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• In the Home

lAMES MOIR';'

A discussion of the factors affecting the power required for satisfactory repro­ duction of typical program material and the methods of calculating it.

H'I'D1ATt;S OF TIlE AU1HO POWER re­ Power dissipated power figure being twice the rms power quired to produce adequate loud­ figure. As there is a fixed ratio between E as heal from the domestic = 2 the two ratings there appears to be no IlPSS (.707V) volts are eharacterised by a very wide diver­ 1] good reason for departing from the prac­ R gence of opinion e\'en among authorities, tice of quoting the rills power output the figures ranging from 100 milliwatts to standard practi('p in other engineering

50,000 milliwatts (50 ) having been v = PEAK VALUE fields. quoted by different writers. It is interest­ • = RMS VALUE - .707V ing to examine the problem and to at­ Measuring the Power tempt to produce some reliable data. There need be !l0 ambiguity in measur­ As a preliminary it is necessary to clear ing the power output of an audio ampli­ our ideas as to what is mrant by the fier for sinusoidal test signals can be em­ '' for it is evident that the ployed and special meters are not re­ same basic power may be expressed in Fig. Relation of peak and rms values quired, though it should be noted that several ways. Thus the same 1. of voltage for a sine wave. the power specification is meaningless may be quoted as having an output of unless the Itwel is also quoted. ten 01' twenty watts both figures being same peak voltage as the speech wave. However our presrnt interest is not accurate statements of the performance. It should be appreciated that this is not in what power an amplifier can deliver the rms power in the speech wave but but in what power it deliver when Expressing the Power dol'S a figure which may be perhaps ten times used in the home. This is a ml1ch more In a mains frequency power circuit higher. troublesome problem, for speech and the supply voltage and current have the On sinusoidal waveforms the rIns music waveforms are irregular, and substantially sinusoidal waveform of power will only be one half (ie have a high ratio of peak to rms power Fig. 1 and without ambiguity the power (0.707)' = 0.5) the peak power and thus due to the intervals between words or di�sipatrd as heat in a resistance load of the same amplifier may be rated in either phrases when no signal is present. Reat­ B OhlllS will be given by (0.707 V)' / R peak power or rms power, the peak ing (a function of the rIns voltage 0.707 where V is the peak value of the ap­ plil'd voltage. To eliminate the necessity of always multiplying the meter indica­ 0.20 SEC 0.21 SEC tion by 0.707, commel'cial meters used "00' AS IN POOL in the heavy engineering field are scaled to indicate, not the peak value, V, but v = the nns () value 0.09 SEC. 0.10 SEC 0.707 V. Within the usual engineering tolt'rances the value of voltage or cur­ "0' AS IN TONE rent will be indicated quite accurately by ordinary commercial meters and the readillg will be independent of the 0.14 SEC 0.15 SEC physi('al size of the meter. "A" AS IN TALK The multiplying factor, 0.707 applies only to a sinusoidal waveform but in the communications field sine waves are gen­ 0.25 SEC 0.26 SEC erally confined to test equipment, speech and music signals having the much "A" AS IN FATHER "spikier" waveform indicated by Fig. 2. Thl're is no equivalent numel'ical factor relating peak and rills values that can 0.24 SEC 0.25 SEC be applied to such irregular waveforms "A" AS IN TAPE and thus the output of an amplifier may be expressed either in terms of its peak 0.17 SEC 0.18 SEC power, Vi /R, or as rIns power (0.707 V)%/R the lakr figure being the power � �,..� "E" ASINTEEM dissipated as heat in a resistor of R by a sinusoidal voltage having the

* 73, Bawnmoff Road, Bilton, Rllgby, England. Fig. 2. Waveforms of typical vowel sounds. (From Fletcher, "Speech and Hearing.")

