What is the evidence that soo6bf; v ;o8cuvund travels as a wave?

What is the evidence that sound is a form of euk 4s:v1c/wwlmvy csa-3a)3 ;6jhtpdh0pq0 d nergy?

Children sometimes play with a homemade “telephone” by attac2/c5f p no1 j6piy4 liir6(wzuhing 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 4li6yco ui 6(j5/fpp n2izw1rother cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passesmr sx( 2r /)q1qyi+bxg from air into water, do you expect the frequency or wavelength ixsqmr2qr)1gy/b + (xto change?

What evidence can you give that the speed of s,:d* mgv n izek+f.64jsmrfq7ound in air does not depend significantly on fre g kn d.,+4s7fmrj *i6fqem:vzquency?

The voice of a person who has inhaledtdtek j.4(gm ;b p/nuyn 0j/lyl;t0+i helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pdb kegi o5,l t3 .xah.(9jxju9ipes?

Explain how a tube might be used as a filt(8idw5 pl0 x 0ql1prnmer to reduce the amplitude of sounds in va l5dp nwl8i1 00qprxm(rious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togh1 qgrwp3fl c d*8h9;8;owvpgether as you move up the fingerboard trvwc;w1hqhog 8d* 8pf9 gl;3poward the bridge?

A noisy truck approach7 w/4;youwhrx3xz pp2 es you from behind a building. Initially you hear it but cannot see it. When x24w roph;7z u/wx3 pyit emerges and you do see it, 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 said to be:jo/nltzgh;d x+f-t0 due to “interference in space,” whereas beats can be said to be due to “interference in timtjx0f/ h onzg;l+t:-d e.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulsrce x:9e7g f:d the points D and C (where d9csfre7: :eg xestructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work inwm-23d.hww * r9 uvzlk 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 a-mkwr*hz92d w.vlw 3uddition 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 thought8bj 8br4 s.rihyr,h7s 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 frequencies farther apart? Explai8h7r8hysjr. r bsi, b4n.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move )iu q(e11tk xc1qsc)f in the same direction, with the same velociccstkqu( 11 ) e1qfi)xty? Explain.

If a wind is blowing, will this al)( wqmmwsc/ gxn.4.o4 wgawa/ter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chaq4 (./m w4wow w/a)agsgmcn .xnged?

Figure 12–32 shows various positions of a child in motion on a swing. A monito/. nlczpe/ ro+/i+obir is blowing a whistle in front of the child .zboe c/+nr/ lpi/io+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 her shoutd6mwy.dt;s f 4 reflected by a cliff at the far end of the lake. She heam;df6s. 4wtdy rs 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. He hears the echn;xe3p r) .goyo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is e px. 3royg);nthe 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 8vyo58 0l4djtix yeu.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 drifting just above a school s;w*j ss(ro sb)v1y+b/-ld gsof tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is rsbyg/s1 );svd+jlsos* wb -(heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking svdo4 *zy/vs*q o6q 6rw ja/0hthe water below is heard 3.5 s later. How high is the cliff? w 0sohj*s oyq 4z*adv/6rv/6 q   m

