sign in sign up
<<
Home , Overtone, Waveform

Lt-... ':L PHYSICS OF

TEACHER UNIT GUIDE NOTES

INTRODUCTION Sound is produced when something vibrates. Such disturbs the air around the vibrating object, creating variations in air pressure. These variations in Fig. 2-1 air pressure are transmitted through the air in sound , much like the way that waves are created when throwing a rock into a pond. As the sound travels through the air, air molecules are pushed together or pulled apart creating Fig. 2 - 2 alternating high and low pressure. The higher pressure of molecules pushed together is called compression. The lower pressure of molecules pulled apart is called rarefaction. When sound waves reach our ears, the air pressure variations cause our ear to vibrate, ultimately causing nerve impulses to be sent to the brain which are perceived as sound.

Sound waves travel through the air at an average of about 1,100 feet per second (depending on air temperature), which is quite slow when compared to the speed of light. This is why we see lightning that is a few miles away several seconds before we hear the thunder.

There are three components of sound: Pitch, , and .

PITCH The vibration patterns of certain are repetitive in nature. Another name for the vibration pattern of a sound is or waveshape. Each repetition of a waveform is called a cycle. The number of repetitions that occur per second (i.e., cycles per second, which is abbreviated cps or Hzl ) is called the of the Fig. 2 - 3 sound. The frequency of a sound is what we perceive as pitch. Those sounds with a high frequency are perceived as high pitched sounds, and those with few cycles per second are called low in pitch. When the frequency of a sound is doubled, we perceive it as being an octave higher in pitch.

The normal range of human hearing is from 20 Hz to 20 kHz. (FrequenCiefffu the thousands are usually represented in kilohertz or kHz; thus 20 kHz = 20,000 Hz.) That frequency range is approximately ten octaves from the lowest distinguishable pitch to the highest. The frequency spectrum of sound is considerably greater than the range that humans can hear. Many animals can transmit and hear that are far below or above what we can perceive. For example, a blue whale call

, The abbreviation "Hz" is derived from the name of Heinrich Hertz, a German scientist who did pioneering work in electroma etic waves durin the 19th centu . in the water may be as low as 5 Hz and dogs can hear frequencies well above that of humans. A dog whistle works by producing a frequency that is above the range of human hearing but within the upper range of a dog's hearing.

In addition to measuring the number of cycles per second, we can also measure the actual physical length of the cycle or wave. This is called the . The approximate wavelength of a frequency can be calculated by dividing the velocity of sound by the frequency (l,l00/frequency). The wavelength of a single cycle of a

5 Hz blue whale call is 220 feet long! I A' 440 Hz, concert tuning pitch, is 2.5 feet and a frequency of 14,000 Hz is less than one inch long.

The waveform of a sound can be graphically represented. In such representations, Fig. 2 - 4 the relative air pressure at any point is represented as height, and time moves across to the right. See Figures 2 - 4 and 2 - 5. It is easy to see the repetitive nature Fig. 2 - 5 , of in such graphs.

LOUDNESS The relative strength of the deviations in air pressure created by a vibrating object Fig. 2 - 6 determines the loudness (or volume) of a sound. The greater the variations in air pressure, the louder we perceive the sound. These deviations are referred to as the Fig.2 7 of the waveform.

To create , energy must be expended. It follows that more energy must be used to create a louder sound. The amount of energy expended in making a sound is called the power of the sound and is measured in watts. (Watts are used Fig.2 8 in measuring other forms of energy as well, such as in power company meters, light bulbs and amplifiers.)

As sound emanates from a source, the concentration of power becomes less and less as the distance from the source increases - the same amount of power is spread over a greater area. The amount of power per square meter is called the intensity of the sound.

Humans do not perceive sound intensity in a linear fashion; that is, for a sound to be perceived as twice as loud, the intensity must be ten times as great. Because of Fig. 2 - 9 this, the perceived intensity level of a sound is measured in a logarithmic scale using a unitcalled the deciDel (or dB)2. The softest sound that a person can hear-the "threshold of hearing" -is defined as 0 dB. A sound that is so loud that

it actually causes pain- the II threshold of pain" - is about120 dB. With the Fig. 2 -10 . logarithmic scale in mind, the threshold of pain (120 dB) represents an intensity 1,000,000,000,000 (1 trillion) times as great as the threshold of hearing (0 dB)!

2 This unit of measurement was named for Alexander G. Bell, who invented the telephone. The use of the capital UBI! in the abbreviation is in his honor. The following "rules of thumb" about loudness might prove helpful: To double the perceived loudness of a sound, the power (in watts) must be increased by 10 times and the sound pressure level will increase by 10 dB. Example: A sound pressure level (SPL) of 90 dB produced with 10 watts of power will double in apparent loudness when the power is increased to 100 watts and the SPL increases to 100 dB.

Doubling the power of a sound nets a 3 dB gain in perceived loudness. Example: A sound pressure level (SPL) of 90 dB is produced with 10 watts of power. If the power is doubled to 20 watts, the SPL will increase to 93 dB.

