Sands
Sound-producing dune and beach sands
JOHN F. LINDSAY Marine Science Institute, University of Texas at Galveston, Galveston, Texas 77550 DAVID R. CRISWELL Lunar Science Institute, 3303 Nasa Road 1, Houston, Texas 77058 T. L. CRISWELL Battelle Pacific, Northwest Laboratories, Richland, Washington 99352 B. S. CRISWELL Department of Microbiology, Baylor University College of Medicine, Houston, Texas 77001
ABSTRACT discernible once prolonged avalanching is established, hence the term "booming sand." Humphries (1966, p. 139) described the Field and laboratory investigations have confirmed differences low frequency as beating at about 1 Hz. Dryness is essential for between the acoustic and seismic emissions of "singing" and sound production. Warm or hot sand generally seems to boom best "booming" sands and revealed that booming grains possess ex- but heat is not essential. Avalanches can be many metres on a side tremely smooth surfaces. Singing sand is the most common of the (and as much as a few centimetres deep) in the natural case or only two types of sound-producing sands. It occurs widely as a beach a few cubic centimetres when the sound is evoked by pulling one's sand and consists of well-rounded highly spherical grains that have fingers through the sand. Avalanche velocities range from 20 to 30 a well-sorted highly symmetric grain-size distribution. Sound is cm sec-1 in both silent and booming events. The sound-producing produced when the sand is mechanically sheared, possibly causing sands are commonly termed "desert thunder," "booming dunes," the closely packed grain array to dilate in a coherent manner. Fre- and "roaring sands." There have been no reports in which one type quency (>500 Hz) is controlled by grain size, and amplitude may of sand (squeaking or booming) could be manipulated to evoke in part relate to grain morphology. Booming sand is a relatively both the high- and low-frequency emissions. rare phenomenon that occurs in some desert regions. This sand The properties of these two types of sands are not well known produces a low-frequency (f„ = 80 Hz) sound during avalanching. despite the widespread although rare occurrence. In this paper the The process efficiently (=0.1 to 1 percent) produces very narrow morphological properties of sound-producing sands are studied in band seismic energy in the 50- to 80-Hz range. Simultaneously an attempt to understand their unique characteristics. Criswell and produced audio signals are broader band but are composed of others (1974, 1975) described in detail the first quantitative mea- signals that peak at the same fundamental frequencies as the seis- surements of seismic and acoustic emissions of a booming dune. mic emissions. In addition, the acoustic emissions display first and Application of the booming phenomenon to lunar seismic data and second harmonics. Acoustic production is ~ 400 times less efficient thermal quakes on the Moon was discussed by Criswell and Lind- than seismic energy production. Booming occurs in quartz and say (1973, 1974). carbonate sand grains that are well sorted, fine skewed, and mesokurtic. The individual quartz sand grains are only moderately BOOMING SAND well rounded. When compared to normal eolian grains, however, they have highly polished surfaces that are smooth on the 1-/Ltm Booming dunes have been mentioned in mideast literature for at scale. The exceptional smoothness of the grains may facilitate least 1,500 yr and in Chinese literature from as early as the ninth booming. The effective Q (magnification factor) and compressibil- century (Stein, 1912). Booming sand has since been reported from ity (k) of the grain system may be the key physical quantities in- the Middle East, the Sahara Desert, southern Africa, Chile, Baja volved in booming. Thus, whereas booming is rare in the terrestrial California, California, Hawaii, and Nevada (Fig. 1, Table 1). environment, it may be common in the high-Q soils of the Moon Instrumental measurements of the acoustic and seismic output of and the near waterless dune environment of Mars. Key words: booming sand have never been reported. This is clearly of impor- sedimentary petrology, extraterrestrial geology, dune sand, beach tance not only to obtain quantitative information on the relative sand, eolian, seismology, acoustic, deserts, geophysics. spectral output of the dunes but on the efficiency of conversion of the slumping energy of the grains into seismic and audio output. INTRODUCTION Of several known booming dunes in the U.S., two were visited and sampled, and acoustic and seismic signals were recorded at one Two types of sands emit loud and distinct — often music-like — locality. sounds when they are sheared. Most common is a particular type of beach sand that emits a short note in the 500- to 2,500-Hz range of a few tenths of a second or less duration when sharply poked or stepped on (Brown and others, 1964; Takahara, 1973). Colloqui- ally, these are called singing, squeaking, barking, or whistling sands. Sound production by desert dune sand is less common and has been likened to that produced by a kettle drum, zither, nakus, bass violin (Curzon, 1923), or low-flying propeller aircraft (Humphries, 1966). All describe a loud, relatively low-frequency sound being produced by loosely flowing or avalanching sand. Lewis (1936) estimated the frequency of the sound between 132 and 300 Hz, whereas Humphries (1966) placed the frequency at between 50 and 100 Hz. Also common to many descriptions of the sound produced by the desert dune sand is that a much lower beat frequency is Figure 1. Map showing the location of booming sand.
Geological Society of America Bulletin, v. 87, p. 463-473, 12 figs., March 1976, Doc. no. 60316.
