University Physics Volume I Unit 2: Waves and Acoustics Chapter 17: Sound Conceptual Questions

Transcription

1 Unit : Waes and Acoustics Uniersity Physics Volue I Unit : Waes and Acoustics Conceptual Questions 1. What is the difference between sound and hearing? Sound is a disturbance of atter (a pressure wae) that is transitted fro its source outward. Hearing is the huan perception of sound.. Sound waes can be odeled as a change in pressure. Why is the change in pressure used and not the actual pressure? Consider a sound wae oing through air. The pressure of the air is the equilibriu condition, it is the change in pressure that produces the sound wae. 5. When sound passes fro one ediu to another where its propagation speed is different, does its frequency or waelength change? Explain your answer briefly. The frequency does not change as the sound wae oes fro one ediu to another. Since the speed changes and the frequency does not, the waelength ust change. This is siilar to the driing force of a haronic oscillator or a wae on the string. 7. You ay hae used a sonic range finder in lab to easure the distance of an object using a clicking sound fro a sound transducer. What is the principle used in this deice? The transducer sends out a sound wae, which reflects off the object in question and easures the tie it takes for the sound wae to return. Since the speed of sound is constant, the distance to the object can found by ultiplying the elocity of sound by half the tie interal easured. 9. Six ebers of a synchronized swi tea wear earplugs to protect theseles against water pressure at depths, but they can still hear the usic and perfor the cobinations in the water perfectly. One day, they were asked to leae the pool so the die tea could practice a few dies, and they tried to practice on a at, but seeed to hae a lot ore difficulty. Why ight this be? The ear plugs reduce the intensity of the sound both in water and on land, but Nay researchers hae found that sound under water is heard through ibrations astoid, which is the bone behind the ear. 11. You are gien two wind instruents of identical length. One is open at both ends, whereas the other is closed at one end. Which is able to produce the lowest frequency? The fundaental waelength of a tube open at each end is L, where the waelength of a tube open at one end and closed at one end is 4L. The tube open at one end has the lower fundaental frequency, assuing the speed of sound is the sae in both tubes. 1. Two identical coluns, open at both ends, are in separate roos. In roo A, the teperature is T = 0 C and in roo B, the teperature is T = 5 C. A speaker is attached to the end of each tube, causing the tubes to resonate at the fundaental frequency. Is the frequency the sae for both tubes? Which has the higher frequency? Page 1 of 18

2 Unit : Waes and Acoustics The waelength in each is twice the length of the tube. The frequency depends on the waelength and the speed of the sound waes. The frequency in roo B is higher because the speed of sound is higher where the teperature is higher. 15. Consider three pipes of the sae length (L). Pipe A is open at both ends, pipe B is closed at both ends, and pipe C has one open end and one closed end. If the elocity of sound is the sae in each of the three tubes, in which of the tubes could the lowest fundaental frequency be produced? In which of the tubes could the highest fundaental frequency be produced? When resonating at the fundaental frequency, the waelength for pipe C is 4L, and for pipes A f = /. and B is L. The frequency is equal to Pipe C has the lowest frequency and pipes A and B hae equal frequencies, higher than the one in pipe C. 17. A string is tied between two lab posts a distance L apart. The tension in the string and the linear ass density is such that the speed of a wae on the string is = 4 /s. A tube with syetric boundary conditions has a length L and the speed of sound in the tube is = 4 /s. What could be said about the frequencies of the haronics in the string and the tube? What if the elocity in the string were = 686 /s? n Since the boundary conditions are both syetric, the frequencies are fn =. Since the speed L is the sae in each, the frequencies are the sae. If the wae speed were doubled in the string, the frequencies in the string would be twice the frequencies in the tube. 19. The label has been scratched off a tuning fork and you need to know its frequency. Fro its size, you suspect that it is soewhere around 50 Hz. You find a 50-Hz tuning fork and a 70- Hz tuning fork. When you strike the 50-Hz fork and the fork of unknown frequency, a beat frequency of 5 Hz is produced. When you strike the unknown with the 70-Hz fork, the beat frequency is 15 Hz. What is the unknown frequency? Could you hae deduced the frequency using just the 50-Hz fork? The frequency of the unknown fork is 55 Hz. No, if only the 50 Hz fork is used, listening to the beat frequency could only liit the possible frequencies to 45 Hz or 55 Hz. 1. A showy custo-built car has two brass horns that are supposed to produce the sae frequency but actually eit 6.8 and 64.5 Hz. What beat frequency is produced? The beat frequency is 0.7 Hz.. Three stationary obserers obsere the Doppler shift fro a source oing at a constant elocity. The obserers are stationed as shown below. Which obserer will obsere the highest frequency? Which obserer will obsere the lowest frequency? What can be said about the frequency obsered by obserer? Page of 18

