What is the evidence that sound travels as a w3v ycu27m)qu iave?

What is the evidence that sound is a 56 )ih*r3infechxhjn h6 x -a0form of energy?

Children sometimes play with a homemade “telephone” by att9gz2,6x3jrxojd ra. baching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into o x.rgaxjbd,o 9z 6j3r2ne 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 from air into wa4 8*+:rsdxddzzw klf -l7r/bt;+ r xdster, do you expect the frequency or wavelength to +ds l74rd8sfbklzxw /-d zrd;t*x: r+change?

What evidence can you give that the speed ovr6 *1t gjz*.tbtvt9,h *;wn z6ktwq8xo:rqi f sound in air does not depend signifz rtthx;rqotq*vk bvt8*n6gwt: ji,1*69 w. zicantly on frequency?

The voice of a person who j0 11ad18wp,3uf )i lbbnhuidhas inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orga yw+g;c 1o 9if:j;fkcwn pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun q-plm j+*1x/ma 1lcpo f6qa cfr6w9d)ds in various fre 1q-+p/19qlxmoc*jwa6l ffaprc6) md quency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–ki 1c*x hl4*uc30) spaced closer together as you move up the fingerboard toward the b lckcix*4h u*1ridge?

A noisy truck approaches you from behind a bu3-h p4+eacog bp cw(8hilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — 4pe3- 8aocbgwh(cph+ you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sait. / apy8lo967iifob jd to be due to “interference in space,” whereas beats can be said to be due to “interference in ti.78/6p9foiao tlbi y jme.” Explain.

In Fig. 12–16, if the 4k h120 tw(mfizmxmuub m+l15frequency of the speakers were lowered, would the points D and C (where destructive and constructive interfere 2fmi5xt+hkw1 m4ulm 1mbuz(0nce occur) move farther apart or closer together?

Traditional methods of protecting theu -wmj.q0id3se eb) x8 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, heauqe-3)xmb8.sie 0 w djdphones 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.udj /gc 4y6xbfeq6rq;a/ kv* ( 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 aygrkqb 4q6*ev/(fd6cx/ uj;the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourc2ly vc.ub 1bc;bc/ (uie and observer move in the same direction, with the u.b/i cc1bcyl(;bvu2 same velocity? Explain.

If a wind is blowing, will this alter the frequenc9fqh 1 cbg el.wxetlf14e,* kqbi:4(cy of the sound heard by a person at rest with respect to tc4*q felexf419 hbc(q, wi:l.1kb egthe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of 9who0a8 p9fn ea child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E,0hpoea w99f8n will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines th.untf hc fnz8-( 0qgr*e length of a lake by listening for the echo of her shout reflected by a cliff at the far end of thfu nf0q (gchzn8r.- *te lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. p bbs,tyg.+0h 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 shb , spb0+.gtyeawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wacpluc5vhou- -t) *c- ;2gqjllvelengths in air 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 tunaxsyx raj7u7 +u ))jek3 on a foggy day. Without warning, an engine backfirx)u j yea+)jrsxu37 7ke 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 t-w dn4wdh )g3lop of a cliff. The splash it makes when striking the www-3 h 4)lnddgater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ea +ma8b wfo79mnr to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occw nb8om a+9mf7ur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one -;q6px6syavlsg , p7emile of distance by the “5-second rule”xysplps-gav ;e,q 676 for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1ga-3zc2 9ow tx:j,dgb20 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of7n v5accj dt6/gsltsg(f t.oc:m;8 4u a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultany58xlae6meha 9dl v- 3eously at a certain place, what will be the sound level if only one is exploded? [Hint: Add in 6v9ax mae5-l3d8 heyltensities, not dB’s.]    dB

  A person standing a certain distance from an airplane w, ovq-sk* t:ylxag5jxc / f7*kith four equally noisy jet engines is experiencing a sound level bordering o/qak-xcfg ty v7:l, 5skxj **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-noise rak ob.2cm(n: k,n0kuqctio of 58 dB, whereas for a CD player it is 95 dB. What is .nk(k2 qmocnubk:, 0cthe 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 speaking j0fv/x ;4. d ycjdo;;bai*1chhjnvi( in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere n; 4ih0jd;v(; j/1xy.ahjo*df vi cb ccentered 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 v4i.d p2z;ovreardrum 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 at0cu+ey z8-wk csl j+h- 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 loudl-cyh + -ek +cjz0sw8uspeaker 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 reg a8lixa5 x0 ys( mt5cuib(rp+;-ldp2sistered 130 dB when placed 2.8 m in front of a loudspeaker 8uxbdc5p (;t- m2al(yxs ipsa+ 5 irl0on 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 soun hoj/r z8: x+xik)*jpjd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9k/p8 r+)jz*j hox jxi:.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will t g*pmdj ;:2okzhe intensity increase? Increase by a dzpjk;g2 m:o*factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, buelgx;a8n bn 44t one has twice the frequency of the other. What is the ratio of their int;x bl48gan4n eensities?   