463
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TABLE 1. LOCATION OF BOOMING SAND DUNES
Name and location Type and size Comments and references (lat, long) (height x width X length)
Hill of Sounding Sand Dune field Like rumble of distant carts, drums, or thunder; audible 5.4 to 10 km; near Tunyang, China 100 m X 20 km X 40 km small lake at "Caves of Thousand Buddhas"; possibly at toe of dune field 40°03'N, 95°00'E) (1, 2, 3, 17) Reg-i-Ruwan Sand drift On detached foothill of Paghman Range; sand supply not obvious; booms 64 km north of Kabul, Afganistan 130 m X 130 m spontaneously about 12 times a year; loud hollow drum sound
(approx. 35°N, 69°E) (1) Rig-i-Riwan Sand drift On detached ridge of Calakoh Range; on southern face; no sand on adjacent Between Herat, Afganistan, and 200 m x 800 m hills, surrounding terrain not sandy; audible at 16 km; like vibration of Sijistan due north of district of telegraph wires of Kalah-i-Kah (1) Jebel Nakus Sand drift Faces Gulf of Suez 3 km to the east; in situ humming sound; from a distance, 11 km north of Tor, Sinai like distant cannon or deep bass of pipe organ; ground vibration and sand (28°18'N, 33°33'E) detachment during flow (1,5) Bedawin Ramadan Sand drift Audible at 30 m; bass note Wadi Werkan, Sinai, north of Jebel, 13 m x ? x ? (1,5) Nakus Oh Shomar Sand drift Bass note Mountain of the Sinai group (1) Rowsa No details Several nameless dunes identified by nearest oasis, Nefuz desert near El-Hyza, Deffafiat Arabia Subbia (1) Itzum Wadi Hamade No details Northern Arabia, north of Medina (1) Nameless Probably barchan In Uruq Adh Dhahiya region of the "empty quarter" of Arabia; like foghorn, Sand of Yadila 30 m x ? x ? 2-min duration (22) Nameless No details Near dead city of Jahura Arabia (1) (approx. 22°N, 51°E) Jebel-et-Tabul No details Between Medina and Mecca Arabia (1) Nameless No details Near Taif in sand belt of Arq-al-Subai; many booming dunes Abraq-al-Manazil, Arabia (1, 19) Nameless No details 150 km ESE of Medina Khanug, Arabia (1) Nameless Sand sheets On or close to Nubian sandstone plateau; sand coated with iron oxide; Gilf Kebib Desert Seifs many booming sands in area (23°N, 26°E) Barchans (2, 4) Es-Sadat Sand drift In cave on hillside in western Beirut facing "Pigeon Rock"; sound resembles Beirut, Lebanon beating of tambourines (1)
Sand Mountain, Nevada crophone. A complete report on the acoustic and seismic observa- tions, instrumentation details, and analysis procedures was given in Sand Mountain (Fig. 2) is a booming sand dune that lies 5 km Criswell and others (1975). At the time of the visit, the dune sand north of U.S. Highway 50 about 25 km southeast of Fallon, was extremely dry. Sand at most places on the dune, but especially Nevada. The dune lies on the northeastern end of a large salt pan on the ridge line, could be made to produce a sound by setting in and in the constriction of a rocky pass. The prevailing wind direc- motion a mass of sand more than 10 to 15 cm in thickness. On the tion is to the northeast across a salt pan; the wind is then deflected gentler slopes at the base of the dune, slumping had to be induced down the narrow rocky pass in which the dune has formed. The artificially; however, higher on the dune where the slope exceeded dune location appears to be static, and little change has occurred in 52 percent (27°), sound-producing avalanches were readily ini- dune morphology in the last 10 yr (C. Snyder, 1973, personal tiated. Aural observations during the traverse were comparable commun.). Sand Mountain is a complex seif dune approximately 6 with earlier descriptions of other booming dunes (Bagnold, 1954; km long by 1.5 km wide and has a maximum relief of 122 m. In Humphries, 1966; Lewis, 1936). Only a single frequency was cross section, the dune is almost symmetrical with surface slopes up heard during the first second of an avalanche. After two to three to 32° (Fig. 2, bottom view). seconds, however, a much lower beat frequency was established. It Sound Production of Sand Mountain Booming Sand. In June was possible to stand on the firm subbase of the sand while the 1973, simultaneous seismic and acoustic recordings were con- upper layers of sand flowed ankle deep around one's feet and feel ducted at Sand Mountain utilizing a vertical-axis geophone (4.4 Hz the vibration produced by the avalanche. resonance frequency) and a wide band (1 to 20,000 Hz) air mi- The experimental results from one test are presented in Figures 3
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TABLE 1 (continued)
Name and location Type and size Comments and references (lat, long) (height x width x length)
Nameless Barchan dunes Libyan desert west of Nile Valley; after-reverberations of Big Ben or hum- Dakhla Oasis 20 m X ? x ? ming of telegraph wires (approx. 25°40'N, 28°50'E) (1,5) Nameless Barchan dune Western Sahara between Timbuctoo and Morocco, Igidi Region; one of a near well Bir-el-Abbas chain of barchan dunes; sounds like a trumpet (25°N, 6V2°W) (1) Nameless Sand drift Libyan-Chad border region; sounds like low-flying aircraft 11 km northwest Korizo Pass 30 m x ? x 300 m (6, 7) (22°30'N, 15°25'E) Nameless Barchan dune Very loud, synchronous effect similar to over-flight of B-29 bombers Umm Said, Persian Gulf 30 m x ? x ? (8, 9) (approx. 25°N, 51°E) Kalahari Dunes Toe of dune field Only on southern toe (lee) of dune field; humming and roaring, possibly Witsands Farm, South Africa 30 m x 0.5 m x several km higher frequency than other booming dunes (22°28'S, 28°34'E) (10) Great Sand Dunes All types Booming simply noted as event common to the region Namib Platform Very large dune field (11) (approx. 24°S, 15°E) 160 km x 160 km in area Sand Mountain Seif Short note on bass violin and roaring (recorded) 25 km east of Fallon, Nevada 120 m x 1.6 km x 7.2 km (1, 12, 13) (39°15'N, 118°36'W) Kelso Dunes Barchan dunes Roaring sounds from lee slopes East of Barstow, California 180 m X 16 km x 16 km (14) (33°55'N, 115°45'W) Roaring Sands Backbeach dune Carbonate sand; 100 m from sea; sounds like thunder, buzz saw, or hoot- Mana, Kauai, Hawaii 30 m x ? x 800 m ing, possibly broader bandwidth than quartz dunes; similar dunes at (22°N, 159°48'W) Kaluakahua, Niihau (1, 15, 18,21) Cerrito de Huara (or El Bramador) Isolated dune 10.4 km west of Pozo (well) de Ramirez Tarapaca, Chile (1, 16) (20°S, 69°W) El Punto de Diabolo Sand drifts in gullies Moaning sounds detected at 400 m; undulations make standing difficult Copiapo, Chile (1, 17) (27°22'S, 70°20'W) Mountain of the Bell Backbeach Sound of bells or sound made by rubbing finger along edge of glass bowl; Baja California, Mexico 20 m x ? x ? dune lens-shaped (possibly barchan); approximately 100 km north of Cape (23°42'N, 110°30'W) San Lucus on Pacific Coast (1, 15)
References: 1, Curzon (1923); 2, Stein (1912); 3, Cable and French (1927); 4, Bagnold (1954); 5, Hume (1925); 6, Humphries (1966); 7, Humphries, D. M. (personal communication, 1973); 8, Bagnold, (personal communication, 1973); 9, Mathes, D. M. (personal communication, 1974); 10, Lewis (1936); 11, Logan (1960); 12, Bolton (1884); 13, Lindsay and others (1974); 14, Sharp (1966); 15, Bolton (1890); 16, Bollaetf (1851); 17, "Tun Huang Lu" (1915); 18, Bryan (1915); 19, Palmer (1871); 20, Resident of Hawaii (1973); 21, Thomas (1932).