3 Unit : Waes and Acoustics Obserer 1 will obsere the highest frequency. Obserer will obsere the lowest frequency. Obserer will hear a higher frequency than the source frequency, but lower than the frequency obsered by obserer 1, as the source approaches and a lower frequency than the source frequency, but higher than the frequency obsered by obserer 1, as the source oes away fro obserer. 5. Prior to 1980, conentional radar was used by weather forecasters. In the 1960s, weather forecasters began to experient with Doppler radar. What do you think is the adantage of using Doppler radar? Doppler radar can not only detect the distance to a stor, but also the speed and direction at which the stor is traeling. 7. Due to efficiency considerations related to its bow wake, the supersonic transport aircraft ust aintain a cruising speed that is a constant ratio to the speed of sound (a constant Mach nuber). If the aircraft flies fro war air into colder air, should it increase or decrease its speed? Explain your answer. The speed of sound decreases as the teperature decreases. The Mach nuber is equal to M = s, so the plane should slow down. Probles 9. Consider a sound wae odeled with the equation 1 1 s x, t = 4.00 n cos.66 x 156 s t. What is the axiu displaceent, the waelength, ( ) ( ) the frequency, and the speed of the sound wae? sax = 4.00 n, = 1.7, f = 00 Hz, = 4.17 /s 1. Consider a diagnostic ultrasound of frequency 5.00 MHz that is used to exaine an irregularity in soft tissue. (a) What is the waelength in air of such a sound wae if the speed of sound is 4 /s? (b) If the speed of sound in tissue is 1800 /s, what is the waelength of this wae in tissue? a. l = f = 4 /s Hz = ; b. l = 1800 /s = = f Hz. A sound wae is odeled with the wae function ( 4 P 1.0 Pa sin kx s 1 t) sound wae traels in air at a speed of sound wae? (b) What is the alue for ( ) Page of 18 = and the = 4.00 /s. (a) What is the wae nuber of the P.00,0.00 s? 1 a. k = = ; 1 P = 1.0 Pa sin s 0.00 s = 1.11 Pa ( ) b. ( ) ( ) 5. A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency f, creating a sound wae that oes down the tube. The wae oes through the tube

4 Unit : Waes and Acoustics at a speed of = /s. The sound wae is odeled with the wae function ( ) ( ) s x, t = s cos kx t +.. At tie t = 0.00 s, an air olecule at x =.5 is at the ax axiu displaceent of 7.00 n. At the sae tie, another olecule at x =.7 has a displaceent of.00 n. What is the frequency at which the speaker is oscillating? s = s cos kx + = 7.00 n, s = s cos kx + =.00 n, kx + = 0 rad ( ) ( ) 1 ax 1 ax 1 1 s 1.00 n kx + = cos = cos = 1.18 rad sax 7.00 n 1.18 rad 1 k ( x x1) = 1.18 rad, k = = = = 1.11, f = = 06.1 Hz k 7. A sound wae produced by an ultrasonic transducer, oing in air, is odeled with the wae 4 1 s x, t = 4.50 ncos x 5.00 MHz t. The transducer is to be used ( ) equation ( ) ( ) in nondestructie testing to test for fractures in steel beas. The speed of sound in the steel bea is = 5950 /s. Find the wae function for the sound wae in the steel bea. 6 1 ( s ) k = = = /s ( ) 1 (, ) = 4.50 n cos ( 5.00 MHz) s x t x t 9. Bats use sound waes to catch insects. Bats can detect frequencies up to 100 khz. If the sound waes trael through air at a speed of = 4 /s, what is the waelength of the sound waes? = =.4 f 41. Consider the graph shown below of a copression wae. Shown are snapshots of the wae function for t = s (blue) and t = s (orange). What are the waelength, axiu displaceent, elocity, and period of the copression wae? Page 4 of 18

