What is the evidence thawr2wb:,ey)t gt4s jp .t sound travels as a wave?

What is the evidence that sound is a form of energyec-z 9 njbp2/d pe 9/lwth.z6v94rw+ndfxoq/ ?

Children sometimes play with a homemade “telephone” mio(3ro/ja rz 8q1x/yq,c ;layf/ 5fw by attaching a string to the bottoms of two pap fx/qaw/ ;r (yoo53zjr8yi amclq,/1fer 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 palxwl ht ;(t1:msses from air into water, do you expect the frequency or wavelength l;:twm(t h lx1to change?

What evidence can you give that thellblp/9fv5ze ua bm(jjf,m a7h/ ;*y 8 speed of sound in air does not depend significantly on frequency,y(eu7 ama mjh8z5vlfl//fb* bj l9p;?

The voice of a person who has in4 l60co;kp bojhaled helium sounds very high-pitched. Why?

How will the air temperature in a roo m *5plscuveauz80j(6*hbe 3zm affect the pitch of organ pipes?

Explain how a tube might be urvdtmv,3,-vg *q7s0ofh w)m 7hj *mfosed as a filter to reduce the amplitude of sounds in various frequency ra v-*j3 fqg, h whs m7m)otmvv7rofd0,*nges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togete67mmras +cj(3osi rj dj+3w5her as you move up the fingerboard toward the bridge?r5ja3m iom r(c63+dj+7wsj se

A noisy truck approaches you from behind a building. Initially you hear it bu /) v;q0r6zvonm.jfrg t cannot see it. When it emerges and you do see ir zg.) qjor0vm/nv6f ;t, 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 due to “interference in space,” g)lb2tsw *v)df;0a phwhereas beats can 2 tvhal *)b) 0gpfd;swbe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of tf+. rvvq e9 r5r.sh(jpewh. k4he speakers were lowered, would the points D and C (whsj fehpqhvr.+ kwr( .4.9r5ve ere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the h33flkwf0mj7 i earing 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, 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 nwkf307m j fil3oise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fqb) qx2fd;1 8 p2wfrjgig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compqrx )1; 8bfj2fq2dgwponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same duktg:he 8q ,8ilhxhi6o, xo6 ,8jyw+jirection, w8k,qto+,x eih:8 wgjlj8uxio6 y,h6h ith the same velocity? Explain.

If a wind is blowing, will this5svz6i ia c8e; alter the frequency of the sound heard by a person at rezsi6; iec5 va8st with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motio .nzc6va1 *t7a ch c61wgmpfl1n on a swing. A monitor is blowing a whistle *1g m6cazw67 1f 1.clhvapnctin 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 p- ya c1g,c0bqlength 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 apc -10cgyb,q s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hbxw5i 6 kn -wt0o(vl6his ship just below the 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? Asinlo0- 5bwh 6 wv(k6xtsume 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 a ht se71k0v3mlir 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 scho)e: c aw.d4jabjbl+ e m4g9bd:ol of tuna on a foggy day. Without warning, an engine backfire occurs on anote9. djg b4c+: )mj daab4elb:wher 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 splashwit 0 f 8jz.fm0p: bvv(qxs /s2rrp*v5 it makes when striking the water below is hf.s/vimw25t(qrp jr0p sv:z*bx 8vf0eard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge st8 miv 3eo 8fdq2ae2:duone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other iodq u223ae8vfm8d: ein 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 /un8mcu5( 7 nuyubj2u mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a)28 5u7 ybcm(ju nu/uun 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120dy3fd ac0:l1r zu ptw5*zpn3 ; dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whqew: i ,*,qil:gmh8:qf e)aprose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produc l2+we2d5leq fsrg7+z rydi50e a sound level of 95 dB when fired simultaneously at a cert +fgw7qz l2yee 0ds5il+5rr 2dain place, what will be the sound 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 noisy je:1p 5 bi-iuih*f2ifbhe: *lbwt engines is experiencing b*pw hibh i:*fei5ib2l:1 u-f a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-5 zk7yitd.r *vnoise ratio of 58 dB, whereas for a zk5y*.7r vdtiCD player it is 95 dB. What 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 of sound from a person spt0ro mzu*rm.u v,dg 5pwio 9u80 96xgpeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere ce9 ppzgv8 900xrw.d6 ,*gtu m5 mouruiontered 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 fwfzo4*uu5 , t,ujtd: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 atfk4ip/gaq98 t q-n1m:r,/ 3lagnb mai 250 W, 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 louds /qga-l9ti8:,m pg 1ni4 k fqabamn/r3peaker 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 registe.dpv6ufg; -:vtl2b26maa .wmy -z mb fred 130 dB when placed 2.8 m in front of a loudspeaker 6pdmgf2v 6 a.mbwbzvyu .-la-f;:t2 mon the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB.v6adl) 9 a88 ovb,rgyj What is the ratio of the amplitudes of two sounds whose ley8drjlv vg6baao8 ,)9vels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,e yxuo, d0o46j (a) by what factor will the intensity inoju xy,0o46de crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eq3ddan.yb3 j m9m bz*nl3j nulty-v*h:;s94kw ual displacement amplitudes, but one has twice the frequency of the other. What is the ratioyw3n.hdv 9d9* l: jumsmyjn ;*tnklza-b433b of their intensities?   