  What would be the sound level (infx p(v8 (0ei5rso0-arly:n vv dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecul:5rvo8f0py( ael -x(v nri0sves 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 6qf *k;zwap bgty1a e)n33w5tthat has a 50-dB sound levelapqy tkeb5;*t f1gz naw363w )? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wz( xfc 7(xxm-ohen the sound level is 30 dB? (See Fig. 1(xx( z fm7cox-2–6.)

  Your auditory system can accommodate a huge range of sound levels.1v+g 3 tkv+upa7a lmhly(85nq; e0vnz What is the ratio of highest to;yptlm1(78l+u qnvna+ 3 vhaze50vk g 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 frequencyk48 j/:wb kwg i)b ;syhmxj,.o of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.jby k; g.xm)ws/,khw8o 4 bij:35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audiblel h-ifjr:)12uwv* e/ki qj1r w ovlj1qf* rhw - :jiviuerk )w/21ertones 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 blo29oa qk(dn mi ho)6r5wwing across the top of an empty soda oma5h2d9 ( qwkri6n) obottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pf.zm g3o.5na igew: -.4qxtjq ipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of oe m5. fg..a-j4qzwinqtxg:3 pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic aptkl(h-z*sy /3v qa3)sfd h6. What will ky3d6q/*l sfht) zv3-sph a a(be its 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 andv*nf e)m0a0kd*y (g b-nrxi6k is tuned to play E above middle C (336 keygr) -a*xfnkdi(0n 0vb*m0 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 organ pipe that emits middle C (262 Hz) whenybr5qp* 8y *cddy p24e thedp*c*q4y5r2y 8pb dye temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20+ 8go9de 7svnmq70vs5txhe2 v $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be +c fip1ds/ br5that must be uncovered to play D above middle C r/+pbdis15fc 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 tt .wl9 c4w7baHz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is c4t97t aww.lb 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 l )c*6hc.sufxt ong is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and stf*ch uc6x).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 t,tuw 4 +fpzdi6 *:oym$^{\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 rango(sd1gbq;og0b)mv kx+vd9 xqm4; .j ge for a 2.14-m-long organ pipe at 20 qjvboqg 4m;d+; k x g9bmx(1)ogdsv0. $^{\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 ouhzt99j;7tau- o a/bj itside and is closed at the other end by the eardrum. Estimate the fuoaitz-j9 ta/h9;b7j requencies (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 yezv,y.c.8f xt 4cjk2gv1z5 vw;)nlic )uox * trying to adjust two strings, one of whicv*clyy1 o.i)c vevx2jtk).f,8 w;zx u4g c5n zh is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frelxj; 75.ng ne;n7vojdy8d.t gquency if 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 operates at 23.5 kHz, whwi,2 q0go ,ogu(dba3 kwvqdg* +n-8jyile 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 tg nqud+w30 ywggk2v j,,o8qba *d-(iohey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 7s .)e5pre ;cmnaoha 5350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What i55eea.mo )ar ;7scnh ps the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fre7*hzjh ta ft-ze87z rhk-m d:2quency, 294 Hz. The tension in one string is tht-fdz8rzzhk a:*m2 he7t-jh7en decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will bej:o 8d-z6(tjy px3by .i qa(oq heard if two identical flutes each try to play middle C (262 Hz), but onzx to(j8d jpiyq(3-boqya. 6:e 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 frequency of 441 Hz;kz4 c jp m-rm-h6enkq6(/q 1)unrh79tdwfbx6 when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency 96 ewku-fc-kqnmt/h)4jdhmp 1 rq nx6z6r b( 7is 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 stan 3+ear0brc 8ea*2s e s1gx:gmeds 3.00 m from one speaker and 3.50 m c1xa2 * m a+sgbr03s8eee:ger 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 piano tuner hea-si3 bqss8ld 2xg7im/gv-j 91f p:wiz rs three beats qbw8: 9isg-gl21ix js - izsf/dp37mvevery 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Ho(t6gavnmwub- :: lnv4 w many beats per second will be heb vgu-nm(6twv n:a:l4ard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginegbwwqots4jt-0d :2,v ’s siren is 1550 Hz when at rest. What frequency d0dtwg,v2 toj4 :w -bsqo 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 do you detect if a fire engine1c3etcgs2/, jric8m k whose siren emits at 1550 Hzc i/ 3c2,8sgmtjk r1ec 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 moving toward you at j9 4 fsmnz7cv+15 m/s versus you moving toward itvf+z c947njms 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 with the same single frequencyosuh5yzn)rj.n8od yw7 vl* )5 horn. When one is at rest and the other is moving toward the first at 15 m/s the drino z lro h))nu58js5yv7wd.y *ver 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 ultrasox3 d7sxaros lpgrhtym-zqj;9870 0(vnic sound waves at 50.0 kHz and receives them returned rap;7sdlsj 7h00(8o3xrqzgt9yx vm -from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed okg yt1khe*d 2( amkmcz9p:3 j4f 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 k 421gkct9 az3(*ydk hemp j:mkHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on 0q/ry4we,v 1wfrjy-/9 api s.hxit* aa moving flat train car at a frequency of 75 Hz, and a second identical tuba played tw9xa/f y 1qvwrhasi-pi0 /j 4,rey.*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 waveiuk r e6 ypze:9fc25u/s to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away frok9u c2y5:ufz6/ei rep m the sound source?   Hz