5 Unit : Waes and Acoustics = = 6.00 s ax = = = 600 /s s s T = = 0.01s 4. A guitar string oscillates at a frequency of 100 Hz and produces a sound wae. (a) What do you think the frequency of the sound wae is that the ibrating string produces? (b) If the speed = 4 /s,, what is the waelength of the sound wae? of the sound wae is 4 /s (a) f = 100 Hz, (b) = = =.4 1 f 100s 45. What frequency sound has a waelength when the speed of sound is 40 /s? 40 /s f = = = 400 Hz (a) What is the speed of sound in a ediu where a 100-kHz frequency produces a 5.96-c waelength? (b) Which substance in the following table is this likely to be? Mediu (/s) Gases at 0 º C Air 1 Carbon dioxide 59 Oxygen 16 Heliu 965 Hydrogen 190 Liquids at 0 º C Ethanol 1160 Mercury 1450 Water, fresh 1480 Sea Water 1540 Huan tissue 1540 Solids (longitudinal or bulk) Vulcanized rubber 54 Polyethylene 90 Marble 810 Glass, Pyrex 5640 Lead 1960 Aluinu 510 Steel 5960 a. f ( ) = = Hz = /s ; b. steel (fro the preceding table) Page 5 of 18

6 Unit : Waes and Acoustics 49. Air teperature in the Sahara Desert can reach 56.0 C (about 14 F ). What is the speed of sound in air at that teperature? 56.0 C = 1 1+ = 6 s 7 C s 51. A sonar echo returns to a subarine 1.0 s after being eitted. What is the distance to the object creating the echo? (Assue that the subarine is in the ocean, not in fresh water.) t 1.0s x= seawater = 1540 = 94 s 5. Ultrasonic sound waes are often used in ethods of nondestructie testing. For exaple, this ethod can be used to find structural faults in a steel I-beas used in building. Consider a eter long, steel I-bea with a cross-section shown below. The weight of the I-bea is N. What would be the speed of sound through in the I-bea? Y = 00 GPa, = 159 GPa. ( ) steel steel V = = 0.05 ( )( )( ) ( )( )( ) w N = = = 9.5 kg g 9.8 /s = = 7850 kg/ V 9 Y 0010 N/ = = = /s 7850 kg/ 55. During a 4th of July celebration, an M80 firework explodes on the ground, producing a bright flash and a loud bang. The air teperature of the night air is T F = F. Two obserers see the flash and hear the bang. The first obserer notes the tie between the flash and the bang as 1.00 second. The second obserer notes the difference as.00 seconds. The line of sight between the two obserers eet at a right angle as shown below. What is the distance x between the two obserers? Page 6 of 18

7 Unit : Waes and Acoustics T C = 5 ( 9 T - F ) = 5 C, = 1 s 1+ 5 C = /s 7 C Dx 1 = ( s 0.10 s ) = 5.16, Dx = ( s 0.15 s ) = 5.74 Dx = ( 5.16 ) + ( 5.74 ) = Suppose a bat uses sound echoes to locate its insect prey,.00 away. (See the following figure.) (a) Calculate the echo ties for teperatures of 5.00 C and 5.0 C. (b) What percent uncertainty does this cause for the bat in locating the insect? (c) Discuss the significance of this uncertainty and whether it could cause difficulties for the bat. (In practice, the bat continues to use sound as it closes in, eliinating ost of any difficulties iposed by this and other effects, such as otion of the prey.) Page 7 of 18