and 4. These coincident bursts of acoustic and seismic energy were string instrument such as bass violin. The air microphone is more obtained by shoveling in the sand approximately three metres from complicated than the geophone trace and appears above the noise the geophone that was buried just below the dune surface. The air level approximately 0.05 to 0.1 sec prior to the recording of an microphone was hand held immediately above (30 to 50 cm) the appreciable signal on the geophone. In other examples, there was shoveling area. The sound of impact of the shovel into the sand is no discernible difference in start times. However, the air- discernible in the air-microphone recordings (off scale to left of Fig. microphone signal and the geophone signal terminated at approx- 3). Subsequent deposition of sand from the shovel downslope on imately the same time. the sand dune produced virtually no discernible amplitude on the Figure 4A displays the power-spectral-density distribution of the traces. The distinct oscillations that were recorded occurred during output of the geophone and Figure 4B displays the root-mean- the time the shovel was being withdrawn from the sand. The boom- square amplitude distribution of the output of the air microphone ing sound produced by the sand was audible 20 m away. Unfortu- corresponding to the event in Figure 3. An air microphone re- nately, a sustained avalanche could not be induced at point A. sponds to pressure fluctuations in the air. The pressure fluctuations Acoustic output of sustained avalanches was recorded in later ex- are proportional to the amplitude of the pressure differences that periments and has been reported by Criswell and others (1976). carry the propagating acoustic waves. This means that acoustic The amplitude traces (Fig. 3) for both the air microphone and the power per unit frequency is directly related to the square root of the geophone show the very distinctive nature of the emissions pro- absolute amplitude of the value of the propagating pressure wave duced. The geophone oscillation is extremely sinusoidal and clean, (Morse, 1948). Therefore, the root-mean-square distribution is di- comparable to what one would obtain by recording a very fine rectly proportional to the power per unit of frequency in the prop-
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Figure 2. Two views of Sand Mountain. Top view is looking approximately northeast from a point on U.S. 50 6 to 8 km from the dune. Sand Mountain is composed of two seif dunes whose major axes are parallel to the strongest prevailing winds. Bottom view is looking approximately north at a point on U.S. 50 5 km from the crest of the smaller dune. The seismic and acoustic measurements were performed at point A.
agating air wave. All modes of ground motion (vibrations of the B 0 9 28 4005 surface both perpendicular and parallel to the local surface) will 1 1 1 1 1 produce air-pressure fluctuations (Fig. 4B). AIR MICROPHONE
Conversely, the geophone responded to only the vertical compo- 61 HZ nent of ground motion. The power propagated by the seismic wave 66 HZ was, therefore, proportional to the product of the wave velocity times the square of the maximum vertical ground velocity. The power-spectral-density distribution is obtained by squaring and time averaging the observed corrected amplitude of the geophone output. Therefore, the power-spectral-density trace is directly S '0 proportional to the power per unit frequency transmitted by the seismic wave.
————^wwwwWWVVWVWVWVVVwvv^—«
GEOPHONE (DC)
AIR MICROPHONE (DC)
50 100 50 li100 t HERTZ — HERTZ — Figure 4. The power spectral distribution in cm2/sec2/Hz (geophone) and 3 SECONDS ? root-mean-square amplitude trace in N/m2 (air microphone) were obtained Figure 3. Simultaneously recorded amplitude traces from the geophone by digitizing a 2-sec interval of the amplitude recording ( =1,024 samples and air microphone. The microphone amplitude is proportional to instan- sec-1) about each event, correcting for amplifier response, prewhitening, taneous air pressure. The geophone amplitude is proportional to ground and then computing the spectra. All data below 20 Hz were suppressed. velocity. Neither trace is corrected for recorder roll off, which is significant The small geophone peak between 135 and 140 Hz is a system artifact. The between 20 and 40 Hz. Both signals are well above the noise levels. noise level of the air-microphone trace is below 2.10 2 in this instance.
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The extremely narrow band output of the geophone at 66 Hz mass to either external or internal oscillatory forces (Wu, 1971). Q (Fig. 4A) is not an artifact of the recording system. This can be is equal to the average energy of the system during an oscillation proven by comparing it with the root-mean-square trace for the air divided by the energy lost from an oscillating system during one microphone, which also has a peak at 66 Hz. These coincident oscillation. The resonance frequency of a system decreases as Q peaks were obtained through the two entirely separate physical increases. Viscous (fluid) drag at contact points is a major energy channels. The existence of the higher amplitude peak in the air- loss mechanism. Q will increase as the grains become smoother and microphone trace at 61 Hz is not inconsistent. It indicates the the amount of fluids present between asperities is decreased. Thus, presence of a second mode of ground oscillation to which the single more energy will be conserved during each oscillation. The ex- axis, vertically directed geophone was not sensitive. Apparently, tremely dry and smooth contacts between booming grains will tend the shoveling first initiated a mode of ground vibration (61 Hz) to make the grain volumes at asperities either deform elastically or perpendicular to the sensitive axis of the geophone. However, the permit the slipping of grain contacts with little energy loss. The air microphone could detect the air-pressure fluctuations generated spring constant (k) is also increased by grain smoothness and sur- by this ground mode. Approximately 0.05 to 0.1 sec later the am- face dryness. A large value of k means the extremely dry and plitude of the vertical ground mode (66 Hz) rose above the noise smooth grains near the peak of Sand Mountain can store more level of the geophone. Propagation delay of the seismic signal recoverable energy of elastic deformation than rough sand grains. would be only a few milliseconds and, therefore, negligible (Fig. 3). The importance of fluids (not necessarily wet but even chemically The audio output recorded by the air microphone between 110 absorbed) at the asperities is clearly demonstrated by the fact that and 140 Hz is the first harmonic of the fundamental emission. Very Sand Mountain will not boom during periods of high humidity but likely the >110-Hz portion of the spectrum is what most adults will boom after an interval of hot dry weather. Additionally, the perceive aurally, which may account for the higher estimates of areas of spontaneous booming are confined to the top of the dune frequency that are usually reported. Modern investigators liken the where constant aerodynamic recirculation of those grains produces tactile sensation of booming dunes to a mild electrical shock by a complete drying of each surface grain (Figs. 5, 6 — avalanche common 60- or 50-Hz household current. This is inside the range zone). High Q (>1,200) is characteristic of the lunar soils and of 50- to 80-Hz emissions generated at Sand Mountain. Quantita- lends support to the speculation that "booming" may occur on the tive data were not obtained for frequencies below 20 Hz due to Moon. limitations of the recorder. However, it is clear from the literature Grain Size of Sand Mountain Booming Sand. During a traverse that strong beating effects do occur in the 1- to 10-Hz range. made across the highest part of Sand Mountain to the dune crest, Analysis of the increase in background noise level of the geophone 26 sand samples were collected at regular intervals of approxi- channel during tests qualitatively confirms the presence of prop- mately 24 m (Fig. 2, bottom view). The samples were taken from agating seismic