Moving twice the distance from a given sound source will result in one-fourth the loudness (i.e., a 6 dB loss). Example: At a distance of 20 feet from a sound source, a sound pressure level (SPL) of 90 dB is produced. Doubling the distance from the source to 40 feet will result in a SPL of 84 dB.

TIMBRE or TONE COLOR The property of sound that allows us to determine the difference between a saxophone and a flute is called timbre (pronounced TAM-ber) or tone color. Different occur because most sounds perceived pitch actually contain many frequencies. Thus, when one hears the note "middle C" on the , many other frequencies are present as welL The predominant pitch, in this case middle Fig. 2 -11 . C, is called the of the sound. The other frequencies present occur in a mathematical series called the series or series. The frequency of each harmonic (sometimes referred to as "partial") is a whole number Fig. 2 -12 multiple of the fundamental frequency (i.e., 2X, 3X, 4X, etc.). See figure 2-12 and notice that the second harmonic is an octave above the fundamental frequency, the third harmonic is an octave plus a fifth above, and the fourth harmonic is two octaves above the fundamental frequency. (When using the term "," the first overtone is an octave above the fundamental; i.e., the second harmonic.)

While most musical sounds have overtones that are direct multiples of the fundamental frequency, some do not. When the overtones are not whole number multiples of the fundamental, they sound out of tune and are called clangorous overtones. dangorous overtones received their name because they give the sound a quality that resembles a clanging bell.

The number of present and the relative strength of each determines the Fig.2 13 timbre of the sound. Many sounds have timbres which change over time. In such cases, the relative strengths of the harmonics vary as the sound is produced. For instance, a low note played firmly on a piano sounds "brighter" at first, but becomes "duller" as the sound decays. In this case, the higher harmonics die out more quickly than the lower harmonics.

Different timbres result in different shapes in the plotted waveform. Certain wavpforms entlv rtain tim res have Ion been used as buildin blocks of synthesis. These include the , the , the triangle Fig. 2 -14 wave, and the .

CONCLUSION While independent of each other, the three components of sound work together to give each sound we hear its unique qualities. A clear understanding of the role of each component is necessary for delving into the realm of electronic sound production. Figure 2 -1. Sound waves traveling through the air.

tW'ir 1 ' " 1 Wrl1r~' trW""

High Pressure

Air molecules • •• •••••••••••••• • • • ••• ••• •• • •• • • •• •• •••• • • • • •• ••• •••••••• • •• • • • • ••••••••••••••••• • • • • ...... :..: : . ... • .:••••••• •• • • • • • ...... :..' . .. • · . .••• ...... •• • ••• . • • • • ••• •••••••• • ••• • • .....\ '.~ ...... ,. ... ••. .. • ••• •••• •• •• ...•• • • •• • ••• ••••• ••••• • • ••• •• ••••• ••••• • • • • ••••••• •••••••••• • • • • •••••• • • •••• ••• • • • .. .. ~ .....: •• • ••••• ••••• • ••• • • • •• ••• •• ••••• • •••• • • • ••••••• •• • ••• •• •• • • • • • • •••••••• • •••• •• •• • • • ••••• ••• •• • • •• ••••• ••• •• • •••• •• • ••• • • •• ••••••• ••• • ••••••••••• • • ••• • ••••• • ••• •••••••••• ••••• • ••• t t Compression Rarefaction

Figure 2 - 2. Compression and rarefaction in A-1760 Hz A-880 Hz A-440 Hz

A-220 Hz A-110 Hz

Figure 2 - 3. Frequencies of 5 octaves of the pitch A. Notice that the frequency doubles with each increase in octave.

Nrr rwt"$ 4 'fhm" >H t 1 r1 tW7"rt'l At "~W7X' }]WtrutZ'°·'tz'T'rur 7)t1'11';'1 v'tciwtt",rtt

1 Cycle

Figure 2 - 4. Three cycles of a waveform.

r tM 1/ "·2 "Mill"

1 Cycle

Figure 2 - 5. The same waveform, 1 octave higher. Nr.tirp th>'lt thPTP >'ITP twirl" ::t<:< m>'lnv rvdp<:< in thp ~mp amr.llnt r.f timp A m p I i t u d e

Figure 2 - 6. Amplitude changes of a waveform over time.

C1t7" '~'~"7t ,-~; 1'#---"''1', 't t f t T "f

A m p I i t u d e

Figure 2 - 7. The same waveform louder. Notice the greater deviations in amplitude.

:tr# rtdrltn '*.f t fttzl m i!'i %

Electrical Use Power Meter Light Bulb Stereo Power Amplifier 120dB Threshold of pain Extremely Loud 110 dB Typical Rock concert Very Loud gO dB Orchestra playing at ff Moderately Loud 70 dB Noisy classroom

Moderate SO dB Normal talking Faint 30 dB Soft whispering

OdB Threshold of hearing

Figure 2 - 9. A range of loudness levels.