8 Unit : Waes and Acoustics t = s, t = s ; b. % uncertainty = 5.00 %; c. This uncertainty could a C 5.0 C definitely cause difficulties for the bat, if it didn t continue to use sound as it closed in on its prey. A 5% uncertainty could be the difference between catching the prey around the neck or around the chest, which eans that it could iss grabbing its prey. 59. The warning tag on a lawn ower states that it produces noise at a leel of 91.0 db. What is this in watts per eter squared? W/ 61. What intensity leel does the sound in the preceding proble correspond to? 85 db 6. What is the decibel leel of a sound that is twice as intense as a 90.0-dB sound? (b) What is the decibel leel of a sound that is one-fifth as intense as a 90.0-dB sound? a. 9 db; b. 8 db 65. People with good hearing can perceie sounds as low as 8.00 db at a frequency of 000 Hz. What is the intensity of this sound in watts per eter squared? W/ 67. Ten cars in a circle at a boo box copetition produce a 10-dB sound intensity leel at the center of the circle. What is the aerage sound intensity leel produced there by each stereo, assuing interference effects can be neglected? A decrease of a factor of 10 in intensity corresponds to a reduction of 10 db in sound leel: 10 db 10 db = 110 db. 69. If a sound intensity leel of 0 db at 1000 Hz corresponds to a axiu gauge pressure 10 9 at (sound aplitude) of, what is the axiu gauge pressure in a 60-dB sound? What is the axiu gauge pressure in a 10-dB sound? We know that 60 db corresponds to a factor of increase in intensity. Therefore, 1/ 6 10 I X I 9 6 1/ 6 I X =, so that X = X1 = (10 at)(10 ) = 10 at. I1 X1 I = 9 1 1/ 10 at(10 ) 10 at. 10 db corresponds to a factor of increase 71. Sound is ore effectiely transitted into a stethoscope by direct contact rather than through the air, and it is further intensified by being concentrated on the saller area of the eardru. It is reasonable to assue that sound is transitted into a stethoscope 100 ties as effectiely copared with transission though the air. What, then, is the gain in decibels produced by a stethoscope that has a sound gathering area of 15.0 c, and concentrates the sound onto two eardrus with a total area of c with an efficiency of 40.0%? 8. db 7. The factor of 10 1 in the range of intensities to which the ear can respond, fro threshold to that causing daage after brief exposure, is truly rearkable. If you could easure distances Page 8 of 18

9 Unit : Waes and Acoustics oer the sae range with a single instruent and the sallest distance you could easure was 1, what would the largest be? k 75. Can you tell that your rooate turned up the sound on the TV if its aerage sound intensity leel goes fro 70 to 7 db? 7 db 70 db = db; Such a change in sound leel is easily noticed. 77. A person has a hearing threshold 10 db aboe noral at 100 Hz and 50 db aboe noral at 4000 Hz. How uch ore intense ust a 100-Hz tone be than a 4000-Hz tone if they are both barely audible to this person?.5; The 100-Hz tone ust be.5 ties ore intense than the 4000-Hz sound to be audible by this person. 79. What is the length of a tube that has a fundaental frequency of 176 Hz and a first oertone of 5 Hz if the speed of sound is 4 /s? Calculate the first oertone in an ear canal, which resonates like a.40-c-long tube closed at one end, by taking air teperature to be 7.0 C. Is the ear particularly sensitie to such a frequency? (The resonances of the ear canal are coplicated by its nonunifor shape, which we shall ignore.) 11.0 khz; The ear is not particularly sensitie to this frequency, so we don t hear oertones due to the ear canal. 8. A 4.0--long pipe, open at one end and closed at one end, is in a roo where the teperature is T = C. A speaker capable of producing ariable frequencies is placed at the open end and is used to cause the tube to resonate. (a) What is the waelength and the frequency of the fundaental frequency? (b) What is the frequency and waelength of the first oertone? a. = 1 1+ = /s, 1 = 4( 4.00 ) = 16.00, f /s 1 = = 1.51 Hz; s /s b. = 5., f = = Hz A nylon guitar string is fixed between two lab posts.00 apart. The string has a linear ass density of = 7.0 g/ and is placed under a tension of N. The string is placed next to a tube, open at both ends, of length L. The string is plucked and the tube resonates at the n = ode. The speed of sound is 4 /s. What is the length of the tube? string = l 1 = L = f 1, F T = /s, l L = f 1 = = ( /s ) = 1., f = = Hz 1. 4 /s ( Hz) = 1.5 Page 9 of 18

