What is the evidence that sound travels as a wq3r.hm a61bco 3bm e1save?

What is the evidence that sound is a form of enerlwk j2/km)b3t gy?

Children sometimes play wit4.+x 2e : rl;z) jlqh p rvwrgv,isnu()wi1-wsh a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the oth1l w-js (2 vn.rhg) z4rirv)wes:wu+qx p il,;er.

When a sound wave passestejzzya2) kb.)-mxy*c +c:l yhv4t* s from air into water, do you expect the frequency or wavelengkty-y2)b+ j . htx:scy* *zl4aczvem)th to change?

What evidence can you give that the speed of z;nqp(x3 zeb9kfku :/gq v02v sound in air does not depend significantly on frequencvb3zz0qnqk ;g (9v:pkux2fe/y?

The voice of a person who h zbjg )ptgvt/jcte-kk m vn*a8-,l-72as inhaled helium sounds very high-pitched. Why?

How will the air tempe7 7jj jal c49ua1 :0rmqpyv+vnrature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sg6 i c42hpd1urounds in various frequency ranges. (An example is a car muffler4 pd1gi c2h6ur.)

Why are the frets on awswf ev216xtf30a ar : guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridv 6t ww02sf3 x1ae:rafge?

A noisy truck approaches you from behind a building. Initia : 4py;5 je;so)qiq0u sizw6yylly you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency nojswz;pyiq 64y)y: 0su ;oiq 5eise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas cg*upd*p-b*cp7pqzxfdfmv 0 /53y s, beats can be said to be due to “interfeu 3dcq*,s0mz* pvppc xg*b /y7pdf5-frence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wer0vdn:0p(ssmew:d :k. uvb uopd sq( :,3,islk e lowered, would the points D and C (where destructiv3pd (q:,isv:slkws,e mv bksudu0npo :. (:d0e and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areal :.slfoc+nkuvk7+*w s 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 noise. How could adding * kw vu.ocl7sk+ :+lfnmore noise reduce the sound levels reaching the ears?

Consider the two waves smy/zh ku **hy3 nwh1)shown in Fig. 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 component fre yw* * znhy/m)1suhk3hquencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same; hiuwka57 io( direction, with the o7au5w ikh;i( same velocity? Explain.

If a wind is blowing, will this al7g8rzr(z4ax49lyam3z;g w +0 mrb w nlter the frequency of the sound heard by a person at rest with respect to thbgzal( nwrr9+a ;g7 l4zx83zwyrm0 4me source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a yt;1fxjbl6 ;(l n)nrlchild 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, will the child hear the highest frequency for the sound of the t ;lbjl ly)nr; 61f(nxwhistle? Explain your reasoning.

  A hiker determines the length of a lake by listen+t,r lhxvki1)ing for the echo of her shout reflected by a cliff at 1txi,)lr hv +kthe far end of the 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 belo6v p * lhef 9ui*)0uw8vkbuaz5w the waterline. He hears the echo of the sound reflected from the ocean flpu)9 bfk v6iuwe* 5v8a *uzh0loor 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in e;ybaz:4 y*vlair 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 abovln/tz7lot: a0lx bb54e a school of tuna on a foggy day. Without warning, an engi bntal x5z tbl0o4/l7:ne 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 clif3 u-fmabxv 5/bf. The splash it makes when striking the water be b xa/-mubf35vlow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tkauxf8v(9 ft/he concrete pavement. A momek8xf(v/ f9 taunt 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 one mile of distanc * htw(srmf+ 44 )v)a.iwukyhee by the “5-second rule” for estimating the dishm. twe fwr*i k)h44ay( u)+vstance 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 atq4jiz9-i7 * nwndqh f0 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 sound whose intensitym5 p9q h*b ldl5j+fbf9dem,-c is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce ayms,ahq 6f9 o/9 kya*a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Ha*of/ym,9qa 6s ayhk9int: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an 5gru81q: bhjzairplane with four equally noisy jet engines is ex 58 hqzjbgur1:periencing 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-noise ratidrf d.x;*/m tm2px, ok9rov9h o of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bv9;9 xo*kdh/.m xmdt o,fr 2rpackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking ifmv g. 1ar*r+yqi241q n2b tqin normal conversation. Use Table 12–2. Assume the sound sqyqmfv2trag+ i.4iq n1 2r1*bpreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose areys:6r z/ uzne(a 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 rateim::54 pjotp0w 1dvy 7iofs0zd at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at afp j00i:z m1 i dy4ws:v7to5op point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of ab8 1z*ejzkfs -(5 hctg loudspeaker on the sta8j t(- *z1zchgbke sf5ge.
(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 4crtzszy -,s6level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this a ,6s 4-rzstyczmount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensi(zw vtmiua pxrs0 6.qyh4;o /9ty increase? Increase wqp/;oi hay( t4xmrs zuv. 960by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frequ63 sc vr9lq;zbh a5d1cency of the other. What is the ratio of their intens5cdlq3 6a;1s cvrb 9zhities?   

