What is the evidence that sound trave)omx)+v hzt4w,h4 e2pqjyj,g ls as a wave?

What is the evidence that sounhp:4wae j zeve24q)x/ d is a form of energy?

Children sometimes poj ,*4pxdn/v+eu 6w bpgk:fa 5lay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how j*5/4uk+ :v,px6oe pawn fgdb the sound wave travels from one cup to the other.

When a sound wave passes fr(qpai xp7n 9*jom air into water, do you expect the frequency or waveleng9qi7j pp *(nxath to change?

What evidence can you give that the gaf(.e0 bo*wg(kwkb :q aa q81speed of sound in air does not depend significanfgebw:ag a o. 0k(1(kaq8q bw*tly on frequency?

The voice of a person who has inhaled helium sounds very higha s n6e,hlqk :muxa*j53;d;,rqoae 3 c-pitched. Why?

How will the air temperature in a room oavhk )) +qg+qaffect the pitch of organ pipes?

Explain how a tube might be used as a filter tosfpy87 d42mua reduce the amplitude of sounds in various frequency r8dfu2m7 y4pasanges. (An example is a car muffler.)

Why are the frets on a7n0/z-pjnuz jxp0( dl guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward j d(np jlxp-/07u zn0zthe bridge?

A noisy truck approaches you from behind a building. Initially you hear tm/d ,sc ;hg3cit but cannot see it. When it emerges and you do see itt scd;mh3/g,c, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be saxzt:b r-.2 jvtid to be due to “interference in space,” whereas beats can be said to be due to “interference in time.”-rzb.jxt : vt2 Explain.

In Fig. 12–16, if the frequency of the speakers were lo+ wv io*9 umbp:na;b,we,.ikjwered, would the points D and C (where destructive and constructive interference occknij.,,wavb;i ub o+mew 9*:pur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who k nl1 ue1b6bgn oyw7t3s 6usa f1n1v;8work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sav7yne tb ss8bfu o 6nku1l1gw;16 3n1ound levels reaching the ears?

Consider the two waves e)tna8hhng2h8; bf; sshown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencg a;ef b8)th;h8nsh2 nies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsegoxt*x vk /; 7v:li :*i-kecx 9;catekrver move in the same direction, with the same vee gke7::xlv* k-/txc ci vkti9xo a;;*locity? Explain.

If a wind is blowing, will this alter the frequency of iccdxn22*80md)iq (blsp* w j the sound heard by a person at rest with respect to the source? Is the wav0*jpd2cwx in8lscidb) 2 *mq( elength or velocity changed?

Figure 12–32 shows various positionaw/,0w3a )c irbr709vi:2cxn opqz ko s of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child heaw b2rzok9np0w,o/7 )cq avr i3:a cxi0r the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echq*8 *vpgw3sa .3o8wb-l2p k ls1)siiwo)invlo of her shout reflected by a sbpi *wpn*wwol-2i.8g 3)8ov1asqs kvl l 3)icliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.hlir.o0(u* xh He hears the echo of the sound reflected from the ocean floor di.ri0oh*u hx(lrectly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airbkanp4 x lzu 0i3v-g/,v;2 fha at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifti4(y 7c.gop:yvyhm4px ik9o f5ng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awc.(mxov4 y h5 94ofy7p: pgikyay (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from g n) coj+v)7z,d zkxm9the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later))79dxkzzgc, nj ov+m . How high is the cliff?    m

  A person, with his ear to the gcwh 5d:q :j1tqgyf4: uround, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the airwqhc1 f::j45uqd :yt g and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by g,:gio8l *gkxhm4zo l-+xpm -the “5-second rule” for estimating the distance from -: p oxl lhkg8mg -+,zg4iom*xa lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lepjbbtult; vb 9v114xsuyy/68 vel of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a s k .i.voy+hpa:nn*bn(,mi*p gound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prob.,b+inh6mr: a: hcwvduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensivh6:mh :iabw rb,nc. +ties, not dB’s.]    dB

  A person standing a certain distance from an airplane wqvuk):mzlo5 z;gk u52ith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What : uqz;)lgmkuv o525zksound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to ha07lrjvx;/c,6ne nn /:ilwpzda3b sp4ve a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB = br;nlzlnawi,3j/pn xsec 74/v:6pd 0    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fr wvft kb(qczr re7e+bp5( r,bqjh9-33om a person speaking in normal conversation. Use Table 12–2. Assum c-+9rveberk 3hz3qbtwr5f,jp7q(b(e the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whosw6v1 ere pm)sr a: *ks6*qu-ome area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the m p+3jqu9 wuwed/i(/e oore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connecte/eue(ud jw 3/w+o p9iqd in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whn3fth+3t fee 5en placed 2.8 m in front of a loudspeaker on the stagt3fh +ef5ten3 e.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound(rfrg8w /xo34+xy lmkm l1uc/ level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amorcuw3km+(rx1y x o/lgl 4mf8/unt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensih8+ngo6ifn4 h rti+.h ty increasg +4ii6t8nhnr.h+ho fe? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displ c/j7 supo.-7kfnnab :acement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitifck : nojpn.a bsu7-/7es?   