energy for <20 Hz. the upper 3 cm of the dune surface. The almost silent avalanche of normal sand would not produce a The mean grain size of the sand ranges from 1.380 (384 /Am) to detectable air-microphone or geophone signal on the recording sys- 1.968(/> (256 fjm), with a grand mean of 1.696 ± 0.1810 (309 H tem employed. Recordings were made of such slides immediately (Folk and Ward, 1957, measures). As with the dune profile and the after the example given here, and there were no discernible signals surface slope, the mean grain size of the sand is approximately above the noise level of either channel. We cannot, therefore, symmetrically distributed about the dune crest (Fig. 5). Overall, the specify the conversion efficiency of silent slumping into either surface sands of the dune are finer grained near the crest and acoustic or seismic modes. In the case of the booming effect, how- coarser away from the crest. The main variables controlling the ever, the efficiency of the conversion of slumping into seismic mean grain size of a dune sand are surface slope and wind velocity. energy was calculated to be between 0.1 and 1 percent. Energy When mean grain size and slope are plotted against each other (Fig. conversion into the propagating air mode is approximately a factor 6), the samples fall into three distinct populations. of 400 lower. It is very likely that the efficiencies change from one slumping event to the next and probably from one type of sand to Stable Zone another. It should also be noted that these efficiency estimates apply to short bursts induced artificially while withdrawing the This zone is equivalent to what Bagnold (1954) called the shovel from the sand and may not apply to a fully developed av- "plinth." It includes the lower slopes of the dune that range from alanche. 10 (6°) to 37 percent (20°). This zone is essentially a zone of The mechanism that produces booming is not presently estab- deflation and net accumulation with coarser particles being left lished. Bagnold (1966) suggested that a nonclassical dispersive behind as fines move upslope. Consequently, grain size gradually pressure is generated in the shear plane along which the overburden decreases with increasing slope. of sand is moving. Coherent associations of sand grains in this shear layer produce the booming effect. The primary frequency is Mixed Zone predicted to be This zone includes slopes from 37 (20°) to 52 percent (27°). Sand reaches this zone in one of three ways: (1) it is transported upslope by the wind from the stable zone, (2) it is carried in from the where X = 14, g is approximate local gravitational acceleration, opposite face when the wind comes from the other direction, and and D is the average grain diameter. However, for Sand Mountain, (3) it avalanches down from the avalanche zone above. Periodi-
D = 300 to 380 fxm, which means fB =211 to 295 Hz. The cally, the dune surface in this zone oversteepens, and sand from all predicted frequency is a factor of 3 to 6 times greater than the three sources is mixed by avalanching. Consequently, sand from primary emission frequencies of short bursts observed at Sand this zone has a full range of grain sizes, although in general grain Mountain. This is a nonclassical approach. Linear theories of soil size decreases toward the dune crest. vibration may be applicable in the low-amplitude (much less than grain diameter) events. The resonance frequency of typical dry sand Avalanche Zone (Zone of Maximum Aeration) is approximately 80 Hz (Ho and Burwash, 1969) and thus not too different from the booming-dune output-frequency range. Q and In this zone the measured slopes range from 52 (27°) to a max- the effective spring constant (k) of the sand are the significant and imum of 62 percent (32°). Here the sand is always at slopes be- interrelated properties that determine the response of a granular tween the dynamic (=32°) and static (=27°) angles of repose. Av-
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alanching occurs, therefore, as soon as sand from either downslope Kurtosis values range from platykurtic (0.674) to very leptokur- or from over the crest begins to accumulate. There is a general tic (1.556) with a mean value of 1.016 ± 0.227 (Fig. 5). Like tendency in this zone for the grain size to decrease toward the crest skewness, the kurtosis values are symmetrically distributed about after a sharp increase at the boundary with the mixed zone. the dune crest. Some peaks, however, are not as well defined as At the time Sand Mountain was sampled, it appeared that wind others. At the dune crest the sands are platykurtic (that is, the had most recently been eroding the northwestern face and carrying curves are flatter than a normal curve). Progressing downslope, the the sand across the crest to the southeastern face. Consequently, kurtosis values increase rapidly to a peak at the boundary with the the normal grain-size pattern of the dune, which could be expected mixed zone. Once into the mixed zone the values decline again to to be symmetrical, had a pattern of net erosion superimposed on the middle of the mixed zone and then rise to a peak toward the the northwestern face and a pattern of net accumulation on the boundary with the stable zone. On the southeastern face, the sand southeastern face. This has resulted in the lower slopes of the in the stable zone is noticeably platykurtic, whereas the values are northwestern face being deflated to a layer of wet sand and leaving much closer to one (lognormally distributed) in the stable zone on coarser materials behind, thus increasing mean grain size abnor- the northwestern face of the dune. mally. Some of the smaller sand grains were carried across the dune The extreme platykurtic values in the stable zone on the south- crest where they accumulated on the upper slopes of the lee face of eastern face are consistent with deflation, which generally leaves the dune. Where the slope became oversteepened, avalanching oc- behind a sand with a broad bimodal distribution. The more sub- curred that carried material from near the crest down the lee slope. dued values on the northwestern face probably indicate that sand Very small sand grains, however, were carried by the wind beyond was being transported across the stable zone from the reg during the avalanche zone to the mixed zone on the lower part of the lee the last erosional period. There seem to be two parts to the mixed slope (Fig. 5) — hence, the marked increase in mean grain size zone, a lower leptokurtic part and an upper platykurtic part. This downslope followed by an even sharper decrease in grain size in the suggests that the kurtosis values in the lower portion are dominated more stable zone. The asymmetry of the distribution is essentially by sand moving upslope, whereas the upper portion is determined determined by fines being removed from the lower slopes of the by fine sand carried over the dune crest. In the avalanche zone (the northwestern face and accumulating on the middle slopes of the zone of maximum aeration), the kurtosis values increase consist- southeastern face. ently downslope, which suggests that the avalanches are producing The remaining three grain-size parameters (standard deviation, more peaked curves as they move downslope in grain flow. skewness, and kurtosis) are all controlled by the same factors re- Deflation of this zone by the wind would cause a decrease of the sulting in a general symmetry with a weaker asymmetry super- kurtosis values. imposed. Thus, the lower portion of the dune, the stable zone, is domi- The sand samples range from moderately well sorted (standard nated by erosion and the upslope movement of sand. The av-
deviation = cr1 = 0.509
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MIXED ZONE
Figure 6. Inclusive graphic mean grain size versus surface slope for sand samples from Sand Mountain. Dots and circled dots indicate south-
eastern and northwestern slopes of the dune, re- DISTANCE m spectively. Starred symbols indicate sampling Figure 8. Inclusive graphic mean grain size of localities that avalanched and boomed spontane- booming sand samples from Kauai, Hawaii, in ously when disturbed. relation to position on the avalanche slope.
