What is the evidence da1vm9q 7n v d9j0zdh5that sound travels as a wave?

What is the evidence that sound is a fr4ku: hxn3( ( ozeitb+orm of energy?

Children sometimes play with a homemade “telephone” by ae6g.p0wd rfj 5ttaching a string to the bjpfr 05edg .w6ottoms 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 cup to the other.

When a sound wave passes zjvyx*f.nc75u0 xe l*from air into water, do you expect the frequency or wavelength t uxlen .v057yf*cz*j xo change?

What evidence can you give ;kpfn z5 gkbd9juz7v/,hd6-if9(quh that the speed of sound in air does not depend significav7g;uhb6fi /f ,(z5zh 9dkuk9n- qjdp ntly on frequency?

The voice of a person who has inhal v lox :+)hzwfh*c.x9aed helium sounds very high-pitched. Why?

How will the air temperatu/0sg.wq jb(xk -+sh q/epaah/b oev/ 0re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitumm-axw4mf26 qb89rcj h tq:r0de of sounds in bqt4a x2qcjf hm:6 8-0mwr9mrvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fahixpy*g.o60 q0 z4 swig. 12–30) spaced closer together as you move up the fingerboardsw0*4hyg qap6z0 x .oi toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but jgmf+qs8-vh. akrg40 cannot see it. When it 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 qs0r gfv8m+-4k haj .gon diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatsx jp xvyq 82x6bf:y/2l can be said/vy:fj b628p xqlx 2xy to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the po mr*,r;),hcwkxfmi 8dints D and C (wherec)dwh,rrm x k;*m,8if destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of p jj/riq8r) 7jrrsv2wbmt)f .5rotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, h.r5wvmj)r/sj f itjq 7rr) 82beadphones 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;thsvio6 y/ *;fx7.pwla-nwso2cg u6 wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Exp *2ohw g yt7oxv;p/n-6cwf; au.lss6 ilain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the20o saj e(jfhx+ggk/, same direction, with the saxse,(g 0kf/joj g +2hame velocity? Explain.

If a wind is blowing, will this alter t;thz fd* u+ gzt9-smk;he frequency of the sound heard by a persotm u-fz+khd;s ;g9z* tn at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a 9h* qoz8)s3mceyqia 5 swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the chc q8)yh* 3s9 zqio5aemild 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 shoutyfl.qp5psa -q w to(+5 reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the5+pq t. -lp(oyawqs5 f lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below 7q i8ee63quxycq800efas mn4the waterline. He hears the echo of the sound reflected 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 signif4y0xequa30 qs fmee 768i q8ncicantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atqy/a 4or7kl(/3kt.j zcgkdx* 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 isp zl kif.080)n5o u-1tzfsdim drifting just above a school of tuna on a foggy day. Without warning,oflf 0kz. s )imiut0 d81-z5pn an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikinlh hy-,mso h*xd/l/-z (1 pmdbg the water below is heard 3.5 s later. How high is the *lxm / h-lz mohddp,/b1h-(y scliff?    m