  What would be the sound level (in dB) of a sounq,0 ps ;5h6swm izqdh;d wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?5ph6 m;q ;qszd0w s,ih    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 10dwegz15pbr: s .)of;k0-Hz tone that has a 50-dB sound level? (See Fig. 12–5)rpbk ges.odw:f ;1z6.)    dB

What are the lowest and highest frequencies that an ear can deteco+/ap t+ as+ac2nq yj-t when the sound level is 30 dB? (See Fig. 12–6ao++-/a+2ya ncqpjs t.)

  Your auditory system can accommoda ohd+yq5p+2okte a huge range of sound levels. What is the ratio of highest to lowest intensd5++pkyo2oqh ity 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 o438m +je biiidd6ih3 gf 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the sj4hd8emdi ig3 6i3+ibtring be placed?    N

  An organ pipe is 112 cm long. What are the fund en3b -59 -sagwl8q.lyukeq7 samental and first three audible overtones if the pipe i5y kqsaq ge.ebun7w 9 l-l3s-8s
(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 fn)hr sr+g2bj +5slc1 srom blowing across the top of an empty soda bottle that is 18 cm bl1j gs5n2r s h++s)rcdeep, 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 orgvxbnh6(wg) oav 4 +ok2an with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes req2h +( xobgvn6 w4)okvauired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz asmwo+y m p7zh;; its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of i;zmhy pmwo ;7+ts original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abo:awxb + 0pe:kkve middle C (330+ wb0 a:k:xpke 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) wh 2d6(xipm;egog 2z- gzen the temperature is 21pm-z(d2gz6 i ;2 xegog $^{\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 20tc3r+qu8d y vgd7* m-j $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute igyu*w9b9 jzdy.h 8n 8)3n aw0w npq(don Example 12–10 should the hole be that must be uncovered to azyny8n3ojdb9(h 8.*)pgu dnqw0 ww9play 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 res/ +1ffyz1tniv z5o au8onate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wu+v1i a/zty5 noz1ff8hy 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 at both eel(fb0pd t8 2inds. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whad8eli 2b(t 0pft 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 ;kuju l;q)fs0 $^{\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 pzl6rxz(6z 3bvss f02 within the audible range for a 2.14-m-long organ pipe at 266zlr fpz3 xbvszs(020 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It i zt(yv:77ml x gjj4t7vs 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 4l7yjvx(j7ttzm :v g 7in 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 bpaf,qgngim 0 2z vcl62gz62 e6eat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othg , gp mq6izl2fe v6gc2n06za2er string? ±    Hz

  What is the beat frequef vtw.a edj kfv ;uq( 98nf-a5b,6bee7ncy 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 operatn/q3f ./6is /6d ojrrev5oojjes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simulta j6/njo3sir f/ovr6oje q./5 dneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 : on g4/fhg1bnotv 9e:hq/iyn4nti ;+beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational f//4 fyn4tg:hto+nhb 9eq ni ;nvo :ig1requency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The te4r8 lbwyrfhd az 8o*y+j *:zdgu8t,;ansion in one string is then decreased by 2.0%. What will be the beat frequency heard a, jdr: lyg + 8*fwyba8u4;*zo zhrtd8when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes6st,ou2 g z)vx each try to play middle C (262 Hz), but one 2 t)6 vgx,suzois at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fo( gkk9nr; 7+ ehz+uz9s wlh)ci2sm8ngrk B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possg)hh;knmr2s ui(8cesw l7+ 9zz9k+ gnible 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 perh(hnl cyl;d 4(son stands 3.00 m from one speaker and 3.50 m y(chn(l 4hl;dfrom 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 tou9k7gb5 wt /uw be vibrating at 132 Hz, but a piano tuner hears three bg7 5kb u/tu9wweats every 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 2sokcgu+ )wt r20/uoz-.76 m in air. How many beats per se+z )w0o2u-krg /uoc tscond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain ,/ z1d. gowra;:4kx+hbbcylofire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you mov;+l o r 41bxc,.hkyg/wodb:zae with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency dose6gme1fot *c t;8 9n:de 3 kty0zi9ry you detect if a fire engine whose siren g8en1 99fiek*m:3;t0et sroyc6d zty 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 frequabr sco01;5h(,x. t ewdcmm0mency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the tobwct5x. m m0, m1ha;sc0r ed(wo 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 frequency horn. When one is5yc4*byu8j lj at rest and the otb5lc* yj8 4yujher is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves /wo 0rj 6brli5at 50.0 kHz and receives them returned from an object moving directly away from6i/l jb ro50rw it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spe8 u . 1ynw3,ncr,hqszked of 5 m/s As it flies, the bat emits an ultrasonic n.cwk,qhsn z,1yr3u8 sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimf:1u5 ejde3nq pca52lents, a tuba was 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 hearuald2e 5epn3 cf:q 15jd if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoundz8uizl9cd 74uc7: ss 6hx0czy waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in hu0du9c6 zz czsx4sicyu :h7l8 7man tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usin.u0bz neer doiw1ky 6rm03i1:g ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind veloe5qzuied-gcg-4 r99d2p *ej)x ats.qcity is 12 m/s from the north, what frequency willz9d xqeug4 ej2-gap9di.t-sq* 5) rce observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving i7)qylw0tv p, on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whatbt v pcsd *.y)rn3zf;3 u.5qqb is the angle the s3qsq t5 uprfc y;d3b.*bz)v.nhock 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 fi+cr (9,h0oc 4r:jet6rbnuu a planet where the speed of sound is only ab fhj9tiucreu, obr4n 0c(+r6:out 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 m3:lw osze lh0)/s strikes the ocean. Determine the shock wave angle it z )l soeh:l0w3produces
(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 f4 .gwsv 6bo0kdd u-3/ 7cfhbonr st2+$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground flf qa3by+l,m7 jft:. lzying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0.ztf+ all,qb3m f7 yj: 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 sonavil;nm fo/ xg2l2es+*,kjdv 4r device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects ech/ng4x2,kl ivd s2fj*v;+ m elooes. 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 thc3bj-/udju1u r8,;c b fins4h,ahw 5iere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a .hr*eo* xwsjh3p2nm - display called a sewer pipe symphony. It consists of many plastic pip-h3r2pn *s wo m*ehj.xes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the t56+va .enfyxqdx o sm+4l4ly2hreshold of human hearing (0 dB). What will be the fdq6l y4a2.vl 4nmxseo++5yx sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soj0zjr/ 1ndd* 6db0psuund and an 87-dB sound are heard sj0drds bzudnj0p6 * 1/imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wh j njd2:ys-a1yat is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions? nyj:1 saj y-d2   W