16 AUDIO • MARCH, 1957 TABLE I suIt supported by similar tests in Amer­ ica which indicated a preference for Preferred Maximum Sound Level levels about 8-9 phon lower than the db above watts/cm2 10-1" B.B.C. Public Programme EngineerS results suggest. Musicians Engineers Sound levels approaching 114 phon � � Men Women Men Women occur in concert halls and there is not

Symphonic Music , , the least evidence that these are anything 78 78 88 90 87 88 Music ... but satisfying, but the available evidence light . .. 75 74 79 89 84 84 Dance Music ...... 75 73 79 89 83 84 does suggest that these levels are not Speech ...... 71 71 74 84 77 80 optimum in the home. The reason for this difference is not clear, but in the writer's experience a level of 110 phon V) is of little consequence in either What Constitutes Adequate sounds "louder," though "smaller" and or and in con­ more oppressive in a slllall room than Difference of opinion as to what con­ !lequence it is more reasonable to measure the same level in a concert hall. stitutes "adequate 10udneSB" is responsi­ the peak values of signal voltage and A major discrepancy between the for considerable discrepancies bp­ express the speech power in terms of hIe val'ious estimat,ions of "power required" tween writers' estimates and the im­ its peak value, V'IR. llIay thus be attributed to the choice of portanre of clearing the air will be fairly The measurement of the peak voltage maximum loudness thought desirable. An obvious when it is realise.d that a differ­ of such irregular waveforms is by no {'stimate based on the very reasonable ence of 10 db in specifying the'maximum means easy. Pointer-type meters of any that concert-hall loudness loudness level thought to be desirable a��ulllpti(JlI kind have movements of sufficient in­ le.vels are necessary in the home will will result in a change in the required ertia to prevent them reading peak val­ suggest a power some at least 20 db amplifier output power of ten times. ues and the indications may easily be (100 times) higher than another esti. Published figures seem to indicate that in error by a factor of ten times. Large mate bas(�d Oil achieving only the maxi­ the differences of opinion embrace a well damped meters of high nominal mum prefel'red loudness level of 90 phon. power range of something nearer 40 db accuracy invariably have heavy moving As it will be seen from Table I that the (a power difference of 10,000 to 1) so systems and are particularly inaccurate general public only require a maximum it is absolutely necessary to have our when used to "measure" audio voltages. loudness level of about 80 phon, a "log· thoughts clear on this point. Measurements using pointer-type instru­ ical" ('ngineering estimate of the power At first sight it appears reasonable to ments of the programme voltage across, necessary will be about 30 db (1000 approach the proh!nm hy reviewing the into a loudspeaker are therefore com­ times) higher than i� really required. volume ranges, ellcountere.d in original pletely valueless. Three types of instru­ This preference for lower levels in speech and music on the assumption ment are in current use for measuring the home is providential because some that "a perfect reproduction" will re­ , the sound-level meter, the consideration for the neighboun> is quire the same volume range. The high-speed level recorder and the cath­ 1IIost necessary. In flats, terraced houses or difficult case, ,an original performance ode-ray oscillograph. houses built in pairs, a house-to-house by a large symphony orchestra may in­ The sound-level