Figure 7. Inclusive graphic mean grain size versus inclusive graphic standard deviation for booming sand samples from Sand Mountain,
100 200 300 400 500 600 700 Nevada, and Kauai, Hawaii. Dots and circled DISTANCE m dots indicate southeastern and northwestern slopes of Sand Mountain, respectively; starred Figure 5. Grain-size parameters (Folk and symbols indicate Kauai. Nevada booming sand Ward, 1957, measures) of booming sands from outlined with broken line; Kauai booming sand Sand Mountain in relation to location on a outlined with solid line. traverse southeast to northwest across the dune • MEAN * axis.
boom. Bolton (1890, p. 29) described the sound produced by the except that the booming sand contains an excess of fines. Perhaps, Kauai dunes as a "deep bass note of tremulous character" that significantly, the silent beach and dune sands from Hawaii fall well could be heard for up to 105 ft from the dune. He also noted that within the range of the Nevada booming dune sand (Fig. 7). vibrations could be felt through the hands and the feet. Grain Size of Hawaiian Booming Sand. A total of 11 samples Particle Morphology of Booming Sand were collected at 0.5-m intervals up the avalanche slope. The mean grain size of the samples ranges from 0.886 (541 /j.m) to 1,428c/) Two-dimensional sphericities (Lindsay, 1972) were determined (372 /urn), with a grand mean of 1.109 ± 0.2040 (464 firn) (N = for particles from the modal 1$ class interval for booming sand 11). The Hawaiian sand is significantly coarser than the Nevada from Sand Mountain, the Korizo dune described by Humphries sand (io.o5 = 2.210 < 8.258, d.f. = 35; Fig. 7). The mean grain size (1966), and a silent backbeach dune sand from Aransas Pass, Texas decreases in a linear fashion in an upslope direction (p = 0.887, (Table 2). It is readily apparent from the tabulated values that io,o5 = 2.262 < 5.772, d.f. = 9) (Fig. 8). This suggests that a sorting shape is an inherited feature that is determined by the way in which process is operating such that coarser particles accumulate at the quartz fractures. It thus seems unlikely that shape alone determines bottom of the slope. The most likely candidate is grain flow during avalanching (Bagnold, 1966), which tends to deposit finer materi- als first and produce reverse graded beds. TABLE 2. SPHERICITY OF DETRITAL PARTICLES FROM SOUND-PRODUCING AND SILENT SANDS The Hawaiian sand ranges from moderately well sorted (cr, = 0.525$) to very well sorted (cr, = 0.258$) with a mean en of 0.349 Mean Number of ± 0.075$. Comparison with the Nevada sand shows it to be simi- Name and Location sphericity Std. dvn. measurements lar (io.o5 = 2.210 > 1.023, d.f. = 35). The shape of the grain-size curves varies from near symmetrical Booming dune sand (Sk, = —0.020) to strongly fine skewed (Sk, = 0.402), with a mean Sand Mountain, 0.814 0.055 146 skewness of 0.152 ± 0.103. Comparison with the Nevada samples Nevada indicates that there is no significant difference between the two Korizo (Humphries, 0.809 0.062 391 1966) populations (i0.05 = 2.210 > 0.199, d.f. = 35). Kurtosis values range from 0.981 (mesokurtic) to 1.328 (lep- Silent dune sand tokurtic), with a mean value of 1.158 ± 0.109. There is no Aransas Pass, Texas 0.808 0.064 392 significant difference between the kurtosis values for the Nevada Victoria Valley, 0.831 0.048 173 Antarctica and Hawaiian sands (f0.05 = 2.210 > 1.877, d.f. = 35). For comparative purposes, a sand sample was collected from a Squeaking beach sand nearby silent sand dune and from the beach between the dunes and McMasters Beach, 0.802 0.069 93 the sea. Because the dunes consist of coralline sand, it can be pre- New South Wales, sumed that both the silent and booming sand dunes were derived Australia from the same beach sand. The silent dune sand is slightly finer Squeaky Beach, 0.817 0.068 215 Victoria, Australia grained (Mz = 1.614$) than the booming sand and considerably more negatively skewed (Sk, = -0.125). However, sorting (cr, = Silent beach sand Barwon Heads, 0.087 104 0.385) and kurtosis (KG = 0.912) values are quite similar. The 0.761 Mana beach sand is very similar to the silent dune sand (Fig. 7). Victoria, Australia Bolivar, Texas 0.794 The booming dune sand is thus very similar to its source materials 0.066 160
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If the smoothness of the sand grains is of primary importance in the booming process, booming dunes should occur in situations where a considerable amount of energy has been expended in the polishing of the detrital materials. Before a grain can be polished, it must be rounded to a certain degree; otherwise, the concavity of some surface will be too great for polishing to take place. Rounding of sand grains requires both considerable time and a reasonably energetic environment. Most desert sand has been rounded to some extent prior to being incorporated into desert dunes. Sharp (1966) also found that sand grains in desert-dune environments become rounded with increasing distance from the source. This suggests that at least the first of the conditions for a booming sand is most likely to be met on the downwind side of a large dune field or where the sand has been transported a considerable distance before being incorporated into the dune. This is consistent with documented booming-sand localities (Table 1). The initial condition of roundness is also likely to be met on beaches where sediment supply is limited and longshore current activity minimal, such that the sand has a relatively long residence time in the beach environment before being carried by the wind to form backbeach dunes. Further, sorting and skewness appear im- portant, and if longshore current activity were too great, all the fines would be carried away, which would result in a very well sorted sand with no fines. Having established at least a modest degree of rounding, it is necessary that the particles remain in an active eolian environment for an extended period of time until polishing can take place. This requires either that the sand grains be transported long distances by the wind or that they remain effectively trapped for long periods within a dune environment. Most of the available descriptions of booming dunes indicate that booming occurs under very dry conditions. Even small amounts of moisture stop the booming completely. This, in con- junction with the observed smoothness of the grains, suggests that booming is dependent on the surface properties of the grains. Many of the observed physical parameters associated with booming dunes may simply be related to optimizing the condition of the grain surfaces so that other variables may come into effect. For Figure 9. Quartz sand grains from booming (a through c) and silent (d example, it may simply be that polished surfaces dry more rapidly through f) sand dunes. Scales on a and d, 500 fjm; b and e, 200 /nm; c and f, and completely. This would suggest that if the sediment