10 Unit : Waes and Acoustics 87. Students in a physics lab are asked to find the length of an air colun in a tube closed at one end that has a fundaental frequency of 56 Hz. They hold the tube ertically and fill it with water to the top, then lower the water while a 56-Hz tuning fork is rung and listen for the first resonance. (a) What is the air teperature if the resonance occurs for a length of 0.6? (b) At what length will they obsere the second resonance (first oertone)? a..0 C; b What are the first three oertones of a bassoon that has a fundaental frequency of 90.0 Hz? It is open at both ends. (The oertones of a real bassoon are ore coplex than this exaple, because its double reed akes it act ore like a tube closed at one end.) first oertone = f = (90.0 Hz) = 180 Hz; second oertone = f = (90.0 Hz) = 70 Hz; third oertone = f4 = 4(90.0 Hz) = 60 Hz 91. What length should an oboe hae to produce a fundaental frequency of 110 Hz on a day when the speed of sound is 4 /s? It is open at both ends An organ pipe L =.00 ( ) is closed at both ends. Copute the waelengths and frequencies of the first three odes of resonance. Assue the speed of sound is = 4.00 /s. The pipe has syetrical boundary conditions; n n = L, fn = =, n = 1,, n L = 6.00, =.00, =.00 1 n f = Hz, f = 114. Hz, f = Hz A sound wae of a frequency of.00 khz is produced by a string oscillating in the n = 6 ode. The linear ass density of the string is = kg/ and the length of the string is What is the tension in the string? 6 = L = = f = 1000 /s 6 6 FT = = 6500 N 97. A student holds an c lab pole one quarter of the length fro the end of the pole. The lab pole is ade of aluinu. The student strikes the lab pole with a haer. The pole resonates at the lowest possible frequency. What is that frequency? 510 /s f = = = 6.40 khz 0.80 Page 10 of 18

11 Unit : Waes and Acoustics 99. By what fraction will the frequencies produced by a wind instruent change when air teperature goes fro 10.0 C to 0.0 C? That is, find the ratio of the frequencies at those teperatures. 1.0 or % 101. What beat frequencies result if a piano haer hits three strings that eit frequencies of 17.8, 18.1, and 18. Hz? f = f f B Hz 18.1 Hz = 0. Hz; 18. Hz 17.8 Hz = 0.5 Hz; 18.1 Hz 17.8 Hz = 0. Hz 10. Two identical strings, of identical lengths of.00 and linear ass density of = kg/, are fixed on both ends. String A is under a tension of N. String B is under a tension of N. They are each plucked and produce sound at the n =10 ode. What is the beat frequency? FTA FTB A = = /s, B = = /s, A = B = (.00 ) = /s 15.4 /s f = = Hz A string with a linear ass density of = kg/ is stretched between two posts 1.0 apart. The tension in the string is N. The string oscillates and produces a sound wae. A 104-Hz tuning fork is struck and the beat frequency between the two sources is 5.8 Hz. What are the possible frequency and waelength of the wae on the string? N = = /s, kg/ f f string string Lf = = = = string 104 Hz 5.8 Hz Hz, n 16. Lf = + = = = string 104 Hz 5.8 Hz Hz, n The frequency is Hz and the waelength is The iddle C haer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to Hz. What frequencies could the other string hae? f = f f = Hz 1.50 Hz, 1 B so that f = Hz or f = Hz w w Page 11 of 18

