What is the evidence that sound t ( hki5hdy,fn9pk z gb/,bdqrc0w1m*)ravels as a wave?

What is the evidence that sound is a form of enerq.db6ku w:)-boj 8ys hw.vcs9gy?

Children sometimes play with a hda8c+m f-m+-xu8a exbomemade “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 the sound wave travels fxu m dm-fc 8xa-+e+ab8rom one cup to the other.

When a sound wave passes from air into water, do you expectd;l)ced 7ri h, the frequency or wavelenlr;ce 7,hddi )gth to change?

What evidence can you give that the speed of sound inq- b71y1lrsc4v1vuc k air does not depend significantly on frequeb1l 71 1uc4kqv sycr-vncy?

The voice of a person whgxv jw83) 4gbko has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect by4z*)xlp, okcygop 2*eeg8(the pitch of organ pipes?

Explain how a tube might lsfp;p4su -byx)d:/ x be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An exlbf 4s) -xpx: /;yupdsample is a car muffler.)

Why are the frets on a guwi4b* fjrtz;1pp 9h2y,;h k onitar (Fig. 12–30) spaced closer together as you move up thj*2y4 , 9pz inofph1bwt;k;r he fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but n:,(brzwfy g5 cannot see it. When it emerges and you do see it, its sound is suddenly “brgbf5w ( ,nr:zyighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfe vg; 8.h7+vpm1dyhcq(. o u;v r;qimqmww 55nxrence in space,” whereas beats can be said to be due to “interference v d5 5h m.u;r hqwqmv.8yv;1c+om;7w xpg(qniin time.” Explain.

In Fig. 12–16, if the frequencu5+3 m qjtu3mku0((eawvdz 6h y of the speakers were lowered, would the points D and C (wh5+jaw(v h0 ukt( umzmq6e3d3uere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work i;ps5 h xe8l;xen areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new teelxh8se x;p 5;chnology, 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 sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought4bxec ,:oq2qmbl b .t+ 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 o2b q:bm ,4+tlc. xbeqthe two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move i0ht, nwi+a4zgn the same direction, with the same velocity? Explait 4+ zhnaig0,wn.

If a wind is blowing, will this alter the frequewros3gs9 8ghom0-k- w ncy of the sound heard by a person at rest with respect tog3- o w0o-shw8sgm rk9 the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positix,p+86ng( q qp *i/pe0yn7mxiu 3ovqf ons of a child in motion on a swing. A monitor is blowing a whist (m pqi7+fx3vo0/n g6*pnqx8upyq i e,le in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of hey pmg +bm;q4t1y8e33al vrul,r shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengtmtb+4 uy3y vla;glr183 pm,eqh of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echo k+r wq)a 3.y+scew)mo of the sound reflecra)cso yw.)qke3+m+ wted from the ocean floor directly 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 air at ;1 9vg; o4ubupmn:gj 7e ;pvpc20 $^{\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 drifting just above a school of tuna on a foggy day. Wipu n:6w sue mg-6:azt7thout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before tn t6u mwezg:6-u7psa: he backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff.8 ,cmjque:-:nexn: j35rz mku The splash it makes when striking the water below is heard 3.5 s later. How high is the cl5zn j-er:mex:8 , unu:q jkcm3iff?    m

  A person, with his ear to the ground, sees a huga3m,(olmkj 9-o 2rrc+ r 6anmte stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did tm arml 32r+,mr ktj(a -6cono9he impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by tj9y9jgngjnq-f9lr p:y 1 8fe /he “5-second rule” for estimating the distance from a lightning strike if the temperature is (a)q jgpn/9ejn8 rfj1gf9: yyl 9- 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at tf ji.mp d4r.)o99zuvphe pain level 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 sound whose intensity is b)1e bd0gfr tnr:s9 6f$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound 0 rdyk + 5axj-7x0zdmglevel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,+xgyjxda0kr-5 7z0md not dB’s.]    dB

