What is the evidence that sound travels as a wave?; bkacme z4,c7

What is the evidence that soubar3f zn( m-g9d d4b+wwj l:q-nd is a form of energy?

Children sometimes play with a homemade “t itrj/ )r50bu.uylw-dos-:h p elephone” 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 from one 0yudj- wbr /h.:)5l rsuitpo-cup to the other.

When a sound wave passes from air into water, do you expect the frequenqnmvd9-g)g cvrbx xu,7f05x 2cy or wavelength to changnr27 xu-5v,qbdxmvggf)0 9x c e?

What evidence can you give that the speed of sound in air dkuutn)s; bm m+kae+cw9h zu8l k/7/ 7koes not depend significu/;9+ek87ub kwc/7tknu)km+ alhzmsantly on frequency?

The voice of a person who has inhaled helium s:ff4 7x c8fqbeh21xin ounds very high-pitched. Why?

How will the air temperature i9ojd bn7 )r-bx57(3gy vhdtiw uxr+,jn a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ampws .ii6 4kejjru1meg9 / qv,g*c6yca8 litude of sounds in various frequen8c e9s6,i 6gym.cau/4 vjqg 1 *wjkreicy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mfx k0q s* cd-8gv ndlfl230jf(ove up the fingeq kd (lsfx0g lfn2d3 -j0vf8*crboard toward the bridge?

A noisy truck approaches you from behind a building. Initdey)v qt0q f+6ially you hear it but cannot see it. When it emerges and you do see it, its sound qe yt60d+)fvq 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 due to “interference in space,” whereas beat. cb b;cucq/zgzq h2s1 wbld(fw;+a(-s cabzacl b(f;s- 2chguqd q1/.;bw c(w+ zn be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the freqa7u-t5ekcrgu 2,2rb2epq/ cw uency of the speakers were lowered, would the points D and C (where destructive and constructive interf- 2euac 7rkep,c2rq52tbg u/ werence occur) move farther apart or closer together?

Traditional methods ofrxby:x3: 5t fd protecting the hearing of people who work in areas with very high noise levels have consisted mainlbf35 x:xyt: dry 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 sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be dez :xt x4v c j(() ws8zi+1l+lcaqf;pthought 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 frdec(sq14llw:)p zt iaxx8++jf (;cvz equencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction, (i,sxq j/wxbzf2yeecu k.ky08 55 -pkwith the same velocitz(-yqi k s82x,/x 5f. bukewckejy0p5y? Explain.

If a wind is blowing, will this alter (v67- 4 )qhr kohne1idb,fuiu the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chan)f1ri oi,eh7vk4 6bhn(u d uq-ged?