  What would be the sound level (in dB) of a sound wave in air ;776 nuddzx e0 onhk;fthat corresponds to a displacement amplitude of vibrating air moleculehn0;zx6eno7d df7u k ;s of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone g s2j ,vbbw 96p7tio6 pi8uwr/that has a 8 ij b76t9i wos2g,wpuv 6bp/r50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soun v3.;*wxnuyoa d level is 30 dB? (See Fig;nuo*v w3.ayx. 12–6.)

  Your auditory system cmdhlje ;:9hb ./-r irmdsajuo2:p 9p3an accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity ajrd u9mi le.m h3 ppdah: sb29:/-ojr;t
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 44c;- )/ nu bvi:wkm:fye0 Hz. The length of the vibrating portion is 3 /ubcy;ime:v-) wk:fn 2 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thrdxh 1 g(t4iy/ree audible overtones (g1 d4txyih/rif the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect bv e:9ybiy3e kr8.1zcb1qrp /from blowing across the top of an empty soda bottle that is 18 cm deep, if you assue.: vq9z keyrc bb1b83i1 /rpymed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning 43bkbg3/dp;m b1evx,shpsg )ek)8wq f tr/8 p the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes reqspt m33wf)b4gbqe8xv 8 ph,; ek/bsgr)pd1k/ uired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz vu8z0tte2h 7bwk2qoo2yt x17 as its third harmonic. What will be its fundamental fre zthoob2qx 1v072t 7ewyk2 tu8quency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tundlcul/j,gw-j;g+*/ j3* xj m 46s itnd.cjazred to play E above middle C (330 Hscjj mc-z g tij,d ;4gwj +anlrdxl3j/ *.u*/6z).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe thau4 ak2es7iyxghmg:z 1/2+tipc4u/ 3 d)ggywqt emits middle C (262 Hz) when the ti+ksm//ed iyu3g2w g )7q pg2:1xtuych4 a4zg emperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune , bzyy:iz*q c-lx2 4qyqy a6z7at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hol/o0yrw/b h9yuzw0ux * e be that must be uncovered to play D above middle Cuy/9wyb0/ ou0hwz rx * at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipg/a0;l1akgz4sw qn6 :mub ttnoi3y6jx) 9kv9 e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a c0ynaztxgam3/g9 ;os6:1kbvi4n k6 utqj w) l9losed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both en icn57s7 k3vlhds. It resonates at two successive harmonics of frequencies 275 Hz and 3l 7h5cv7knis3 30 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 q.nhhz g( sdb5;.)dsy$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are prese u,x96dsnx4 zvn48p y.ov8th ynt within the audible range for a 2.14-m-long organ pipy zsvdn89 x,4vu6n8o txh .4ype at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal isklnhy5pm :y-p,s +9i;px (ldd approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of yollkpd d;pn,9-pmy (:y 5ix s+hur answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2c6 /zrs yo7h3s.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in rh oz6sy7/sc3frequency is the other string? ±    Hz

  What is the beat frequency if mid4ew5 /qf 9dyo*tet-3;b b mlckdle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle mz zdh31z 3oi ,fpoz/:operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estima,33 phdz ozimfz z/1:ote the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and (av4px)lcww dr7o;:l 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain ) (pv w:x l7rldoa;cw4your reasoning.    Hz

  Two violin strings are tuned to the same frequencyoik4p0;pqok ao/t 1ia *61etk, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playoa*0;1op/1oiat kk 4pq it e6ked together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each 7y.uvg2u zo: otry to play middle C (262 Hz), but one is at 5:2ugozyou 7 .v.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a - zkv/n5h:ylq 8mip)s frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded to mqvy) h/lin8:- 5kszpgether?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speake1g0q9tt o.vz kr and 3.50 m from the othet9.1tz 0qvg kor.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, butml 5-asbd(:/3vb vj sp a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mujl: dvm3v(/ps 5a-bbsst be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.767x*r ,,5g v mwphc7hjr10 tqis m in air. How many beats per second will be hearcmw* srr1 itg7v 0h7qjp,h,5xd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when:s97 z 7 wkqzwtu:)qmw at rest. What frequ : wq7w7zkwu)zqt9sm: ency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequt li9l:r2far4fz36 tdency do you detect if a fire engine whose siren emits at 1550 Hz rl:dt4zt 3l9 i2afr6fmoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency di-/skqr, xo.j+2ak4wh u oi vool8 25if a 2000-Hz source is moving toward you at 15 m/s h8a oxqo5 j 2visku l,i.+-4okwr2 /doversus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is bg24uojb n;i83id u /gj*nc2wat rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. Whatd ; uijgbn2 u/ingb43j28ocw * is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recetav4u : nrix9rdkx1g7*d rqfx3s0 sig255 r6pives them returned from an object moving *qr 4g1 6 ddf ivat 5 rp79sx5urikxgxs2n3r:0directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at;mo .3uvqub2 p a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected waq;.3bpvmu2 ouve?    $ \times10^{4}$ Hz