  A person, with his e*jqm/ /g azj0jar to the ground, sees a huge stone strike the concrete pavement. A momentjzj/g/j q *am0 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 the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one7)9wqyo yd . kf:zfv/hu+,2wd z-lisj mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temped)9l:,f vkzq+ ozujfhs-dy/2yww 7i . rature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensit/dq mcv7-( tkyy 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 a so64 0h asuvvhf5und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d0+qxao:)e9noqy az4 (lk3tv2zg+j y jB when fired simultaneously at a certain place, what will be the soujtna9z02vel(3:4ax+o zgjy o+ q q ky)nd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally n7xsd gm,p vk z/n:jn.:oisy jet engines is experiencing a sound level bordering on pain, 12np nzj, vmk: 7dgxs.:/0 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,rh0 pm6 3psyp said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Whapr6pm03sp y,h t is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output( cz+nqjeci65o3 (pk)b 6qek -h (hvyz of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformlye )nzc +hkiv -jo(3p (bc(qy5k6eq h6z 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 arxnd6e8yx(lrd; l1rs rpy19 b 1ea 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 z izhk bazb*8e*i1w;f/hqk6) 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 connectedbf zz1bh;*8kqi a e kw/)ihz6* 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 whi ) 1fpw-ims8len placed 2.8 m in front of a loudspeaker on the st 1mi-wfsip)l8age.
(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 de,co* pfle7*g sma, ,z(jk;qj obt9co 3tect a difference in sound level of 2.0 dB. What is the ratio of pacofq,zj og le bj* ;3s9,(m*7,oktc the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wvgds. 9 ql x,43.xqn ejaix+m:ave is tripled, (a) by what factor will the intensity increase? Increase by .x a :m4q9jex.g3l vnsqx +d,ia factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twi,i:gqrv4zkti( q88l jce the frequency of the other. What is the ratio,vrl(k4qjiiq : gt8z 8 of their intensities?   

  What would be the sound level (in dB) of a sound wave rsr:sketg-; d)v*b8 z3g-faz in air that corresponds to a displacement amplitude of r*e8t) : zkv-rsg g3abzsfd;-vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thg0;ib -j5vtr zat has i;trjvz -bg 50a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear caov 5ap5x+xrm, vy1gn 4n detect when the sound level is 30 dB? (See Fig. 12–xv4 +nrpm5 x av5g1oy,6.)

  Your auditory system can accommodate a huge range of sound lavfme2xpgiwte1p,nji+y*/f56 -+ mlevels. What is the ratio of highest to lowest intensity axi plvew1me2n6+f-, p/ 5tgj i mfy*+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 fundamenta)l7w fd ur :e7. xyy(,wxug4ssu3vwv6l frequency of 440 Hz. The length of the vibr6,7vs7r3.fvxeys( gw l w)w4uxd:yuuating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whaox(c4*qi -6, lznqukbyu0 hv0t are the fundamental and first three audible overtones if the pipe-uo lz ynqcx6,kvq bui(400h* 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 wohwg 2 w+ )40izag5q xhlbuz7z8uld you expect from blowing across the top of an empty soda bottle that is 18 cm dz 5g48z7 qwwa h0+uhi)xz2 lbgeep, 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-tuboc op730 ol*lio-p vf1e pipes spanning the range of human hearing (20 Hz to 20 kHz),op-ofovi*l 3p0loc17 what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequen6e633c xrj:mrxcqz y:cy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of iqx:x6c zjrc6y :rm3e3 ts original length?   Hz