  A person, with his ear to the ucc dg bmej s43:.fy,.ground, sees a huge 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 conc edj.yc fmb:c.3u4sg ,rete, 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 the “5-seco8b +xqi znqezwm*q.)1nd rule” for estimating the distance from ab8q .zzewmn+ 1x*)qiq lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a souot qe s(555ztp gls0:snd at the 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 levd0shh ;yf ,n4e 3awae.wnhc)os/1e a*el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simults- gd.ov ipx( 2h9bk/saneously at a certain place, what will be the sound level if on sdp/ v2i-gko9shx.b(ly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally n q 2(kb.ji15w:+hsep ohga/dioisy jet engines is experiencing aj5 s/1h+i(2.dw pk qbh :gaeoi 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 to hava xgq n5)voz(r( vws2jiw(- t6e a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of n5sgrx)a2( t(6ww-vio zv(q jintensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powez:jg /.lr deau1m am k0zu)s.a05yj ,kr output of sound from a person speaking in normal conversation. U:/s.0j.z)kk5az y ade1 aj mgl,mr0u use Table 12–2. Assume 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 seu3qnwh ./wr2csp48 an eardrum whose 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,: vf 50wsc)owjt70,xw fhn;u0 fs(tjr while the more 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 connected jf f w0x s,vw:u5rs0no;jw7)tf h0ct(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 metejni0h9x y3xl*z2 avh0g( f,tz r registered 130 dB when placed 2.8 m in front of a loudspeaker on the x0fh9ti jn v,gaz(h0ly *2xz 3stage.
(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 typ n:t k+0l9 iwaoaosz/6ically detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whos ntko 6z:0al/+aiw so9e levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor:)w-yiu t4okn,c5qbyco3 gum(+ykq ) will the intensity increase? Inc tkgq5ui (o)-yy)cmyo+k:cuqn,3 b4w rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitcy wxp (d)xh*ht7p1 t;udes, but one has twice the frequency of the other. What is the ratio of their intensit*ty)t;d7p c 1x(wxhhpies?   

  What would be the sound level (in dB) of a sound wave in air that corresponds c64s8 q;no bn ea8hef9v9bt9shyi-z( to a displac e8;(hfqho8any 9t-bis6be zs4nc9 v9 ement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound l7-v:x vjduj 3x*t9gh h f spoe4s1,ir)evel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–ho pf jirs3)9hj* xv,-v:x4uet g71ds6.)    dB

What are the lowest and highest frequekgfq+ 2m9 dsc; ;rcg)xncies that an ear can detect when the sound level is 30 dB? (Seegc qf g;)2dmcx9;s+k r Fig. 12–6.)

  Your auditory system can *wvgu/,lx zk+prpl ks;1frh. 6v+ lc;accommodate a huge range of sound levels. What is the ratio of highest ;hslvvk+zc rkwp*/;fxp 6l+ g1.,ur l 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 viov; t69 4s(vqymni.pd luaca2 xr7r4n+lin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of rplx c;9 67(i vm atvyu2.nsrd4na q4+0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What a+2 t3 5ohcgfolre the fundamental and first three audible overtones if the52 3fgchto ol+ 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 frequenc ob2jt;r01 wyz ;fn+juy would you expect from blowing across the top of an empty soda bj0o;;zr1 fyj+ t n2ubwottle that is 18 cm deep, if you assumed 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 the ran9mx-6ajs+9i* kbkd gq ge of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes6bk xqjia+k9sg*m d9- required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency om- l3b pgbqi0c9zcq49ncbn(2f 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lembqic324z c9gp 0( q9 -lnbbcnngth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E d51 sz.q*o+3huv l3bo bu,grz above middle C (330 lz h, 3oq o+b .zuu5v3bs1gd*rHz).
(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 organg,v l).pij7tv :6nwim39o bid pipe that emits middle C (262 Hz) when the temperature is )vi.nd p gw:ml3 7iob 6,9tivj21 $^{\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 20 b, s8f uqvac:z*un0mpmjz*5dfo g/0 ; $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute irnzl7 mm k-nu:h b7;,wf qgv9;n Example 12–10 should the hole be that must be uncovered to play D above mih9z , kbngq:lw77ur vn mf;-;mddle 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 pip 0;pl pth3cp1he can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sholh03h1 tp pp;cw 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 a9fhk+b b0*of-l ce6y m long is open at both ends. It resonates at two successive harmonics of frequeefyl*a 9bockf6bh-0 +ncies 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 0 3s0/l45fp hhy nwmmg8blcr1$^{\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 aredlj f)vg uu 0uv346,)iqkp, -lout5 io present within the audible range for a 2.14-m-long organ pipe aglup, )loj5i4 6tdv vf,o uk-uq03) uit 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 to the outside and 7un+pnxjts 20;k3sf i 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 your answer to thep 2tsk73ju+n 0;s infx information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat evh*xfl31 t ut;mtwc:f c67/gxl ery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. *gh 3tx6c/utmtf lwf7:; lc x1How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 a ws2a yov9 3cx 17,q:eww6gkbHz) 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 e * qxzzz+x/-ky6)qm:tzx q 0doperates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans wh-q6x zx z:q)/tzzmyd+ qex0k*en played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350o2p k- c6cr4yy-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain 4-yr62k ccypoyour reasoning.    Hz