  The Doppler effect using ultras (nx1vvv 3yvn1onic 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 sout:zg,)pp4qgi ,x bx z:nd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obs:tbi )gzp4 z,,gpq:xxervers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spee ef0ohm.j/e s.d 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.:d70s -8sjfk ak3 6twkyrkv1/s ew ng-3 where the speed of sound is 310 m/s (a) What is the angleg- 1k vn7-0 6ydtkaw8j /ssk:k rsefw3 the 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 atmosphz9g uw0p69hhcere of a planet where the speed of sound is g9pwh6ch9z 0u only 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 traveling 8500 m/s strikes the ocean. Determine theaq ;x+ 9aero,d shock wave angle ode;a ,q ar9+xit 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 rujw:lrm -hpg 7 1-:vr$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above th n v,4rqj pw8c/ct+8youi+/sxe ground flying faster than the speed of sound. By/yjs+xpv/cqc ,no4i8 t8wr+u the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward fri6tfa6 aq/( 1w1lis jyom the bottom of the boat, and then detects echoesy1 qf1i j(a6wt6ia /sl. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hum t+,ah,sy(q fxbodwdx2e9-m9 an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe95 ey5dwcyi( m symphony. It consists of many plastic pipes of various lengths, which ar5 dy5cmiw9y( ee 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 bn0vw 0 /3c*(ixq,igslb aa d;threshold of human hearingbind b*; qa/caiwg0v30 s(lx, (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level wh*s jdz iim-vk//h f+k-en an 82-dB sound and an 87-dB sound are heard simultaneouslyki/mj-khz- sdvi*/ +f ?    dB

  The sound level 12.0 m from a loudspe.;lr6tr4tl i yaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it rar6.llt4 t;yridiates equally in all directions?    W

  A stereo amplifier is rated at 150 (9vg:3eryx+j7 nuelt-e /g.jq6q bjzW output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outputqbx.9qz+:te u /rj7ge ej nj6lvyg3- ( in watts at 15 kHz?    dB

  Workers around jet aircraft typicallynljl tqmbaru;9, * 93v wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of t;b*jl3 rq9 a,vu mn9l2.0 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, krvk+y r mk,4.the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to eh/bg2asi+f4a 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 fuzh2u zh2vvp4qh6 ah3(n8lc h1ndamental frequency of 440 Hz821z (h6 q3v chhzvhu2pa4nl h and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open ta3g**y j7n:atfewq rt t(;9 ieube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water levele*w37ieg a9;ytatr*(qfn:j t 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 tdgl mzu: bd3o );t,9n)t m6kdsube 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 m m:) ,kn;ddzl9ds )t u3b6togharmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one b.d2o*3j/s hx,v wvi;bw 8urn 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 thghdl*7 wbir428qku4one in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from thlb4w847g2i q d *uhrkhe two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the w f:ugtlr85q-l 01dxsi- 2 kkdstationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tr 5fg:lrt kxiq-d- 80dlwu2ks1ain?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftcyaf -3yrtim58 6,oqe wetj89 er it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume c5wqif8e69y 8matrey- o3 cj,t onstant velocity)?    m/s

  At a race track, you can estimate the spe-nbfw6 w3p 5rxed of cars just by listening to the difference in pitch of the engine noise between appr5 wnrw3 xfpb-6oaching 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 t rb2lv qv- 3qrk,6kgk44fy 9fmhkl+o4 ogether, produce a beat frequency of 11 Hz. The shortb3g4f- f4vol46k2kvy m+rhq,l9qr k ker one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pase43iy6h ps9s ft a stationary observer at 10 m/s aph36 sife s9y4s 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 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 aboulghs ihs k564:t 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 56sghl:4h k isblood 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 while the moth is fl1 wmzww6i68lpz hh6 3dlnb8 )oying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequencynozl mhw i8d w)6hw16368 lzbp of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mtmdc*f wftki5 ;f)n)m;dk 8x1oth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be c);;m kdkwx n1i*)f ftdt5f8mdetected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38)gqm/5ibkp3, 7eqj n oo;i+ wd* was once used to send 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 inqo /ij; nkb*d3qoi mwe+ 5,7gp such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of standir2r3 1)lekxmi ng waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Cons2)rkerx i1 3lmider 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, calljbv4 ;,e o5dqwed “singing rods,” involves a long, slender aluminum 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 be5 q;b4edwj ,ov 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 9g +f+ kcp2rxjthe human ear at a frequency of about 100gc2p +rkfj+9 x0 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 groun d6t4 ghvzh+78ca.j rbd hears the sonic boom 1.5 min after the plane passes direca h8+d7jrhvt4c.6g bz tly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboy*f*ei/ b4xfd(c iz**gat 8ts at 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