12 Unit : Waes and Acoustics 109. Twin jet engines on an airplane are producing an aerage sound frequency of 4100 Hz with a beat frequency of Hz. What are their indiidual frequencies? f1+ f face = ; fb = f1 f (assue f1 f) ( fb + f) + f face = face fb fb f = = face = 4100Hz 0.50Hz = Hz f1 = fb + f = Hz Hz = Hz 111. (a) What frequency is receied by a person watching an oncoing abulance oing at 110 k/h and eitting a steady 800-Hz sound fro its siren? The speed of sound on this day is 45 /s. (b) What frequency does she receie after the abulance has passed? 5 a Hz ; b Hz 11. What frequency is receied by a ouse just before being dispatched by a hawk flying at it at 5.0 /s and eitting a screech of frequency 500 Hz? Take the speed of sound to be 1 /s Hz 115. A couter train blows its 00-Hz horn as it approaches a crossing. The speed of sound is 5 /s. (a) An obserer waiting at the crossing receies a frequency of 08 Hz. What is the speed of the train? (b) What frequency does the obserer receie as the train oes away? a. 1.9 /s; b. 19 Hz 117. Two eagles fly directly toward one another, the first at 15.0 /s and the second at 0.0 /s. Both screech, the first one eitting a frequency of 00 Hz and the second one eitting a frequency of 800 Hz. What frequencies do they receie if the speed of sound is 0 /s? The first eagle hears Hz. The second eagle hears Hz An abulance with a siren f = 1.00 khz ( ) blaring is approaching an accident scene. The abulance is oing at ph. A nurse is approaching the scene fro the opposite direction, running at o = 7.00 /s. What frequency does the nurse obsere? Assue the speed of sound is = 4.00 /s. 11. What is the iniu speed at which a source ust trael toward you for you to be able to hear that its frequency is Doppler shifted? That is, what speed produces a shift of 0.00% on a day when the speed of sound is 1 /s? Page 1 of 18

13 Unit : Waes and Acoustics An audible shift occurs when obs fobs fs s f s s f f f = = obs s 1.00 ; ( f / f ) 1 (1 /s)(1.00 1) obs s s = = = fobs / fs /s 1. A jet flying at an altitude of 8.50 k has a speed of Mach.00, where the speed of sound is = /s. How long after the jet is directly oerhead, will a stationary obserer hear a sonic boo? æ 1 ö q = sin -1 ç è.0 ø = 0.0 ( ) = /s s = /s tanq = y s t, t = y s tanq = 1.65 s 15. A plane is flying at Mach 1., and an obserer on the ground hears the sonic boo seconds after the plane is directly oerhead. What is the altitude of the plane? Assue the speed = 4.00 /s. of sound is w sinq = = 1 s M, q = æ 1 ö sin-1 ç è 1. ø = y = s t tanq = /s( s)tan56.47 = 9.1 k 17. A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency of f, creating a sound wae that oes down the tube. The wae oes through the tube at a speed of = /s. The sound wae is odeled with the wae function s x, t = s cos kx t +. At tie t = 0.00 s, an air olecule at x =. is at the ( ) ( ) ax axiu displaceent of 6.4 n. At the sae tie, another olecule at x =.7 has a displaceent of.0 n. What is the wae function of the sound wae, that is, find the wae nuber, angular frequency, and the initial phase shift? Page 1 of 18

14 Unit : Waes and Acoustics s = s cos kx + = 6.4 n 1 ax 1 ax 1 ( x ) 1 w ( ) ( ) s = s cos kx + =.0 n kx + = 0 rad s.0 n kx + = = = sax 6.4 n k x = 1.0 rad 1 1 cos cos 1.0 rad 1.0 rad k = = = k = s = cos( ) = 6.90 r ( ) s s kx 1 ax 1 ( ) ( 1, = 6.0 n cos s ) 1 ad + = 5.66 rad s x t x t Additional Probles 19. A long tube is opened at both ends. The air teperature is 6 C. The air in the tube is oscillated using a speaker attached to a signal generator. What are the waelengths and frequencies of first two odes of sound waes that resonate in the tube? 6 C s = 1 1+ = /s s 7 C ; s n = L fn = n = 1.60 f = 16.50Hz 1 1 n = 0.80 f1 = 4.00Hz 11. Consider the following figure. The length of the string between the string ibrator and the = kg/. The string ibrator can pulley is L = The linear density of the string is oscillate at any frequency. The hanging ass is.00 kg. (a)what are the waelength and frequency of n = 6 ode? (b) The string oscillates the air around the string. What is the waelength of the sound if the speed of the sound is s = 4.00 /s? Page 14 of 18