Figure 12–32 shows various v.y.fv59n4 (w, 3 ;wikkng.hbwo jpfu positions of a child in motion on a swing. A monitor is blowing a whistle ink3p f yokv 5ni. ;f4 w9wh.(,uvgwjb.n 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 (zg1avikn va.8)gqhn3 5u cq,of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoutknn8c,v)a5q. iv hq31gz ( aguing. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship -3uio9(98hmhls vug fjust below the waterline. He hears the echo of the sound reflected from the ocean floor directly bemh9v(93sfg-uo i 8 uhllow 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 aimh k;/*gys )njr 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 drifting just above a school of tunp rpseu787, yfh5y--dd+3bd cxkwal6a on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses- fea -cxb,+lw 8p7d3yy6hkdu s7drp5 before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. 9 qzr(z0e6vyda7 bhy1yb;, xhThe splash it makes when striking the water below is heard 3.5 s later. How v d bb,7qy ey6 0(ahzrz;x1hy9high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete o-hs+j/f s,ra pavement. A moment later two sounds are heard from the ima+f/osrhs ,j -pact: one travels in the air 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 s9o78 da 4*dn nock2krmile of distance by the “5-second rule” for estimating the dist74 o dk*cns8k2a9ndroance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensittyn42lv28-nsh qn.m2b fq t s(y of a sound 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 level of aaq)t)ku7q3b 28xqk*,v dwtzc sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a:h he+7k- xnoo sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one oxeh+7kn o-:his exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain di3auxe:(1:9 b8 c7kn tgujxr j ;aymdj3 qgu)f:stance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this perso;cu3u:d rtq y g89 jnxjaf:agjb)k3(xeu1 7m: n experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-trhzckyny8su2 5+ 1v.qw( *mcko-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the si z *h2yr kmqvsuyn8cwck1+( .5gnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal clp kb/n* o4p i))ghq2eonversation. Use Table 12–2. Assume the sooqk)g/*e 4 p2 ilphbn)und 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 st g1q5qy88ta.d9bj*rxq/wd h grikes 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, while the more modest amplifie63d:-*mvfcb p n0zv,h(booslr B is rated at 40 W. (a) Estol0m(3v os*n-hz vcb,b6: dfpimate 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 when placed 2.8 m iq0 up:u 4n:w2fa ej2)* rqroirn front of a loudspeaker on the stage.:w2:2p)ia0eq*4 fjrr o qurun
(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 differe8y( yp* 6okopqc:l;at nce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose lev(c optlp yaq 6k*y8;o:els differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,x5 vc6 qe4qvqo+ jy5/a (a) by what factor will the intensity increase? Increase by q4 c5vy5ovqaejx+/ 6 qa factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hassl45y kiq vl,8 twice the frequency of l 4svy8ki5 ,qlthe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of h:p;mmq: f67m q(lsdut22pisa sound wave in air that corresponds to a displacement amplitude of vibratinmlf:2qmqt sp7: ;6pm2(ui ds hg air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lev pjg/5ysxgsi)jdr2( 4k;b/olel to seem as loud as a 100-Hz tone that has a )jryp;s/jd4xgg5 ik l b/2(so50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whe0dv:b rxvo) t8r97bv6ccl4 ts bb4tc5n the sound level ist bdtvclrx5b98 )v0 rb c7c44vs6:b to 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound leyt iwpv4h25xv-(8 f sxvels. What is the ratio of hi(tshp4v52xwyv-f 8xi ghest 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)c/+xooxo e 4q a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the 4 +e oxxqoc)/ostring be placed?    N