0 0 0 0 0 0 .. 0 0 0 0 r>. .. 0 0 0 '0 0 .. 0 -c: 0 0 0 .. 0 0 0 .. (J) 0 0 0 .. 0 0 0 .. 0 -c: 0 0 0 .. 0 0 0 .. 0 0 -, 0 0 0 .. 0 0 0 .. 0 0 0 .. 0 0 0 .. 0 0 0 .. 0 0 0 .. 0 0 0 0 .. 0 0 0 .. 0 0 0 .. 0 0 0 0 0 .. 0 0 0 .. 0 0 Q. 0 0 Q. ..-- ..-- -- ...- -- -- ...- ..-- ...- -- -- ...- ...­ 0 10 20 30 40 50 60 70 80 90 100 110 120 ..

Figure 2 - 10. Comparison of intensity to decibels. Each time the perceived loudness doubles, the intensity is increased by a f"'.... tn... nf 1 () ,.nrl .. Figure 2 - 11. A fundamental frequency and the 2nd, 3rd and 4th harmonics.

to'&e W&:-@ T f 'etex( "WkW t 7 ~---'-'-n--'mt n Y Mr ; n 7 *ty- ;i"k_--Y" itt? mrf---­

e# - 550 Hz - 5th Harmonic A - 440 Hz - 4th Harmonic ~ E - 330 Hz - 3rd Harmonic A - 220 Hz - 2nd Harmonic A - 110Hz - Fundamental Frequency

Figure 2 - 12. Five harmonics of J A' 110hz. Notice that each harmonic is a direct multiple of the fundamental frequency.

Amplitudei

Fundamental / A 100 m r I t u d e 1 2 3 4 5 6 7 8 9 10 etc. Harmonics A. The sine wave. A sine wave consists of only the fundamental; no other harmonics are present.

"tr Ow

A 100 m r i t 33.33 u I 20.00 ~ I 14i29 11i11 2 3 4 5 6 7 8 9 10 etc. Harmonics B. The square wave. With a square wave only the odd harmonics are present. Harmonic strengths are computed by multiplying the strength of the fundamental by 1I n, with n being the number of the harmonic.

'717 7

A 100 mr I t u d 11.11 e 4.00 2.04 1.23 1 2 3 4 5 6 7 8 9 10 etc. Harmonics c. The . With a triangle wave only the odd harmonics are present. Harmonic strengths are computed by multiplying the strength of the fundamental by lln2, with n being the number of the harmonic.

rrnzTW\V1 ne@ '(*-'------'- ~ - '@@wt1iS ??WaMmr-r r Tn tCrM WW--"- cr:e "t '7 set ""~rtw r tJfnrlwfUffti*?rtz4r A = em 100 A m 50.0 f 33.3 i 25.020.0 t 16.67 u 14.29 d I 125. 1.1.11 e 1 2 3 4 5 6 7 8 9 10 etc. Harmonics D. The sawtooth wave. With a sawtooth wave all harmonics are present. Harmonic strengths are computed by multiplying the strength of the fundamental by lin, with n being the number of the harmonic. PHYSICS OF SOUND

ADDITIONAL RESOURCES

VIDEO: "Hearing is Priceless" (HIP) House Ear Institute 2100 W. 3rd St., 5th Floor Los Angeles, CA 90057 (213) 483-4431 Video geared toward young people warning of the dangers of excessive loudness.

READING: The Acoustical Foundations ofMusic John Backus New York: W.W. Norton & Company. 1977.

Fundamentals ofMusical Arthur H. Benade Dover Publications. Reprint edition 1990.

The Science ofMusical Sound John Robinson Pierce W H Freeman & Co. Revised edition 1992.

The books listed below have chapters that include information on the physics of sound.

The Secrets ofAnalog and Digital Synthesis Steve De Furia Hal Leonard Books. 1987.

Sound check The Basics of Sound and Sound Systems Tony Moscal Hal Leonard Books. 1994.

What's a ? Jon F. Eiche Hal Leonard Books. 1987. ::1 INTERNET RESOURCES: Digital 2.1 http://karserve.ethz.ch/AdS/mac/oscilloscope/ digital_oscilloscope210.sit.bin Digital Oscilloscope enables a Macintosh computer to act as an oscilloscope and a frequency meter. This is a great freeware program for analyzing waveforms and sounds.

Spectro 1.1 http://www.multimania.com/newman/ A freeware, real time oscilloscope and for the Macintosh computer.

Sound View http://www.physics.swri.edu/soundview/ soundview.hhnl A freeware, real time sound analyzer for the Macintosh computer that allows you to record, play, view and analyze a sound in a variety of ways.

The following Web sites provide information related to hearing loss and related problems.

American Tinnitus Association http://www.ata.org/ This site provides information on Tinnitus (ringing in the ears) with links to other hearing-related sites.

H.E.A.R. (Hearing Education and Awareness for Rockers) http://www.heamet.com/ H.E.A.R. offers clinics and school programs, and develops new materials related to hearing and hearing protection

House Ear Institute http://www.hei.org/ This site provides information and research on hearing health and protection. PHYSICS OF SOUND

VOCABULARY LIST amplitude clangorous overtones cycle cycles per second (cps) compression (dB) frequency fundamental frequency harmonic series (overtone series) Hertz (Hz) intensity kilohertz (kHz) loudness pitch power rarefaction sawtooth wave sine wave sound sound waves square wave timbre (tone color) triangle wave watts waveform (waveshape) wavelength