  Two violin strings are f+s;e 0au qnt;ctaqf;0clg21a 91digtuned to the same frequency, 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 played together? [Hint: Recall Eq. 0caqfe+si20g c; t9n;tla1 gdu1q;af 11–13.]    Hz

  How many beats will be heard if two identicaoq3g-t8 cchfy/ fbixseg1lsj9*3kf * 5 r9xu 8l flutes each try to play middle C (262 Hfc9x k/s3*5oj*f -3ixu cyt8qgb9h8re 1 lf gsz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freqod5cy 3aas a*gpl.8w:uency 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.pcw*l 8o.:da3 gs aa5y 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.4ixrliwh,9)39m/7u wex cry f A person stands 3.00 m from one speaker and 3.50 m from the other. 9wfm9w 47xi)xlr e /r3 hciyu,
(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 41 lb8iu5,a,b9zz/c sb dtlta132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one ictd u1 i 4b8blt,,5zz 9sabal/s 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. How many pdt v ikh)7(5o3efsv*fl, tg .beats per second will be heard?5v(p i 7)3e, l t*shgvd.fotfk (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqxa a+vzn f21m4/suu*auency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you de/aa*1aunsxz m2fv4u + tect 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 d)94 b /aapxdo ei*tt6ao you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32eat9) t6 pidoa4ba /x* m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towarn;sqoob 4)*p c wbr+j7+nvb o*d you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they clbo;so+n*qv +bc)w7 j4b*n ro pose? $f'_{source\,movine}$    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 sin x npk9c1up*nat 0s81 u-coh1kgle frequency horn. When one is at 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. What is the frequency the horns emi1 1an8k c- to*p1spn9 ku0cuxht? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out -kpq zi(6t u,kultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sou,k(quikz-pt6 nd frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at azrh+q63p2axb 8u1ngwt , vje9 speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does theuh p6e wgrzbt2 9q38 n,a1jxv+ bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plim*;ay .y ixjj,j55t rayed on a moving flat train car at a frequency of 75 Hz, and a second identical tti yri*j;,aj5 xm5 jy.uba played the same tone while at rest in the railway station. 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 t 8t molhbq h+:3vryw.9o measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be :vmy t rwlh. 398oh+qb1540 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 using ultrasonic waves of frequencyhd 2*7pmo :t;;+rcsfc r u:bau $2.25 \times10^{ 6}$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 o(1mgmr on7st0fot b9+/o5 i 9g6sdarnf frequency 570 Hz. When the wind velocity is 12 m/s from the north, wha9 r it0t159odbsos+ggor f(mn /6nm7at 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 its s iwot1m yc822r5g7k74xjdpkp peed 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 2.3 where the j m;1n/e);nhynjrulm0 h*,w v speed of sound is 310 m/s (a) What is the angle the shock wave makes with tuj m 1ne;*,lh) nny/ mrwh0jv;he direction 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 o mtt u:zhd52c*e6 gh9speed of sound is only a*6m5 cgzuoh9t: et hd2bout 35 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 u*md ;h*;5ov,r3ky4z ipgeco strikes the ocean. Determine the shock wave angle iei m,h;d p;g43cyuor**zk v5 ot produces
(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 orld q27++ojr$/theta$ 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 the mx.xt-jkk ;aw n4 s5gy1tj :vg/:* cmiground flying faster than the speed of soa1j:*;sy4kgc i -v5jtmg /mxktwn.:xund. 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 20,000-Hz sound pulses downwar es9/r2uegg(r d from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what i9 rg/(sr2e egus the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are .oopkksd 9 a3:v3 - jvhartv6wpz+ .z8there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe s)7d+*vf)g/(yy* repbirvn zh ymphony. It consists of many plastic pipes of various lengths, wh7e() i*h bp*f/ygz r nr+v)ydvich 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 flkj6s9h+t g9curzzh 9tw 34sz20mwn 9rom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound 4uh 9j kgw 9c+tmz2lhz3z6 sw9r9t 0snlevel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an klw)jj yh7 w)9ja *qo287-dB sound are heard si w92j qwok ))7jlh*yajmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, pnvj4 -njt rz-1laced in the open, is 105 dB. What is the acoustic power nt1z-4n rj jv-output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops1bkn :1tcw vy 7qhnz2( g)inq5rr9p.x by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? cr 9p5(2t1 nr)7hy gvik.qb n1xnzwq:   dB