is too 40 pm. Note subdued surface relief of the booming sand grain in c com- poorly sorted, drying would be inefficient and again the surface pared to silent sand grain in f. properties of the grains may not be optimized. If this is the case, the ability of a sand to boom, although it may be one of a number booming, which can only occur under very restricted conditions in of prerequisities. the terrestrial environment, may be a very common occurrence in Quartz sand grains from the Nevada booming dune and from a the near waterless dune environment of Mars and the waterless silent dune in Victoria Valley, Antarctica, were examined under a soils of the Moon. That is, booming may be independent of the scanning electron microscope (Fig. 9). The grains from the two sites grain-size parameters and particle morphology and more depen- are similar in shape and general appearance; however, there are dent on the microphysical properties (Q, k) of the component marked differences in surface texture. At higher magnifications grains, except in the terrestrial case where the variable presence of (Fig. 9, c and f), the surfaces of the booming sand grains were water on the grain surfaces may drastically modify the effective Q found to be exceptionally smooth with a subdued microrelief. and k values.
DISCUSSION SQUEAKING BEACH SAND
It is apparent from Figure 7 that the mean grain size and sorting Squeaking sand as a phenomenon is far more common than of a sand deposit are not the critical factors determining the ability booming sand and much more widespread in occurrence. Squeak- of a sand to boom. There may be limits to the mean and standard ing beach sand occurs on the seacoast of almost every continent deviation of a booming sand, but they are broad limits and many (Bolton, 1884, 1890; Julien, 1885; Brown and others, 1961, 1964; silent dune sands fall within the range. The final observation that Curzon, 1923; Ridgway and Rupp, 1970; Ridgway and Scotton, sand grains from booming dunes have smooth subdued surface 1972, 1973; Takahara, 1973), along some lake shores (Bolton, textures is possibly the key to understanding many of the less obvi- 1890), and on the banks of a few rivers (Brown and others, 1964; ous features of booming sand. The smoothness of the grains may be Bolton, 1890). of considerable importance in the booming process by decreasing A series of squeaking and silent sand samples were collected mechanical coupling between grains and enhancing the importance from Australian beaches between Melbourne and Sydney (Fig. 10). of completely elastic contact points between grains. The smooth- Two additional silent sand samples were included, one from the ness of the grains may also be important in allowing rapid and Bolivar Peninsula on the Texas Gulf Coast and one from Mana on complete drying of the grains. the Hawaiian island of Kauai.
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NEWCASTLE 4 X SQUEAKING (NEW SOUTH WALES) 8 ® SILENT SYDNEY i .7
WOLLONGONGf Si .6 Figure 10. Map showing the location of CANBERRA* squeaking beaches (Iocs. 1 through 5) and silent > .5 a s ® beaches (Iocs. 8 through 11) sampled in south- a •* t— eastern Australia. - * (VICTORIA) u> 3 .2 MELBOURNE .1 1.5 2 2.5 TASMAN SEA MEAN 0 Figure 11. Inclusive graphic mean versus in- 100 200 300 I I clusive graphic standard deviation for squeaking KILOMETERS and silent beach sands. Note the relatively tight SCALE cluster formed by the squeaking sand samples.
Grain Size of Squeaking Sand Particle Morphology of Squeaking Sand
Including data from two sources in the literature (Humphries, Two-dimensional sphericities were determined for particles from 1966; Ridgway and Rupp, 1970), a total of seven squeaking and the 14> modal class interval for the squeaking sand from McMasters seven silent beach sand samples were available for the study. Beach (loc. 5, Fig. 10) and Squeaky Beach (loc. 1, Fig. 10). These Grain-size parameters are all listed in Table 3. Comparison of two sand samples have sphericities of 0.802 ± 0.069 and 0.817 ± the mean grain-size values for squeaking and silent beach sand by 0.068, respectively. Clearly, they fall within the range of means of a t test indicates no significant difference between the two sphericities for the dune sand. The two silent beach sand samples,
sets (f0 Q5 = 2.179 > 0.146, d.f. = 12). In contrast, a comparison of however, have noticeably lower sphericities, which suggests that values for sorting indicates that squeaking sand on the average is increased sphericity may also be a prerequisite for sound produc-
better sorted than silent sand (f005 = 2.179 < 2.238, d.f. = 12). tion in beach sand (Table 1). When mean and sorting values are plotted (Fig. 11), it can be seen Scanning electron micrographs of grains from squeaking that the squeaking sand forms a tighter cluster than its silent coun- (Squeaky Beach, loc. 1, Fig. 10) and silent beach (Barwon Heads, terpart. Comparison of skewness values (io.05 = 2.179 >0.442, d.f. loc. 8, Fig. 10) sand emphasize the difference in sphericity between = 12) and kurtosis values (i0.„5 = 2.179 > 0.333, d.f. = 12) again the two (Fig. 12). They also indicate that the grains from the shows no significant differences between the two populations. squeaking sand have very smooth surfaces that could be a Most beach sand falls within a relatively narrow range in terms of significant factor in reducing sliding friction between grains. grain-size parameters. The above limited statistics suggest that the sorting of the sand may be one of the more sensitive prerequisites Sound Production of Squeaking Sand for sound production. In general, the loudest squeaking is produced in the middle of the day by hot dry sand in the tidal zone. However, sand at Squeaky TABLE 3. GRAIN-SIZE PARAMETERS OF SQUEAKING AND SILENT BEACH SANDS
Std. f4 \ c Location Mean
SQUEAKING BEACH SAND 1. Squeaky Beach 1.713 0.324 0.404 2.339 2. Eden 1.372 0.408 0.394 0.807 3. Tuross 1.589 0.440 -0.090 0.789 4. Ulladulla 1.783 0.326 0.037 1.504 5. McMasters Beach 1.195 0.308 0.340 2.275 6. Humphries (1966) 1.790 0.231 -0.869 2.348 7. Ridgway and Rupp (1970) 1.560 0.158 -0.229 0.818 Mean 1.571 0.314 -0.002 1.554 Standard deviation 0.222 0.097 0.457 0.759
SILENT BEACH SAND 8. Barwon Heads, m Victoria, Australia 2.399 0.537 -0.092 1.013 9. Frankston Beach, Victoria, Australia 1.511 0.732 0.429 0.950 10. Picnic Bay (north end), Victoria, Australia 0.105 0.376 0.186 1.953 11. Picnic Bay (south end), Victoria, Australia 1.275 0.481 0.067 1.165 12. Bolivar, Texas 2.739 0.293 -0.217 1.354 13. Mana, Kauai, Hawaii 1.600 0.430 -0.097 0.804 Figure 12. Sand grains from squeaking (a and b) and silent (c and d) 14. Ridgway and Rupp (1970) 1.739 0.431 0.367 2.677 beach sands. Scales on a and c, 500 pirn; b and d, 100 fim. Note that Mean 1.624 0.469 0.092 1.417 squeaking sand grains are much better rounded and have smoother surfaces Standard deviation 0.847 0.139 0.246 0.671 than silent sand grains.