  What would be the sound level )ncroc()xcrjw /2mr ) (in dB) of a sound wave in air that corresponds to a displacementjw /)c nmc( )xo)2rcrr amplitude of 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 th.ir72ssolc g. at has a 50-dB sound level? (See Fgs 2l7.or .csiig. 12–6.)    dB

What are the lowest and highest frequstm9)8t oz6s kqs 68kpuhn7 h*encies that an ear can detect when the sound level is 30 dB? (Seeu6 * 8s)kspsz6mh to89n7qkth Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is)*ti/trr r +hv the ratio of higr h+/rti*)trvhest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The)aeo.k ;61aqr:qidlx 0q tj x6 length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension6t a1qxj0keio)lx6 ;dqa: .qr must the string be placed?    N

  An organ pipe is 112 cm long. W5x-q e7byy:r*up c 1pshat are the fundamental and first three audible overtones if the pipe i1es7 rbx-5ppy *y qu:cs
(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 blowing across the top lo(wto- uyt(o/ (.nb cuuk1+b of an empty soda bottle that is 18 cm deep, if you assumed it was a cloc( tnu.1w-u+oytb ( lkb/(uo osed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe orga2a maz -81dsx pbp+- hbmp;0ftn with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range -2 tp+xbpd0b;s8 mph-ma1 fza of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as i loh:1/urei m-ts third harmonic. What will be its fundahmolir /1:eu -mental 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 to play E above ,ug n / mebthvlti3( 44md(1rcmiddle C (3 nlu(r i/dhe,mt1vg3 4cbm( t430 Hz).
(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 o 3d ep2 a*v9qbsq2 jp35as+vj 5dbbgn9rgan pipe that emits middle C (262 Hz) when the temperature i svb9j2 ddp5*vnae3pj2gab qqb s+593s 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 20kt-ak337x nmv $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fluuz h9g x;v6o4ote in Example 12–10 should the hole be that must be uncovered to play D above middleuoov 964gh;zx 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 Hzma t( 3wk;w,tud, b0ji, but not at any other frequencies in between. (at km 0,autj db(3i,ww;) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open 9crarr;6w io (at both ends. It resonates at two successive harmonics of frequencies 275 Hz a9 crrwioa6(r ;nd 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 t5yhc ny2 -ggb:.kzrh:v+2q l $^{\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-lww:h2 (js 7selong organ pipejseh:2sl (7 ww at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appro me1 m1d-brlgj6h+u)3u abt9 zximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the1a 1+9 g )hutl-umrb3m6djbez 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 two strings, o2om-xq7 20a tdqe4bct ne of which is sounding 440 Hz. How far oboteq- 7m4cqta 2d0 x2ff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) ajh 1al 90jkb)ab+)rnm:nnon .5*vavnnd $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while ano ;y.wbhmv*fb l /-0jdm60qfq yther (brand X) operates at an unknown f f0ql;wj*h b0- bm6/f.y vmydqrequency. 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, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a9, m6 ejdys;as1w, fkp 350-Hz tuning fork and 9 beats/s msjweas ; k,,f1d yp69when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz c-5cqh ob4ygz0/zvdzfe2 er*4 b5;b w. 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. 11–134c qz5 br4bdy05wboczf-ez; h2g/v e*.]    Hz