15 Unit : Waes and Acoustics 6 = ( 1.0 ) = kg 9.80 s a. s 4.00 /s = = ; b. s = = =.40 kg s f Hz /s f6 = = Hz Two cars oe toward one another, both sounding their horns ( f s = 800Hz). Car A is oing at 65 ph and Car B is at 75 ph. What is the beat frequency heard by each drier? The air teperature is T C =.00 C..00 C = = s 7.00 C s i 1609 h i 1609 h A = 65 = 9.05, B = 75 =.5 /s h 1 i 600 s s h 1 i 600 s /s /s f A = 800 Hz = Hz, /s.5 /s /s +.5 /s fb = 800 Hz = Hz /s 9.05 /s f = Hz, f = Hz A,beat B,beat 15. Suppose that the sound leel fro a source is 75 db and then drops to 5 db, with a frequency of 600 Hz. Deterine the (a) initial and (b) final sound intensities and the (c) initial and (d) final sound wae aplitudes. The air teperature is C = kg/. 4 C = 1 1+ = 45.4 s 7 C s ; T = 4.00 C and the air density is Page 15 of 18

16 Unit : Waes and Acoustics a. W 75 db 10 db 1 10 db db μw 10 db 1 10 db I = I = = ; b. W μw I = I010 = = 0.16 ; I I s = = 104.9μ ; d. sax = = 7.4 μ c. ax 17. A stationary obserer hears a frequency of Hz as a source approaches and a frequency of Hz as a source departs. The source oes at a constant elocity of 75 ph. What is the teperature of the air? f f A + 1 f A s + s f A f D = =, ( s ) = + s, = s = 47.9 f f D s fd A 1 s f f + s D T C = 1 7 = Challenge Probles 19. Two sound speakers are separated by a distance d, each sounding a frequency f. An obserer stands at one speaker and walks in a straight line a distance x, perpendicular to the the two speakers, until he coes to the first axiu intensity of sound. The speed of sound is. How far is he fro the speaker? ( ) x + d x =, x + d = + x x + d = + x + x, d = + x d d f x = = f 141. Two speakers producing the sae frequency of sound are a distance of d apart. Consider an arc along a circle of radius R, centered at the idpoint of the speakers, as shown below. (a) At what angles will there be axia? (b) At what angle will there be inia? Page 16 of 18

17 Unit : Waes and Acoustics r = r r1 = d sin a. For axia 1 d sin = n n = 0, 1,..., = sin n n = 0, 1,... d b. For inia, r = r r = d sin 1 1 d sin = n + n = 0, 1, = sin n+ n= 0, 1,... d æ 14. A string = kg è ç, L = 1.50 ö ø is fixed at both ends and is under a tension of 155 N. It oscillates in the n =10 ode and produces sound. A tuning fork is ringing nearby, producing a beat frequency of.76 Hz. (a) What is the frequency of the sound fro the string? (b) What is the frequency of the tuning fork if the tuning fork frequency is lower? (c) What should be the tension of the string for the beat frequency to be zero? F string a. T n string = = 160.7, fstring = = Hz ; s L b. ffork = fstring fbeat = 51 Hz ; c. f fork FT n = = = L n Lffork, FT N 145. A string has a linear ass density = kg/, a length L = 0.70, a tension of F T = 110 N, and oscillates in a ode n =. (a) What is the frequency of the oscillations? (b) Use the result in the preceding proble to find the change in the frequency when the tension is increased by 1.00%. F T 1 FT a. f = n = 68.6 Hz ; b. f f = 1.4 Hz L FT 147. A string on the iolin has a length of.00 c and a ass of gras. The tension in the string N. The teperature in the roo is T C = 4.00 C. The string is plucked and oscillates in the 9 n = ode. (a) What is the speed of the wae on the string? (b) What is the waelength of the sounding wae produced? (c) What is the frequency of the oscillating string? (d) What is the frequency of the sound produced? (e) What is the waelength of the sound produced? Page 17 of 18

18 Unit : Waes and Acoustics a. F T = = ; b. = s L = ; c. f9 = = 9.1 khz ; L d. fsound = f9 = 9.1 khz ; e. 4.00C 1 1+ s 7.00C = = = Hz sound air fsound This file is copyright 016, Rice Uniersity. All Rights Resered. Page 18 of 18