  In one of the original Doppleb/ wm e(0arqv8r experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if th rmvbq /aw(8e0e train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mea (mgdi,iy6 2,bbafd t3z5.ha esure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expef,a bi6 dyhet dzg3ma(5.2b,i cted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic w zf8cfp yxn;vb8u(2 /avvk31p aves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity.yo1inge)a/ 79vqgh b is 12 m/s from the hgogn9 b/vae1.)qi 7y north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if im/)+nzaeq:e ju*j,r6 ngaw n0ts speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.m rc9be* dn-a/3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction e/9n*cd mr-ab of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed oa4et 8e,;p pgd 1-5s7kose dpsf sound is only about 35 8d1s-a,p4kge75eso; dtpe s pm/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oce)z eq2xzvris+ n3a w73an. Determine the shock wave angle it pr32erqazsxwn3+ v7i)z oduces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle z-+wadr3cgm/ $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane e nrql8l+ 1gzz+xactly 1.5 km above the ground flying faster than the speed or1qz l++lnzg8 f sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20r 852a0aybpv *op 6lku,000-Hz sound pulses downward from the bottom 8v*p u5o 6kara0b2lyp of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves armet +6uj)b puib:4,mne there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer ph- +sgea ad/b;ipe symphony. It consists of many plastic pipes of various lengths, which are openghd;a /e-b+ as on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to 5* -8wbgea95vjuh xd nthe threshold of human hearing (0 dB). What will be the sound level of 100 j 9 v5g-nuw5d8ex*hba0 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB so9 dtgqkdy*x, ;und are heard simultaneousld9*g,tyk x;dqy?    dB

  The sound level 12.0 m from a lm bbt3v ka ry-ra*w7k (b.e-4poudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) oapwvby*- kr -kr3etab47b. ( mf the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powemq)vwn pwicj ), btg,/cglv*4 4+.bd+ kmiup(r output drops by 10 dB at 15 kHz. .qp wmk+b b w lc/v)4 mgtv+p,(inu*,4gcj id)What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over*y 9fair kocq)c zsa(7hc*8 y* their ears. Assume that the sas*ar zioc kcq8y 9 y*7fc()*hound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatioy04 pnl/y7rqwns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned tbktfgwc33)t ; d0 pfo9o a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin;o1w)4rmeb c s is 32 cm long between fixed points with a fundamental frequency of 440 Hs ;wbc)m re1o4z and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration abovepk/m 0ygyu)h gkk-h ;3 a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate wiy u /kkhkghy);m0-p3gth the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string 9e dzb4 *hmwh0of mass 2.10 g is near a tube that is open at one end and also 75 cmm e94whh0*bd z long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate x1tw2;b0 +cz uww9rh+lm gn)ias one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hzk t f.c/p1ts5g range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.315/tfgkstc .p 4 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor 1jjc 1 u8gnhujpy(8i6on the stanj (u6jy8gui h1jp8c 1tionary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appr9ulx)r*s n*7weays ,l oaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the ylxn,7)l ra9ue*sw*s train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jc,( kybo- 4xm 3ys0ebnust by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a fk4ox -3n y(m,ye0bsb cull octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a b hhgp++) jri-kz oth8e,y6 3naeat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?g6,8+h3hzohap-t je+ ry kn)i    m

Two loudspeakers are at opposite ends of a railroad car as it moves m:vkj,. e8h 2h2nyykki8pi*mpast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the spe*j8 ,ehiv.ykm2:hn k8yimkp2 akers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is noyw0 hph(8r; wurmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along t urh0;8h p(ywwhe flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flyinmjbz/q7 - ta6ug toward the bat at speed 5 m/s The bat emits a sq/-bmaz7 tu j6ound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a3 0fb zj6msorhxpk ( 2,4o)nga moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms (rs3 boj z2ngm6kpx, 0h)fo4a long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one .hn 3), y)utcowz/keu Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, tnuu ceh. 3kwy/)z)o, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stand3 yk )os),so7o gxphw2ing waves, which can cause acoustic “dead spots” at the locations of the pressure nodek o))w, 7yoops3h2g xss. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumin5a(1j )2rvsnx) nmd jpum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Win(jrs 251 nm)pxjdva )th a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humannqy:d0 u89i;x.pc wyc ear at a frequency of abou wdyqnp8u0;yc9. :ix ct 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonjo3u7 t -txc/)u1fhbj ic boom 1.5 min after the plane pa u t-)fuh/jbxc3o1j t7sses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isjcue0b/qs i9tu0 9rj g;2p-np 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h