  A person standing a ce4z8jc50lgi 7yu 3ztqpi bn3h3rtain distance from an airplane with four equally noisy jet engines is experiehi4g 3it570pbzzq yj83 nu3clncing a sound level bordering on pain, 120 dB. What sound 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 trajcmfvz ,xyy0235 .apc o(z3.aaaz 3o have 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 c5a3vz,a z3xacy3r2. j.0y(a pfma o zand the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ou4h0rm* l nzi-qxh0g3l tput of sound from a person speaking in normal conversation. Use Table 12–2. q0zh-m 4* nixlhrg 3l0Assume 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 whose area is 2ln pskgs1 -l*$5 \times10^{ -5} m^2$ (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 more mkg*q 7qsr )mrz/nb-* modest amplifier B is rated at 40 W. 7r /kn mb)*mr z*qsg-q(a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected 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 whenh7v6jj)cg; cmeto84w 3*:6dluwxy xa placed 2.8 m in front of a loudspeak hoja3c j my:4e c;wx7)v*866wudxgtler on the stage.
(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 typicns .arjgw13x q4vgirr8 2v,*u ally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section ajrwrv8gnx 1i*2v3u.4qrsg ,11–9.]$\approx$   

  If the amplitude of a sound wave is tofdu+.wi mb56;fpim bc vj60;ripled, (a) by what factor will the intensity in.+j6m0wvi d;u6cbom5f fpb; icrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqy fhkuwuc:o s)lb,65, ual displacement amplitudes, but one has twice the frequency of the other. What isysh5w cu6 bu,f :l,o)k the ratio of their intensities?   

  What would be the sound level (in dB) of a sounhkn1e8)ao.a iy)lej(d wave in air that corresponds to a displacement amplitude of vibrating air moleculehye8ko(l.ea) j)a1n is of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem 2l ib7d)ta8tyex 9pn;as loud as a 100-Hz tone that has a 50-yt dx 92a;87)ibp neltdB sound level? (See Fig. 12–6.)    dB

What are the lowest anp:xs7pta0exlk5svatio : 3z5h3tb , )d highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6p,tha ttp: b5zekx7 5x033slova ) is:.)

  Your auditory system can accommodate a hhd 8uggpcxz1y* 5veaqvfq6* p5*( ne1uge range of sound levels. What is the ratio of *aed x5*qvygz81p cg *eh5(pn1u 6f qvhighest to lowest intensity at
(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 frequenc3l)jbnne 5h7by of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Uneb7 )lbjhn5n 3der what tension must the string be placed?    N

  An organ pipe is 112 cm lo/x muti457)3cc mttcn7a nl ,vng. What are the fundamental and first three audible overtones if the 37tm,7 t4xc n) acu nvi/lct5mpipe 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 from bn;.akn)uxvey *yn+5w /e )xyz lowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clo5) ey;znn wavk)y/n x+.xu*y esed 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-tu465skv 67wbk lm0f3i4w nyvv ube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the iws0b lv7kvn4 4mkufwyv65 36lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fre7kaohu f* -e:i1c fn*:(psuvt quency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origiou:fi s*vah ft( :e-upk 17*ncnal length?   Hz

  An unfingered guitar string is 0.73 m long h 7vv:nzunz,36i d m/aand is tuned to play E above middle C (330 Hu d:vznhv i,na3m7 6z/z).
(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 that emits middle C (oviqt7 it40 9d262 Hz) when the tempeo0id7qt i9v4trature 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 at 2v(6;w5rb3vf( -loh g qdooj x.t.i0bm0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of;f:wx graltik07:fc 1. ds, dd the flute in Example 12–10 should the hole be that must be uncovered to play D above middx.sd:l;0rkwtf,1i ad: 7dcf g le C 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 pipe can resonate at 264 Hz, 4z 6q1o ec,k-gv40 Hz, and 616 Hz, but not at any othqz- og,ev61 cker frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 i9x+6(k0dzuvmod6gufsf d 4. lt*5cq m long is open at both ends. It resonates at two successive harmonics of frequencd.u4 6dq kfufvtls59g+* o(dx6 iz0mcies 275 Hz and 330 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 29 te.5g ylaqa$^{\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 present within the ev0iri4, t kq9w;pzab+9 -ns baudible range for a 2.14-m-long organ pipeir;w+vs4itq-b 9z9b0k a n,ep at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open 9ex1;y9t i -pt j fmwweh/1z9ato 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 camwx f/9 -jett a1iz 9hpe91w;ynal. What is the relationship of your 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 d1m/l;s a35i7 ubbipk every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far dab15/7us lb3i ;kipmoff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C -i4:lzw :m1k pvhqjrf 6j )/xp(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 operates at 23.5 kHz, while lz5h4y2m cilp 7h0e *fanother (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 occursl2h7hl4c f5emy0* pzi when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning forkvt 2.jn8nb5z8oyz5do r*r7 cx and 9 beats/s when sounded with a 355-Hz5nzojvob z2r t* 8y7r58xn.cd tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The;0oea-j8 mzczm4; m rq6.ttee tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq.t4 t8-jeqa0r;ezz 6mm.me oc; 11–13.]    Hz