meter has the disad­ insulation of 55-60 db can be achieved volve a power ratio of 80 db (100 million vantage of a pointer-type meter but fairly easily by simple building tech­ t.o 1) but this range is generally only as the mechanical constants of the meter niques but science and the average encountered for a few tenths of a second are closely specified the error due to builder are not yet in close touch, with in several hours, a more frequently oc­ instrument inertia may be roughly esti­ the result that 45-50 db is the flgure curring range being nearer 74 db. mated. A typical meter may give read­ more usually achieved in semi-detached ings that are below true peak by 20 At the receiving end it is reasonable pairs of houses having a 9-in. party db, the error being small when the signal to assume that the listener should ad­ wall. Peak sound levels in the region of is steady and rising to 20 db on speech just his volume control to bring the 110 phon will result in the neighbours signal to somewhere near the signals where the gaps between words minimum enjoying your choice of programme at and sentences may be comparatively room noise level and as an average value a level of 70-80 phon and while this may long. for the domestic noise level is about 40 be just tolerable in the early evening The high-speed level recorder employs phon it implies that peak levels in the when theil' own noise level is in the 114 a tube-operated servo system to drive the region of db (or phon) al'e required. same region as your own it must become pointer and will generally indicate val­ Though this appears to be a very rea­ a little annoying to them when later in ues that are 5-10 db below true peak sonable deduction, experience suggests the evening their own noise level has readings. that it is wise to make a check and this dropped to something nearer 30 phon. The cathode-ray o�cilloscope has no has been done both in England and in significant error due to inertia and can America. The B.E.C .. have made a very Acoustic Power Requirements indieate true peak values on the most careful study of the sound levels pre­ The next steps in the enquiry are to complex waveform, but care must be ferred by their monitoring staff and by make an estimate of the actual acoustic taken to operate with sufficient bright­ the general public and Table I lists some. . ness to show up the faint high-speed of their data taken from a paper by Somerville and Ward. traces characieristi(· of peaks of short TABLE 11 duration. In these tests the listeners were pro­ Failure to indicate whether peak or vided with a high-quality reproducer Maximum Loudness Levels produced by typical sound sources in domestic sur­ rms power is being quoted and the use system of ample power handling ca­ roundings. pacity and were asked to set the loudness of unsuitable power measuring equip­ Small Upright Piano ment undoubtedly accounts for differ­ to the level they considered preferable. Maximum in normal playing 72 db ences of from 10 to 100 times in the The acoustic level at a point about 18 Player asked to play a "loud" selection amount of power thought to be necessary inches from the listener's head was then 82 db Player asked to play "as loudly for domestic reproduction. This is a checked with a standard type of sound­ as possible" db large error but even greater discrepan­ level meter. It is surprising to note that 90 Speech cies can occur if the maximum loudness none of the listeners wished to have Boy normal speech 60 db is not carefully specified. sound levels greater than 90 phon n rr- Man 6S db