  An unfingered guitar string is 0.73 m long 5x6ql.4erloy8gg*v*k+ bucg and is tuned to play E above middle C (330 c+kb5 o48rgqxg6.l**vgul eyHz).
(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 lengtcbmhqqb/ hw3ne4-:/+j1t*wu txg (ww h of an open organ pipe that emits middle C (262 Hz) when the tw/(c+qh/bet-h:n4 tb*3 g umq wj 1wwxemperature 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 at5 zzhe5 f+ta*c 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thee t2e m*wj28rb flute in Example 12–10 should the hole be that must bew8bmre2 *e2 jt uncovered to play D above 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, 440 Hz, and 616 Hz, bz uyd;8q lt. jba79xszv.)3 jfut not at any other frequencies in between. (a) Show why this is an open or a closed pipasz7zfu q3jby l); t9..x dvj8e. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1ljkmew ;02i owva) 4.p.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. ;i ko.pwam4w 0)2 jvleWhat 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 9ob* u37lgq af1xsgmy* ljz4($^{\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 audible range for a 2.14-m-long orgxgm2p8 9vs:b b pfe4w;iv 2qt9an pipe s8pigt2;9q4xvp b b:m2 f9evw 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 to the outsij.,9e-um p*t 7wr-vs;f fwh wrde and is closed at the other end by the eardrum. Estimate the frvt9-rjrfh;*wsf pu ewm.w ,7 -equencies (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 twole*8 w a+zwq+lg,9 www strings, one of whiww 9we+ ,z wla8qgl+w*ch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (c()4f.ha9.d5 wzuy )j /6oy jzy ljy2wk7duj z262 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 23.76dlc 6hfan 9+ 8yu0(vvwhxxg 5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, esw adx6 +vc9n0876h(hlxgvf uytimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s 6 nlb:zfvr+37 , eaylgwhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuni:zfrve6a 7,+n3y bllgng 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 te3d zyz 8m /wdok,ztk;3nsion in one string is then decreased by 2.0%. What will be tk3d,z8m/d3 z ;zwoky the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicae/f h-u,x,i4e/;)zojwcwxnu l flutes each try to play middle C (262 Hz), buthe u 4;wu)i/w/nzxx,o e, -fcj one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, ee..nz t:nm 94gzjc/fB, and C. Fork B has a frequency of 441 Hz; when A and B .9 gzm:en4tce j. z/nfare sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded 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 foplkt ,-b l)+brom one speaker and 3.5l,ot-b) l+bkp 0 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 piac c qp9: of)-;vqcrw.nno tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating awn)qf occr 9;. -c:vpqt 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 wavelengthsb* ao .7x7otyf 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 7 aty fo7.box*$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain276bivehio. y fire engine’s siren is 1550 Hz when at rest. Whati yohe.2 67vbi frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency qujy mlmk.a3; ix 4vw jwd+3)k6 l-9hado you detect if a fire engine whose siren4.l+m 6d) k3h9w-wj3lvaxyamu iqk ;j emits at 1550 Hz moves at 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 source is maxw6lc4 2+ i.cxv bz8toving toward you at 15 m/s versus you w + 6t4ixcxvzlab2c8.moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped wi1nu l8t2sg r4+q7 ytytth the same single 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 otu yqrtg+18nt4s7y 2l f 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 receiv -k ofkdutww3c56u 4v8es them returned from an object moving directly away from it at 25 m/s What is the rew-8tkf5uw36 cvo4kdu ceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall atwsdnh- q3d,x , a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear-xwn, hd3s dq, in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wkb q-18 vkjwrh rik;p 2enj37,as played on a moving flat train car at a frequency of 75 Hz, and a second identr2pn khq -i ke;j,w81bk7r3vjical tuba 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 to measure blood-flow speeds. Supppr9)sq, xlrkhi7(146 t q pkfxsjr++cose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is xpr sks+rt6il j +c7q, 4f)9xkpr q(h1flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freqp gn0d2m0ah3osv7 g 4kuency $2.25 \times10^{ 6}$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 p1bgjdl:e .p(1vf 8oaf frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are locatel.va :pge( 1 f8bpod1jd, 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 +h pvlm0abf5320 $^{\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 wl:a ix-:ge n j;7yx8adhere the speed of sound is 310 m/s (a) What is the angle theg; x8 i7andj:xl :ea-y shock 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 whms z0awflh:6p83i8zq ere the speed of sound is ohs zmi836:w 8 0fzqlapnly about 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 traveling0xn 0 wm787xrj or+h)ylsm1*hl 3vnao 8500 m/s strikes the ocean. Determine the shock wave angle it prolv x*s007l3njwxranm oh+y 18 o7hm)r duces
(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 iee z,.ic/ *zb$/theta$ 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 agrxcehg. c;/q 9 xnqjt *;ov+(bove the ground flying faster than the speed of sound. By the time you hea ; /+gt*xg evj.cn9qoqrhx(; cr 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 w-r):8 gsu* ug-/nakqvtitt ,sound pulses downward from the bottom of the boat, and then detects echoes. If t-8,gqu*wk/trs:gun a-) ti tvhe 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 are there iliw c0;1qmu zmj: 3.2lan eer6z28hsn n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cauf,9i+.. vxc-m 2mar7oqbix d lled a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are opeofc, aviim. m-9xxr 7.b q+2udn 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 q3350u faun e sl)(,oaowg4ola person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level ogqo3)anu5w o3o su4lfa ,el(0 f 1000 such mosquitoes?    dB