  An organ pipe is 112 cm ln1gm/oefp1 9rong. What are the fundamental and first three audible overtones 1gfe1pnrmo9 / if 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 from blowin ;y ,xivc xoo3g31+ yt1s:/ghm7k1 (qzfdmiwdg across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed hdm;w37gf/ s1q g,i+zdy( 1 ioxtm:vkxo3yc1tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pd0z9ky2 y:4p r ckk8ekipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ranye2:9k8krp 4zdk0cky ge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fke*i 8pee3 a.ktnb1pd9u:u 1zrequency of 540 Hz as its third harmonic. What will be iu8 kezi3 aeb*:91k n.eupt dp1ts fundamental frequency 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 tuned ,ocmy.zvoi 80 to play E above middle C (330 Hz)z0o8yc i,. ovm.
(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 h734z+,d80ew;xlyf h vpi f4 ;mfdeo nmiddle C (262 Hz) when the temperature ieo f nxz;3fhvy l0i4dw8+,mfdp;h47es 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 2i6+gz mwey2n*6dqs7mvz p2:c 0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiep0lmni+ 43wjb k.tpt :ce of the flute in Example 12–10 should the hole be that must be uncovered to play D aknjpwibp0tlt:m. +43bove middle 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, 44x 4fzvi,2 ab(x4rj-pn0 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is jz4,f(x -b 42 pxivnraan 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 m long is open at both ends. It resonates at cfe6pq,0 ,tdz: qkgi, two successive harmonics of frequencies 275 Hz and 330 Hz. What is g0qqcpf t:k, d6 i,,ez
(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 8j du. ;:ynizr$^{\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 prese5 b4 wuw)0ipwwnt within the audible range for a 2.14-m-long organ pipe at 20bwww )i5u4w0p $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5dflqvw*+;nuuag98oo q - -p i8 cm long. It is open to the outside and is closed at a-qw ulio9;n8f+pv-u q* gd8othe 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 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 2.0 s when trying to adjust tw,2xvx- p1d/oj nz ja/wo strings, one of whichja//n1o2 w,xz- pjd xv is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency i .v+ mlwz.f1pif middle 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 operate p35xzv0n( lgas 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 theyn 5l 3zavgx(p0 are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350: dbh fqz,b+ jv+xus-4-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain yh j zq:+ 4-bx,udbvsf+our reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tua(.-c,v6e(dvrey axw9k 1 c xension in one string is then decreased by 2.0%. What will be the beat xxu1aw6ec cd vy .-(va,9rek(frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try0f g,7kxl;f e1xegg j6 to play middle C (262 Hz), but o le0k 1jgg, gfxxf7e;6ne 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 freq,s(jm j9oaa 1nuency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B m1 a(n,asj9jo 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 from one speaker ah*c p* q/ qdp7wdl2j01 1u cutpw0yp6ind 3.520*ww y71i0 dcp lcpu/ d6pq *1ujpqth0 m from the 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, but a pianoi bi:g2ia8lj : tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be :a8 g2ijb ii:lthe 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 2.7651q9qlp-ee5w)ejl;i;e t d lj m in air. How many beats per second will pw;);ejj li1ee95e-ld lq5tq be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engoyyt(6z)m 8iiir) w :ucgr,(hr)r4diine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 w )i8(r) ),yugzyr ih4 dtrcm(oii: 6rm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fgw2n0 tz 1dau4l6zq)c ac3j2qrequency do you detect if a fire engine whose siren emits at 1550 Hz move2z62nwqc1tqc g4uj z al 0)3das at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequen..*pmuilq/-ku ueft,r)m0y* ikav4 jcy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencmm. /)qy4lkeikvuat,purf *0-.u j *i ies 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 horyt0 slt f)ln*fqzjq h9o57 ,k1n. When one is at rest and the other is moving toward the firs,)fljtztf*s0k ql7n hy1o 59qt at 15 m/s the driver at rest hears a beat 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 kHz and receives theay,vzv1 5x;zy(ctcwac /6m3wec l 81im returned from an object moving directly aw36m1/ez vwcl1,;5wt8 a iv( czccya xyay from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s )/svheyh bw,jy18jz,As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the rej h,b )e8z,y/ws j1hvyflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mb-v5d-q v ikl0oving flat train car at a frequency of 75 Hz, and a second identical tubav-iv-5q ldbk 0 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(6-4knyjcvn vo measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed vnnvj6 y(4c-k of sound in human tissue is taken to 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 using ult +wpjkhnzv x6 -tuvop-7l (//qrasonic 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 windnqf/ oqx4o8l v58 gv:s r0ggi0 velocity is 12 m/s from the north, what frequency will observers hear who are located, at rxion:g ls4 vfoqq8 r/v85g00 gest,
(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 bz( x ;+llqcj+on land if its 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 2.3 where the speed of sound is 310 m/s (a) What istco 4 8o3adk)drqds0t: hh31m(unz,e the angle the sh, 0n :4hsqa3zo tk r)h1 edtuodc8(d3mock wave makes with the 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 speed qew,6h: vi q1bof sound is only abouqq,ve6:whbi 1t 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 strikes the oceatv-1qv*/ vy ok6fb1y7 bypc.l n. Determine the shock wave angleo.b7bvt/yfl 1-6 ypvcq y*1k v it 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 gqqq e py,a9e,sdq570g a1 4ii$/theta$ 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 kmn q:8jtm ng6q ff4j37x above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the p6j34n tfj:mnq8 xf7g qlane 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 20i, uuodcg) 0 xfk8n xm do91fkm7vb90.,000-Hz sound pulses downward 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 is the minimum time between pulses (in frekd f7k nouuv0m), 99gm ix8.1c f0dbxosh water)?    s