AUDIO • MARCH. 1957 17 TABLE III 0.5 second it suggests that the power difficult to translate the acoustic power Acoustic Power required to produce given shown in Table III will be required for requirements into electrical power to be 80-120 loudness levels in a room of 1540 ft3 and levels of db, the power required provided by the amplifier. reverberation time of 0.5 sec. Computed for 100 db being computed from the from Eq. (7 of Appendix. I equation directly, and being modified Electro·acoustic Efficiency of 80 db .00036 ( .36 milliwattsl by a factor of ten for each 10 db change Loudspeakers 90 db .0036 (3.6 milliwattsl in level. The suggested maximum re­ db There is very little published data on 100 .036 quirement of 90 db is reached with an db the conversion efficiency of loudspeakers, I 10 .36 acoustic power of only 3.6 milliwatts, a db partly because of the difficulty of meas­ 120 3.6 figure that is in substantial agreement urement but also because any single with the power deduced from that pro­ figure can be misleading and liable to power required to produce the loudness duced by a human speaker at maximum misinterpretation. In these measure­ levels thought necessary, and then to output. ments to be described, the figure quoted examine the electro-acoustic conversion Objection has been raised to any as the efficiency was determined by meas­ efficiency of loudspeakers for this will formula that suggests that the power uring the electrical power input to a enable the electrical power requirements required is inversely proportional to the loudspeaker operating on ordinary pro­ to be predicted. reverberation time, on the score that the gramme in the normal living room and The actual acoustic power required to bursts of energy in speech are so short simultaneously measuring the loudness produce acceptable loudness levels is that room reflections do not have time level in the room. Care was taken ob­ very small indeed. A first approximation to reinforce the direct sound from the to serve steady values and from this data to the figure can be obtained by con­ speaker. It has therefore been suggested the acoustic power output was calculated. sidering the data on the acoustic power that the power required should be com­ The efficiency is the ratio required for normal conversation. The puted on the assumption that the loud­ x 100 . most reliable data, that of Sivian, Dunn, ness is entirely due to the direct sound. Acoustic powe1' . and White indicates that the instantane­ The calculation is not difficult but it Hlectrical power ous maximum power rises to about 700 does require a knowledge of the polar With domestic approval a sound-level microwatts (0.7 milliwatt) when making diagram of the loudspeaker over the meter, and oscillator we�e an impassioned speech to a large audi­ frequency range. set up ill the dining room as shown III ence. About 5 per cent of speakers will A sound wave leaving the speaker will Fig. 3 and several listening and watch­ produce powers five times higher than diverge in the form of a solid cone with ing sessions enjoy�d. As a first check the figure quoted, making their acoustic . somc co-operative members of the famIly output 3-5 milliwatts. Declamatory TABLE IV were asked to adjust the loudness to speech of this kind would be intolerably their liking and as it was found that loud in domestic surroundings, rather Electrical Power required to produce a loud­ ness level of 80 db from three typical the levels chosen were in good agree­ suggesting that the maximum acoustic speakers. ment with those obtained by the B.B.C. power required for any purpose is not A-17 -in., 17,000 gauss magnet. (Table I) it was assumed that nothing likely to rise much above 5 milliwatts. B-12-in., high-fidelity type, 14,000 was seriously amiss. The procedure then Data is available on the acoustic output gauss. employed for the power measurement of most of the common instruments but C-8-in., radio receiver type, 8,000 gauss. tests was to set up the CRO and sound­ it is not particularly useful as an indi­ Voice Electro- in close proximity to enable cation of domestic requirements as all Coil acoustic Speaker Level Power Efficiency. both meter and CRO to be viewed simul­ the figures refer to tests in which the db mw percent taneously and to mark the tube face instrument was played as loudly as possi­ A 80 9.5 3.8 each time the meter peaked to 80 db. ble. A concert grand, played loudly, has B 80 55 .66 After a few attempts it was possible to a power output. of about 350 milliwatts C 80 240 .15 draw two parallel lines on the tube face but experience suggests that even a small defining the maximum deflections pro­ upright piano can be intolerably loud in the speaker at the apex but the angle duced when the sound-level meter reached a small room. In my own room a small of divergeDce will be a function of fre­ this figure. A Promenade Concert pro­ upright piano played by a moderately quency, being greatest at low frequen­ vided valuable test material, as it was competent player produced the loudness cies (180 deg. if the speaker is in the possible to watch the meter on one levels shown in Table II and it is per­ centre of one wall) and decreasing as phrase and check the CRO deflection haps significant that normal playing gave the frequency increases until it is down when the phrase was repeated a second maximum levels of 72 phon with a level to something near 25 deg. at 5000 cps. or so latel·. Music also has the advantage of 90 phon reached when the player was There is therefore some difficulty in fix­ that complex tones are held for sufficient asked to produce the absolute maximum ing an effective average angle for the time to provide a steady deflection on output. It should be noted that readings whole of the range. the meter, thus eliminating any argu­ were taken when the sound level was Power loudness and intelligibility are ment about the contribution of the reasonably steady and the absolute peak not li�early proportional to bandwidth, levels are therefore likely to exceed the a fact that increases the difficulty in meter readings by only 4-8 phon. fixing an average angle for the whole frequency range. In spite of these diffi­