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Beach (loc. 1, Fig. 10) could be induced to squeak, although at broadened) in the 50- to 80-Hz range, and they also display reduced intensity, even when completely saturated by water as the first-order harmonics between 100 and 180 Hz. waves receded. The ability of the sand to produce sounds even 2. Quartz sand grains from booming dunes have polished sur- under ideal conditions varies considerably from beach to beach. faces on the micron scale. The grains are only moderately well Possibly significant is the fact that the intensity of the sound pro- rounded but have high sphericities. duced appears unrelated to the grain-size parameters. For example, 3. The average booming sand at Sand Mountain, Nevada, has a the Squeaky Beach locality produced by far the most intense sound; mean grain size of 1.696 ± 0.181$ (309 fim), is well sorted (cri = however, in terms of grain-size parameters, it falls in the middle of 0.384 ± 0.096), fine skewed (Sk, = 0.167 ± 0.244), and mesokur-
the squeaking sand range. tic {Kc = 1.016 ± 0.227). The booming calcite sand of Hawaii is Brown and others (1964) analyzed the sound produced by the similar but coarser in mean grain size. Squeaky Beach sand. They found that the dry sand produced a 4. Booming sand dunes are most likely to occur at the down- fundamental frequency of approximately 1,200 Hz, whereas the wind end of a desert dune field. Alternatively, booming sand may same sand when damp produced a fundamental frequency of ap- occur on backbeach dunes in dry climates where the sand has long proximately 2,500 Hz. Takahara (1973) analyzed the sound pro- residence time on the beach and where longshore currents are duced by sand from Kyoto, Japan, and found a fundamental fre- weak. quency of 525 Hz in the field and 599 Hz in laboratory studies. 5. The terrestrial booming process is greatly facilitated by the surface properties of the sand grains that control the mechanical DISCUSSION coupling (Q and k) between grains. Selection, accumulation, and reworking of grains must combine synergistically to produce ex- The frequency of sound produced by squeaking sand is higher by tremely polished grains in order to result in a terrestrial booming a factor of 10 to 50 than that produced by booming sand. Our dune. observations in general agree with the earlier conclusions of Brown 6. Booming is a relatively rare phenomenon in the terrestrial and others (1964), Takahara (1973), Ridgway and Scotton (1973), environment but may be a common occurrence in the waterless or and Hashimoto (1951). Sound production in squeaking beach sand near waterless environments of the Moon and Mars, if Q and k is dependent upon the sand being well sorted, well rounded, and rather than purely particle morphology are the dominant factors. highly spherical. Hashimoto (1951) also pointed out that the sur- face of the sand grains should be smooth and clean. Our observa- Squeaking Sand tions using the scanning electron microscope confirm this observa- tion; however, it should be pointed out that the surfaces of squeak- 1. Squeaking sand produces sounds in the range from 500 to ing sand grains bear impact pits and are not polished like the 2,500 Hz (Brown and others, 1964; Takahara, 1973). booming sand grains. Hashimoto (1951) also found that the shear 2. Squeaking beach sand consists largely of quartz grains that resistance of squeaking sand is somewhat greater than that of silent are very well rounded and highly spherical. sand. The conclusions suggest that Bagnold (1966) may be correct 3. The particle observations support previous suggestions that in relating the frequency of sound produced by the squeaking sand the ideal squeaking sand should consist of smooth uniform spheres to the mean grain size of the sands. Other variables seem to be at in a close-packed configuration (Clarke, 1974; Reynolds, 1885). work, however, when the intensity of sound is considered. For 4. An average squeaking beach sand has a mean grain size of example, the Squeaky Beach sand produces sound much more 1.571 ± 0.222 (336 H- It is very well sorted (cr, = 0.314 ± efficiently than other sand, and yet it lies in the middle of the 0.097), symmetrical (Sk, = -0.002 ± 0.457), and very leptokur-
squeaking sand range in terms of grain size. Possibly sand grains tic (Kg = 1.554 ± 0.759). with smoother surface textures dissipate less energy in frictional 5. Bagnold (1966) suggested that the sound produced by drag and are more likely to behave coherently during shearing than squeaking sand resulted from mechanical shearing of the sand that sand grains with rough surface textures. caused the grains to dilate in a coherent manner. If so, the mean There appears to be marked differences between booming sand grain size of the sand would determine the frequency of the sound, and squeaking sand that, contrary to Bagnold's (1966) work, sug- whereas amplitude could be controlled by the surface texture of the gest that two independent mechanisms are at work. All the ob- grains. served consistencies in the squeaking sand suggest a simple mechanical explanation for sound production based on dynamic ACKNOWLEDGMENTS shearing of uniform close-packed smooth spheres. Sound produc- tion of booming sand appears to be related to the mechanical cou- We acknowledge the assistance provided by D. L. Reasoner (Rice pling between grains. The sound-producing mechanism of squeak- University, Houston, Texas), D. W. Humphries (University of ing sand is effective under wet or dry conditions (although much Sheffield, England), Captain E. M. Porter (Commanding Officer, more effective when the sand is dry), whereas booming sand re- Pacific Missile Range, Hawaiian Area, Barking Sands), Lt. (jg.) quires very dry conditions. Grains of booming sand are not excep- Barry (Barking Sands Range), C. Snyder (U.S. Geological Survey, tionally well rounded, but they are highly polished. Nor does there Menlo Park, California), L. Napier (Stillwater Recreational Area, appear to be a requirement that booming sand be exceptionally Fallon, Nevada). R. P. Sharp and J. S. Shelton critically reviewed well sorted, in fact, to the contrary. Finally, there are no reports of the manuscript. Portions of this work were also supported by La booming sand that squeaks or vice versa. Trobe University (Bundoora, Australia) and the Johnson Space Center (Houston, Texas). The Lunar Science Institute is operated CONCLUSIONS by the Universities Space Research Association under National Aeronautics and Space Administration Contract No. NSR Booming Sand 09-051-001. REFERENCES CITED 1. Booming sand produces seismic signals composed of one or Bagnold, R. A., 1954, The physics of blown sand and desert dunes: Lon- more narrow frequency peaks that are limited (Sand Mountain) to don, Chapman and Hall, 265 p. the 50- to 80-Hz range and appreciable broad-band output below 1966, The shearing and dilatation of dry sand and the "singing" 20 Hz. Acoustic emissions overlay the seismic peaks (but mechanism: Royal Soc. [London] Proc., ser. A, v. 295, p. 219-232.