  Approximately how many octay/1j tne :ju2dves are 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 co *tl +3tyknbmy )rf()unsists of many plastic pipes of various lengths, wh(mrkf)y lb u* +)ttn3yich 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 a sound close to the threh9xjkdpzz543;( t-fjj.d n nkshold of human hearing (0 dB). What will be the sound level oj jp3k-.d(fj z5tdxzn;k4 9hnf 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 879vvsv)ss5q .s-dB sound are heard simultaneously? v5qssvvs9 .s)   dB

  The sound level 12.0 m from a loudsz(48z nn f8ti(+ dvfcspeaker, placed in the open, is 105 dB. What is the acoustic poweri f+88cvfdszz((n4nt output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 100 dd4buuf ic0g) 67lv-w0 Hz. The power output drops by 10 dB at 15 kHz. What is the powe7d6 -fdi) ucvu40 lwgbr output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over pcoq g6)y6 0rxtheir ears. Assume that the sound level of a x6y)g6c0pq ro 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 communications systems, the gain, ag 9mwdt6.66 k4wlyrfgt a.nq 90;hts$\beta$ 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 to 99/tgok v2u8awgfjc4 u0+ yqka 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)tuhbh h-i(0 b between fixed points with a fundamental frequency of 440 Hz and a mass per unit length oh )(u ihh0bbt-f $6.1 \times10^{-4 }$ 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 tubokk9nzqzyl p;lsyyxw-4t) 3z e( -n/+ e filled with water (Fig. 12–35). The water level is allowed to d+4s yzn-k3)neztpq kyl9l (-/y;wzx orop 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 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 mass 2.10 g is near a tube thatov-)np8 6 yq 6he/)ykj bvhrk9 is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in i6jye8)r q/y hv6 bnhv-op9 kk)ts fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop x0k ac k,ja17/ t*q tb+jr5tjc($\frac{1}{2}\lambda$) 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 to7h e 7-;. lbtxzekzht3ne in 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 ltlhze e7ht37kb .-x; zevel 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 whistles. One train is stationalhka,1d0y zk (a y qcw(;/c amjc0n13fry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Wnjckq ;wa(/h ,1zf 1k3myl daca0y(0chat is the speed of the moving train?   m/s

  The frequency of a steamrabxau2 q ry ;mp0-4:j(o7ljx train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant vx uja( 0:mrxb2;7l-y qa4j oprelocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the d5wu2go*dl k x g4ixh/2ifference in pitch of the engine noise between apgdu/ w5g*hx4ik x2l2oproaching 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, sodhizp63r 0r(lq ,lp3aunding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the o6ld ,raz3i qr (hl3p0pther?    m

Two loudspeakers are at opposite ends ofb9gagoq3y b 95 a railroad 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, wb5 agyb3 9ogq9hat 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 aorta is normally about- ui8i z 5hyt/00hsq 1myemvr)a4-pqx 0.32 m/s what beat frequency would you exph ti0q/1mq50r-a s4ih -pyeymvx z )8uect if 5.50-MHz ultrasound waves 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 speed o6khv tzv /3kh 8*tqj06.5 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 fre8/zk0 v3jhhqko t 6vt*quency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of hwspv))ac) c ro /.fjl)igh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be df arw)j)vsp olc/.) c)etected 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 Aw im(;ty8j3g dlpine 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 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 g d3y(i8mwjt;open tube.

  Room acoustics for stereo ltrz8.niyj 3 (bistening can be compromised by the presence of standing 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 2.8t.jz8r3 nyb (i 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 alumiqdvfcnlv h0 cdx-05wh*o268r num 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 emitrdwhfc v0 onh0c-x2 d6qvl*85 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 hum,dx527vzjbg p an ear at a frequency of about 1000 H, bd gv52xz7pjz 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 trnkfc2c;8;m v he sonic boom 1.5 min after the plane passes directly overhead. What is2r;vcm;knf 8c the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ivs6egp tu2x7aqgci a(76s hl f u(/j70s 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