  How many beats will be heard if two identical flutes each tyr98/ +swmz szry to play middle C (26/mw9sy8s z+ zr2 Hz), 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 ax2i6sj1g: kll 2mxrz 70. *z wiu2jvkq qdsb(8 frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and 2g8k60mq zqbv(jlxrk2iz:.l1 *di 2 7 jssuwxC 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 1.8dfsn 5za 6il)ju5a;/ tj(ftk,lyh)*j 0 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. ,sdl(u l)5;t *y ak z)/5njaij f6fjht
(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 vih4j :5sm ni ow jp)d0eq6vr,9ubrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequenp9 imwe :)6 qd540nsjjo, hvrucy 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. Ho/e-l,6mps e jvw many beats per second will be heard? (Assume T = 20 ,v -l/jepsem 6$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fe5q:+y -mjotfire engine’s siren is 1550 Hz when at rest. What frequency do you dej-f : oqm5y+ettect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enn,lpwe(7b*qwj 4 :pffgine whose siren emit 4:fwb,fpwq*ln 7(epjs 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 f ,,1727f+r mtecvkpllp 9e fgarequency 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 frequencies exactly r17l97ft,lc 2mp,+ pkv agefethe same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. q9tt77+y fh :rpwstp*When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat freqr9 7 spwt*p+y:tqfh t7uency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out u va q )omugl,zq;5*)dxrdk1hi(3(xgm ltrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What ;a kd duhr, x)ioqmz(*51mggqv)lx(3 is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s1jbkip8q 5,f(d(i bgrux9 w -o As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHi i (8(-dbj5w gu9xkop,qbf1r z. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba w:u;dk2nke qtk (,dxszo83id s/ (i z4was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speeeqnuod24wsizz;/ :d3kk (xkd8,t( sid of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-fl- 3yahay7dhz- ow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away froy7ahza-- 3 yhdm the sound source?   Hz