  What is the resultant sound level z,7e,of3r8,p tqb kjgwhen an 82-dB sound and an 87-dB sound are heard simul,jpe,q 3or,7 btk8gzftaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wham6v *qe+pc3w+a :qqc31 u qtlat is the acoustic power output (W) of the speaker, assuming it radiates equally in wp 1 ae+v q33caclu*+qt6:mqqall directions?    W

  A stereo amplifier is ra 8eyafls q. *yo/b 4h0;.fynxh 1v8iugted at 150 W output at 1000 Hz. The power output drops by 10 dB at v . gbsyi/qyh;lx8o. hf 1na48yf*e 0u15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicnv:l,zx+xll m 2fe8ru y7-n0ies 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 of08r,fxy7:-ilxlv nu en+mzl 2 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 k - zl-2jqjh/ngain, $\beta$ 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 a f3nm +w:ugb6c)ea9iyb rzko 1ksu */ 7drequency 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 lonsup, :d dzp36lg between fixed points with a fundamental frequency of 440 Hz and a mass per unit lengthp3l ,:pzd6sdu 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 fi *p (3nc-jcdmblled 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 0j dccnpm(b 3*-.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 one2 wu2on4angg4 end and also 75 cm long. How much tension should be in the string if it is 4o2ng4 gwn2 uato produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loo2 g1tk g--taksp ($\frac{1}{2}\lambda$) 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 sources. p;e r6 9k/f9b5vz hrfbThe sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and findhr 9rk6epv5b9f;z f/b s 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 whistles. One train is stationary. The conductor on the ssc zi bx.auf0;2o7o h0tationary train i0hsfxob0 7za u.;2 cohears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Adsv;hk4:5qmoz.nx f/i h f swhb-49b. fter it passes you, its frequency is measuvkmh d5.. s zhh4sw-n9;:4bfiofb q x/red as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speey5oy2b*dj hdjss-ga0 x7x a05 d of cars just by listening to the difd- jo 0axjdys5xb7a* 2h 50sygference 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 is it going?    m/s

  Two open organ pipes, sounding m;m +tefyh/qt5(v )lz/q7lg w together, produce a beat frequency of 11 Hz. The shorter one is 2tm/+ 7y q(/zq eh wm5lgf);tvl.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends(rzf3ib70idcl nb:q+; 8ruk*4s yb cm of 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, 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 Bmd zy7 l q*c8;+fnku3 ci(:s r4bibb0r, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of bhoiv p, *aadie,t8g-dx0v/ c(lood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and refl, gdc8tdex/*p- hvo a0(iiva ,ected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whi qgs/k( n) azweoape3 vbdf,5*40e:ncle the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Whaa:ek 0 p)d ,q*/ nage(ozf3 54ewsvnbct 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 frequf06bdrt* c(uzzf x. .hency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long.dtu.*cfh (0zfxz b r.6 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 senc *yb+ :trd+msd signals 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 sharp (or G flat) horn. What is thscbrt +*d:+m ye 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 stal8)vr,0pzs hk nding was)8r ,0vplh kzves, 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 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, slendt0+f8p*r4 hkvc vl1cc er aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the c4r* 81vclhcv p+tf k0rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human z41 bxgv *s,b cyva4(tt/g-nuear at a frequency of about ,tyzs(ut4cva4g/x* bv b gn1 -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.ak..*tmy )/ w1 cpop+gxima +g0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitud*)ppako 1xg+m..mg/ay+t wice?    $ \times10^{4 }$ m

  The wake of a speedbz;d3g*3d cngqoat 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