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Bolton, H. C., 1884,1. "The singing beaches" of the Baltic, II. The sonorous Humphries, D. W., 1966, The booming sand of Korizo, Sahara, and the sand-hills of Arabia and Afghanistan: New York Acad. Sci. Trans., v. squeaking sand of Gower, S. Wales: A comparison of the fundamental 3, p. 97-99. characteristics of two musical sands: Sedimentology, v. 6, p. 1890, Researches on musical sand in the Hawaiian Islands and in 135-152. California: New York Acad. Sci. Inst., v. 10, p. 28-35. Julien, A. A., 1885, Recent visits to "singing beaches" in Scotland and Brown, A. E., Campbell, W. A., Robson, D. A., and Thomas, E. R., 1961, America: New York Acad. Sci. Trans., p. 72—76. Musical sand: The singing sand of the seashore. Pt. I: England, Univ. Lewis, A. D., 1936, Roaring sands of the Kalahari Desert: South African Durham Philos. Soc. Proc., ser. A, v. 13, p. 217-230. Geog. Jour., v. 19, p. 33-49. Brown, A. E., Campbell, W. A., Jones, J. M., and Thomas, E. R., 1964, Lindsay, J. F., 1972, Development of soil on the lunar surface: Jour. Sed. Musical sand: The singing sand of the seashore. Pt. II: England, Univ. Petrology, v. 42, p. 876-888. Newcastle-upon-Tyne Philos. Soc. Proc., v. 1, p. 1-17. Morse, P. M., 1948, Vibration and sound: New York, McGraw-Hill Book Clarke, J.A.R. Coutanceau, 1974, Singing sands [letter]: New Scientist, v. Co., 468 p. 222, 26 July. Reynolds, O., 1885, On the dilatancy of media composed of rigid particles Criswell, D. R., and Lindsay, J. F., 1973, Lunar landslides and booming in contact: Philos. Mag., ser. 5, v. 20 to 127, p. 469-481. dunes: EOS (Am. Geophys. Union Trans.), v. 54, p. 360. Ridgway, K., and Rupp, R., 1970, Whistling sand of Port Oer, Caernarvon- 1974, Thermal moonquakes and booming dunes, in Lunar Science V, shire: Nature, v. 226, p. 158-159. Pt. I: Lunar Sci. Inst., p. 151-153. Ridgway, K., and Scotton, J. B., 1972, Whistling beaches and seabed sand Criswell, D. R., Hutton, R. E., McBryde, J., and Shorthill, R. W., 1974, transport: Nature, v. 238, p. 212-213. Audio emissions of a booming dune avalanche: EOS (Am. Geophys. 1973, Whistling sand beaches in the British Isles: Sedimentology, v. 20, Union Trans.), v. 56, p. 1151. p. 263-279. Criswell, D. R., Lindsay, J. F., and Reasoner, D. L., 1975, Seismic and Sharp, R. P., 1966, Kelso dunes, Mojave Desert, California: Geol. Soc. acoustic emissions of a booming dune: Jour. Geophys. Research (in America Bull., v. 77, p. 1045-1974. press). Stearns, H. T., 1966, Geology of the state of Hawaii: Palo Alto, Calif., 1973, Acoustic and seismic emissions of a booming dune: EOS (Am. Pacific Books, 266 p. Geophys. Union Trans.), v. 54, p. 1133. Stein, M. A., 1912, Ruins of Desert Cathay: New York, Macmillan, Inc., v. Curzon of Kedleston, Marquess, 1923, Tales of travel: London, Hodder 2, 492 p. and Stroughton, 344 p. Takahara, H., 1973, Sounding mechanism of singing sand: Acoust. Soc. Folk, R. L., and Ward, W. C., 1957, Brazos River bar: A study in the America Jour., v. 53, p. 634-639. significance of grain size parameters: Jour. Sed. Petrology, v. 27, p. Wu, Tien Hsing, 1971, Soil mechanics: Boston, Allyn and Bacon, 272 p. 3-26. Hashimoto, M., 1951, Some physical properties of the singing sands: First Japan Nat. Cong. Appl. Mechanics Proc., p. 261-266. Ho, M.M.K., and Burwash, W. J., 1969, Vertical vibration of a rigid foun- MANUSCRIPT RECEIVED BY THE SOCIETY JULY 2, 1974 dation resting on sand: Vibration effects of earthquakes on soils and REVISED MANUSCRIPT RECEIVED APRIL 3, 1974 foundations: Am. Soc. Testing and Materials Spec. Tech. Pub. MANUSCRIPT ACCEPTED MAY 20, 1975 STP450, p. 197-232. LUNAR SCIENCE INSTITUTE CONTRIBUTION No. 209
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