Calculation of Sound Power Requirements culties it has been claimed that power re­ LOUDSPEAKER quirements computed on the assumption In the appendix it is shown that the that there is no gain in loudness from acoustic power required to produce a the J'evel'berant sound, do give good sound level of 100 db can be computed agreement with measurement. SOUND o from The earlier discussion suggests that the LEVEL = .0000116 V IT METER P watts maximum acoustic power required in where V is the room volume and T is domestic surroundings is only in the the reverberation time. Applied to one region of 3-5 milliwatts but in the a�­ of my own rooms having a volume of scnce of data on the electro-acoustIc Fig. 3. Schematic arrangement used for 1540 cu. ft. and a reverberation time of efficiency of typical loudspeakers it is audio power measurements.

18 AUDIO • MARCH, 1957 used hy most high fidelity enthusiasts After reviewing the results obtained ouly requires an input of about 55 milli­ it appears that there is great opportu­ watts to produce a sound level of SO db nity for difference of opinion in esti­ and a power of 0.55 watt to produce 90 mating the power required to produce db. If concert-hall levels of 110 db adequate loudness in small rooms. All were required in domestic enclosures a experimenter measuring the power that power of 55 watts would be nccessary gives him adequate loudness will find it but this speaker would have to call for to be in the region of 50 milliwatts if help from at least four of its fellows if he uses a CRO, perhaps 5 milliwatts if this power was to be handled. he uses a high-quality rectifier voltmeter. Though a horn loaded unit was not and something less than 1 milliwatt if tested it is known that electro-acoustic he has an rills-reading thermal meter. A dncieucies of 20--40 per cent can be devotee of Aristotle preferring medita­ reached, enabling the concert hall level tion rather than experiment might be to be obtained for an input of about 1 % excuscd if he based his calculations on watts. As cvidence of this, some reeent the assumption that the loudness level measnrements in a 700-seat theatre hav­ found desirable in concert halls would ing a volume of 120,000 cu. ft. showed prove to be equally desirable in the that the feature film was being regularly home. He would then produce a figure run with a maximum ele.ctrical input to approaching 40-50 watts, but if this thc loudspeakers of less than one watt. was thought to be insufficiently impres­ The IS-in. speaker is shown to have sive, he could with all honesty quote the an eftlciency twenty times that of the same power as SO-lOO watts peak, i.e. (·heap radio speaker but this is insuf­ peak volts times peak current. A differ­ ficient to justify its use where cost is of ence in estimate as great as 100 watts to ROOM VOLUME CUBIC FT. importance, for acoustic power can gen­ .001 watt must be a record for an honest erally be produced more cheaply by the difference of opinion in the engineering combination of a small speaker and a field. Fig. 4. Curves of power required for two sound levels in relotion to room volume. large pentode, than by an expensive Though the reason is probably psy­ speaker and a small triode. chological the preference for reduced reverberant sound to the total loudness. It is convenient to have available for maximum loudness levels in the home is Audience applause is equally effective n'ady reference curves relating to room not understood and should form an in­ for this purpose. The room was in semi­ volume, sound level, and electrical power teresting subject for further study. darkness and a bright trace employed to requirrd. Figure 4 provides this infor­ avoid missing sharp peaks of short mation based on the assumptions that duration. ApPENDIX 1. The acoustic power is computed from Having defined the CRO deflection Eq. (7). If it is assumed that" loudness" is re- characteristic of a sound level of SO db, 2. A loudspeaker efficiency of 1 per cent 1ated to the steady-state the CRO was then switched to the cali­ is obtained. the power required to produce any speci­ The optimum reverberation time rela­ fied intensity can be computed from the bratcd oscillator and the rills voltage 3. tion of Fig. 5 is approximated in all standard exponential relation betweell corresponding to the deflcction noted. cases. sound-energy density and the time interval Three hours checking with three different In the lIIajority of rooms above 2000 during which power is being supplied to loudspeakers provided some interesting ('ubic feet the reverberation times of the enclosure. The sound-energy density in ergs/cc at any time t secs. after the data which is reproduced in Table IV. Fig. 5 arc approximated, but in smaller power is t!lrned on, is given by As the input power to each of the houses current constructional methods 4P speakers was adjusted to produce an appear to give a reverberation time of E = Su. (1- C - osat/4V) (1) acoustic level of SO db in the room, it about half a second almost regardless C is assumed that the acoustic power pro­ of the furnishing scheme. duced is the same for all, a reasonable 2.50 r-----.---r-.,--r--r-I"""T..,....,---.....---.--r---r-T"'""I-rT"l but not a precision conclusion, in view of the different frequency characteris­ tics inherent in speaker units of such widely varying quality. Column 3 indi­ - cates the power in the voice coil com­ � 2.06 puted on the assumption that the effec­ tive resistance of the voice coil is equal z to its d.c. resistance. Column 4 con­ Q � 1.50 -is tains figures for the electro-acoustic � 0 � u efficiency computed from the measured � � VI electrical input to the speaker on the '" assumption that the acoustic power out­ =>� 1.00 put is given by Eq. (7) in the Appendix, �... C>- corrected to a sound level of SO phon. O Speaker A is a large IS-in. cone speaker having a 2%-in. voice coil work­ 0.50 ing in a gap having a flux density of 17,- 000 gauss. Speaker B is a standard type of unit typical of the better quality 0.0 12-in. high-fidelity units, while speakrr , . C is typical of the cheaper S-in. units 10,000 100,000 1,000,0.)1) included in radio receivers. VOLUME OF ROOM - Cu. Ft. Fig. Curve showing optimum reverberation time in relation to room volume. Spcaker B, typical of the units being 5.