  How many beats will be heard if two identical flutes e;z;sm hcxfa p cb063br k83;nn,k/ wzfach try to play middle C (262 Hz), but one is at 5.0°C an,mbrnwpcskahn 3fkf8 x;c0z /z63;;bd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequw k+3 4jr4txpgency of 441 Hz; when A and B are sounded together, a beat frequency of 3 g4 tr3xwjp4 k+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 together?$f_A$ =    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 frop:quclv *+ +b ipvjm7ne)62c sm one speaker and 3.50 m from thele v6ci+p*:2 +n s) mc7bvjpuq other.
(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. ,n qv;altaegdbj 7h20o4e /e, but a piano tuner hears th0g n, t q.e7lbdjhae4o/ev2;aree beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must 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 2.76 m in air. Howh i eox8 4:kd0rktet+g3 ijbte//x4 0g many beats per seitrxg g edi3t+e0xok4t j 0hk84:b/ /econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certag e3t46kcd5 a+ pfsu3ain fire engine’s siren is 1550 Hz when at rest. What frequency do you dst +e 33af4gp65 dkacuetect 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 frequency do you detectkk24mhr h anbg kfpp)idik7 9;m1*v23 if a fire engine whose siren emits at 1550 Hz moves d; *mbka79hhfk12v2 in)k 3primk4 g pat a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz 4epi; s,;i yd0)i krszsource is moving toward you at 15 m/s versus you moving toward it at 15 m/s idi4 i;s,) ; zeryk0psAre 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 oneo8fzi63td72rb .u l zi is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a bea7fii.zd 8b6out 2zr 3lt frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHm j.l /8id1ywrz and receives them returned from an object moving directly away from it at 25 m/s What is the rej.w1idm 8 lr/yceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5tshj v ;pca-e92m//6.msaqvn m/s As it flies, the bat emits an ultrasonic sound wave with frequencea v2 ph- 9a mcv/;6qtn/jmss.y 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppl8b 3 3dfb:ud,7 tmuaumer 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 sta8um ba du:dtu3 7bf3,mtion. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supposv3oj (d moqfdfx35s zvl6 e 9b-34tes2e the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken ojzlsov f4 d9m(32feqvd6xt5b 3e -s3to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usingg;0rso)4tj5 x uwx3)uzf ve0x ultrasonic waves 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 is 0f3:o qdnh hb c;t78ln12 m/s from the north, what frequency will o n :lcfo378b0hqh;dtnbservers 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 its speed at*xt z5j)ni,d i 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 2.3 where the speed of sound is 310 m/s ( w. wvm9qropcw6* m,r-a) What is the angle the shock wave makes with the direction of the airplane’s mq ww 96moprw-,*rv.cm otion?    $^{\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 atmospherssufzw5. ex-ha:,w-/j g.p;y ar3rp ne of a planet where the speed of sound is only about 3e-zw;g hus:wnr -y psp5a. jr/. ,axf35 m/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 strik) (mvbytkc;oi4 8 si.fg)tg99 ayl8 zdes the ocean. Determine the shock wave angle it p 84 vayt.zb9)lmiidtfko 9cs;)gy8 g (roduces
(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 3r dm;naoz 2rco+1i6z $/theta$ 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 exactly 1.5 km above t9s.d*bum r/iehe ground flying faster than the speed of sound. By the time you hear the sonic boom, the pla i.mseb rd*/9une 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 20,000-Hz sound efvru:jx9 j a).:lp-cpulses downward from the bottom of the boat, and then cuva)pje : :-xjr 9l.fdetects 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 arpl0 57403y uwuz9i+em trz;k bnnc hbj,lk(0ge there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manqs) jc5m0sjqja(dv(b,+oi /uy plastic pipes of various lengthu j5ia,)0c m sjs(qd( jb/qvo+s, which are open 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 9am*;xgx wj nph;- zj6tgkcj8)xs q*2a sound close to the threshold of human hearing (0 dB). What will 6 qn2)g*;k*xj ;jxw -89xsaj mtzg chpbe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82vk p3-x80pc ux-dB sound and an 87-dB sound are heard simultaneously?cv8 p0xp-u 3kx    dB