  Workers around jet aircraft typically w6 ,fiovy+ rogar56 lt*ear 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 unprotected ear at a distance of 30 m frtvoog66 5i,ar r +*yflom a jet airplane engine?    W

  In audio and communic tvp44q4..s ib.7fauwobxo3r 2nt (h mations 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 6dugszd7ainn7 ;xz9(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 is 32 cm long between fixe/kdly2f5 yqzsk/ ts-+ix1 te,d points with a fundamental frequency of 440 Hz and a t ids2 ky+-y5 tl, fsk1qezx//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 inb*fph4g o +6w+pfje k/to vibration above 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 with the tuning fork when the distance from the tube opening to the water level is 0fw6 *pj++fho/eg kb 4p.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one eni1g wah15, coti) p9pbd and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fwbc1 p h)agt, oi91i5pundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed o d he;;rqr4oja3jh/ w/ zc au64,ty5hto resonate 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 iyi2p 5 sa+o0m/9r*cklzrww a3n the 500–1000-Hz 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 0.34 m farther from one source than the other. What is the frequenca9/r ao5c+w pmsz32w yri*lk0y of the sound?   Hz

  Two trains emit 424-Hz whifkacuftner1jo0 fy86)j p4,5-i* n w hstles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency whj prtf1youf6 fwci4k*n,aj)0n58- h e en the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whi x.jcqkz+z*u4hk*e:;bj (j8ddo t8wustle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movingxu*zkk(jdoj8eb8q: wz+.h;dc *4 jut (assume constant velocity)?    m/s

  At a race track, you can estimate the speedag-wc7v(yjf; zli34bar/uh0 of cars just 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 full octave (frequency halved) as it goes by on the straightaway. How fast bg a7 ( juz -;43flyrhavwi/0cis it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. l jy4f3.ta2 g*/ux/bcu n49do tra-my The s/ojatbt du/rmf agn9u2l3x -y4c .y4*horter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroafk is:x74i)t)wsa 76mrw de- hd car as it moves past 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, :kwiash7 mt)6 d )e7xsfirw4- 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 aorta is norm4p ho1m2zum22jgs1 sially about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wavesz shomm p2ijs2g4 12u1 were 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 sp kdsx -8x6(zbe91ogz feyw4b-eed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected 8x 4 z6wseo(gk-9f1-eydxz bbby the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high fr .59 yh0cn7 pe*+l bicqs1azxpequency sound pulses as it approaches a moth. The puls5icc.peqyh*xna1 l+ 7pzsb 09es are approximately 70.0 ms apart, 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. 12jh.3c wv)oi7l 0 boq4q–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensihcjqi. 73qow o4v)lb 0ty 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 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 comp vp v1*y-liwxfl0rn.9romised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of they9r f pi*0v 1wn-.lxlv pressure nodes. 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, slende/02jiv46 o brthjh u6kr aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practi2vbrh64otj hku6/ji 0ce, 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 hearingl zxph tom* -zg5a0gq:f0l75j for the human ear at a frequency of about 1 f0opa l- z75x*gg ztql:j05hm000 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 c v-rfh5*n6r yhears the sonic boom 15vrr6 fyc-h*n.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbb4e y,r09b, ykla-sl v4rjcl0xx 0c :x*psr-zoat is 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