AUDIO • MARCH, 1957 19 where 7' = rate of emlSSIOll of the source, crgs/sec. C:= velocity of sound, em/see. S = total surface area of absorbing surfaces, sq. ems. Cl = a\'erage coefficient of absorption of all surfnces. V = total "o(ullle of rooUl, cu. cms. When �tea(ly state eOJulitions are reache,l, theoretically after infinite time, but prac· tically after T sees. where T is the rever' beration time of the enclosure, the brack­ eted term is e\.Junl to unity and the sound eller�y density is given by !.� E- (2 - CSn ) It is more convenient to have a relation involving the reverberation time T and th(' \'olume of the enclosure V rather than S and a and this can be obtained from the normal Sabine relation for re\'erberation time T = k V/Sa, from which Sa = le V/T SUhstituting kr/T for Sa in Eq, (2) gives 4P7' (3) E= CkF from which the source power in Ergs/sec. is gi"en hy

_ CkJ'H P - (4) 4T If some standard intensity is adopted, the arithmetic is simplified and as 100 db is a cOJ\\'enient figure this will be inserted. It corresponds to a sonnd intensity of 10-6 wntts/sq. cm. and a density of 3 x 10-' ergs/cu. cm. Substituting this value in Eq. (4) nn(l including all constants, the acoustic power in wntts required from the source to produce a maximulll intensity of 100 db is given by _ 3.4 X 104 X 16 X 10-4 X 3 X 10-4 F P (6) - 4 xl07 X T = 4.1 X 10-10 V/7' or convertiug to ft. nnits � l' = 1.16 x 10-5 r/1' = .0000116 watts (7)

For nny 10Ullness le\'el other thnn 100 db tlte power reljuired will be doubled for I'llch a db increase in intensity that is con­ sidered nccessnry. The threshold of pain is reached at nn intensity level of about 120 dl.J requil'ing a power 100 times that given by the equation and presumably fixing the ahsolute maximum ,'alue of power that any/wdy might ever consider lIecessary.

REFERENCES Somerville and Ward, "Listeners sound- IC\'el preferences," B.RC. Quarterly, Jnn. 111411. Chinn lln,l Eisenbe rg , "Sound intensit, prcfcrcII('es of Brolldenst listencrs," Proe. I.R.E., Sept. 1945. Sivian, Dunl1, and White, ., Absolute ampli­ tudes and spectra of musical instru­ ments." J. AC01IS. Soc. Am., .Jan. 1931.

68 AUDIO • MARCH, 1957