  The Doppler effect using ultrasonic + 5+j+tocq oq/ofiigg/7,h agyvd*3qwaves 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 emiljsp 6*)n h)* gs 4aoyez7j(xgts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who pzxo6jss4al )(**n)7hjge yg 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 movlb2 l16 eql*b 23h-coceva,d5cbex/i ing 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 mais.y9h,1 xkk fcuntc-lj ..)3pt2 u m/s (a) What is the angle the shock . mhcp,jtuy)t. 3sk92- u1 an.iclkfxwave 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 of sound7a -xr,ux+g3.wyifrej58fad (wkz )mnpe75a is only about 35 m/s 5 7wi j, 8wx 5)7famgeu+zd-xf( r.3peaaknyr
(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 ocean. Determine the shock wave an . u-rsw9evivel3xh: (gle it produce e9wes: ihx3vl.(ruv-s
(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 tx5 5qs7)57 ykfnf lnm$/theta$ 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 exaxjkgm- 6-mmc v76 s3kfctly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveledmmvcs- 6 3x f7k6mgj-k 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 devichg78ug++ :td3atj r/ t1dfe vqe that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximu ge+1d+qvrtfgthj3ta:78 / d um 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 oe t*e58u lifi t*p *yf*pqcu4)ctaves 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. It2.l1i qejkevm f0-p d( consists of many plastic pipes of various lengths, which are open on both ends.vk10q i fdjme(l2-p.e
(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 )qi7wwty rf40 close to the threshold of human hearinww7ft iq4)0y rg (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultantn/1cdaz m*ss4pw, (gc sound level when an 82-dB sound and an 87-dB sound are heard cp(a mss /cg 1nzd*4w,simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed a)g(vxe68 o(n.v/efl gkx3km hwn,0 gin the open, is 105 dB. What is the acoustic power output (W) k3fno,vvwhke(a( g)e nx/0 g6 mg.l8x of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is ra9u1bwxh4gby; ted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What isb4y 9;1uhgbxw the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicallyc g9v:( 3tsld37cpdd78n ltr k wear protective devices over their ears. Assume that the sound l 73c7 tspr8(dtd l :cnd3l9kgvevel of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communiwp7,:r qej6iv2s an uqjd;5rvt:+qm7cations 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 violinby v +cic0(a.+eai-wf is tuned 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 fixed points with a fundamwm2wi9)x mw.t6p nt xn a/ /z8iq.heg+ental frequency of 440 Hz and a mass p.x/wq8tmwin)2p iz6+ gt/9ewxam hn. er unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vert oa.e0+bm8s,p b 3gfmnical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air+a8g s0.3b mfm,eonbp 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 m8 jbhc;irq2i7ass 2.10 g is near a tube that 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 its fundamental mode) with the third harmonj i2;hri87bcq ic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resoolbht9 )y /bv)nate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from twg g:qrpw (6y g,f 4l1krjk/z5jo 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 kjlrg:g(w6p,/1q4g kzry jf5 other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conducsa-wdwrff4* 6 6:ll kgtor on the stationary train hears a 3.0-Hz beat frequed4a:6kf*l rgfw wl6 s-ncy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam ruxe52x2h2g 4 4 2o;kdgavhyktrain 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 constk; v5hy 42x2gx4khu garo22d eant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by ldhi. k25p9rga3s5mn gistening to the diffs9 dpk523hmg.gr nai5erence 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, sound(b)2gc, nyi27m sta7;sc v pua4xibq6ing together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m a;baxn 6mi7gti)7cs,s(byup4 22c vq long. How long is the other?    m

Two loudspeakers are at oppos+gvyzh3g dp -z9rjp90 ite ends of a railroad car as it moves past a stationary observer at 10 m/s as shvyg-+gpzjhpz0 3rd9 9own 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 B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the-d )crxdoym+ -i+ kx6l. ipvj+ 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 reflected from the red blood cells? Assume+ i +xjd k6xco+id-r) .pyvl-m that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a m(s;:ynseanp m) d w-s;oth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The mssn(-as)y:pw ; ;end bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as itllet g smz(pvp(t:t(.i;22;x y nxae8 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 detected by the bat so that the echo from one chirp returns before the next chirp is emitted? x tz.2p(glets2x(tli ;eym;a:v ( p8n   m

The “alpenhorn” (Fig. 12–38) was once used to send signals 8uebi ;nog ldwga+4-4from 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 the fundamental frequency of this horn, and which overtone i4id-u lw eg4no+ga8 ;bs close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compruq3uaag- *0-auwk :/ox8bd-xr: f te somised by the presence of standing waves, which can cause acoustic “dead soud0 wefq3 -/s:g-u aak:8xx-a *urbtpots” 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 demonstrati3 fptv2 cz9fwu9ik,q+ on, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other29ftz3 kwqu+9vfp ci, hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for4bme a4fg05i ojz2di2/baug 7 the human ear at a frequency of about 10 b fi25 4bgo0aai/7ud z2m4jeg00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic aqg/naeu(j-c1 ).bqaboom 1.5 min after the plane passes directly overhead. What iu/)ag-ae ca(jb.n1 qq s the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 152z.3 19urgm mtgx ymc) $^{\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