  The sound level 12.0 m fromw q7;cb i drm92z oc*h x)36hfqihc-:v a loudspeaker, placed in the open, is 105 dB. What is the acoustic pom co x fr q9bich3zi c7-:hvd6*;w2)qhwer output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 15dl5ui kbk9r9+lz nq380 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 19di5 l8 kru3nl +bq9zk5 kHz?    dB

  Workers around jet aircraft typup9/fu g+4y tk-gfkos* x h*z3ically wear protective devices over their ears. Assume that the sound 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 unprfoh-+k g3y kg*zp4uf* 9xsut/otected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thk72 jcuxl ml4bk /p5m /e6vc5se 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 tun)e-d/u3abthqds6(b.d v t:)f 6 d uurqed to 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 6 t.7tig: opuousvy20 is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per7tytv uugp2o 6o0. is: 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 above a vertical open tube filled0 * *)apnxaw8yqv3obc with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tubeoabx n0 3acp 8wv*yq*) above the water level is heard to resonate with 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 of 0fzfrr2nv : *tc; de7zmass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension shoulz2zftc rf7rvd : 0en*;d 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 r707cth 1y8d u.h y/qiusmjs b(esonate as 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-Hz range coming from two source m*l/ wb oyl)om57du+97csze ys. The sound is loudest at points equidistant from the two sources. To determine exactly what the freqme wmc*z7ol +uyl7/5bd y )9souency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whist hn0idb74+*3 f hiyyj ol+ 2-e4tktvrqles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frt+tf o24-30lkdq ji4n +ibervhyy *h7equency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you i(b xlmo*j +m6 jhf*u6(s vzbn2s 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the lxjno(b6j( z 6f*mv2bmu*h s+ train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed ow) k9*r2bq7c8 myxb gdf cars just by listening to the difference in pitch of the engine x7wcq)d k2 by*8rbmg9noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding wwxl; v .mtli0a0sk /*together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is theaim; / wwsxl t*0lk0.v other?    m

Two loudspeakers are at opposite ends of a (gj ura +(qe7lrailroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the s 7u+jlear(g(qpeakers 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 speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the gxyi. a 0e21s12ia azvaorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves wxz221eas1g y.vii a0a ere directed along the 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/el om2 mon 9ufp45c(lmna(1a speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat e mop9cu 2(/1m me(5fal4nnloamits a sound 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 a moth. Th;ydq sgfu 5ok5zu*:q; e pulses are approximately 70.0 ms apak; o5g:;u*dfuqz ys5qrt, and each is about 3.0 ms 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 signasmoq1gk( bzgw 3a/+p(ls from one 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, 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( gsqmo+3(gbpz1w k /a 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 st 01onfmrs3uq 9fu w) )tn./w9gpgjws .17wqczanding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m 0) ounqq) wg1 p1gz.s7fwcusjfwrm n/. wt993 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 alumin4t u) d,*g vfqvrnj g4llm03,oum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing soml lurov)3 ,jvfq4*0n4,d gt gund. 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 heariwrl.4o9sc a d3ng for the human ear at a frequency of aboc.394asodrwl ut 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 s/m8ijj xath6+ onic boom 1.5 min after the plane passes directly overhead. What is the plane’s + /mxai68 thjjaltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 pkb*q)qxx .)q$^{\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