  A stereo amplifier is rated apih9mso / ie83o5z a3ldn9,lk zhpf; 8t 150 W output at 1000 Hz. The power output drops by dh3eh5 ap89psf, 9ozoimzl3 8/ ;knli10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicefe xcng)utr8do(ejv3 4+uh u3e;p( cbolh+5,s over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 14 nto5+cu3dl g4fe 8u(c u3;,ee xh)hvorb p(+j0 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thqutp c v48m0a1(n s3jee 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 8bfxnnf ,uz: fgw7 sq:rhs /2)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 violi 9f, cqi//8c:yieto b+ia6h xvn is 32 cm long between fixed points with a fundamental frequency ofax, oe6t: yvicb/9qc 8h+iif/ 440 Hz 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 opsp ,y4: bp+4 c bwb,0wc+t qqdfg:edo4en tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate wicd ywb0::pbbfcwt + d4,4+4 qqo,s gpeth the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is9hmv.sic) d+rsh26e f open at one end and also 75 cm long. How much tension should be in the string if it isdv6e f)s2rchis. 9+mh to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resoni+ w*boxg rp/ /iyr1u,ate 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 two source6t a51f46 0xitjaqcq /u( kndkaxaq/7s. The sound is loudest at points equidistant f i uk aaq04(dxtqja6q5n /1tcaxk /67from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The con5ml ;co5au)ncductor on the stationary train hears a 3.0-Hz beat frequency when the other train uamlcon )5c5 ;approaches. What is the speed of the moving train?   m/s

  The frequency of a steam traluud,z0u3x).bh4pkb x*kqt0 in whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured,t4 xq) puhul.3 dub*zkb0kx0 as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of carsa 6,kt*iiao f7 just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the str7i a*of i6t,kaaightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 1h 9 yi1orxvz6 990mgyt1 Hz. The shorter one is 2.40 m long. Howzxyy19hg99o m t60ri v long is the other?    m

Two loudspeakers are at opp xveij8.3 lly;5:d 4cou/ zpebosite ends 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 thevlc:xuzb3e 84; eo5jdi ypl./ 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 tp4i7 0lx tkdw5+az6ik he aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were di067 k x4l dkw+iiapt5zrected along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying tow ;yxyr:15uixbss c1r q:2oq. fard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth br ui5;ys1y:rf :2.ox1qsxcq?    kHz

  A bat emits a series of high frequency sound pulses .gh:jc,(w v ln0qt:zq as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away ca z(tnq .0h: lv,jcw:qgn 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 send signals from one A)c0rn6ejc0mt: s/ xislpine 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 alp js0ct /x0ine)smrc :6enhorn 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 bedlp )11: gldwh compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations wl1d1h )dpl:g 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,” invol.pv7434111yoi jfcia iuqra v ves a long, slender aluminum rod held in the hand q4av 3vf. oiapi141uy1ci7rj near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or 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 ear at a frequers8 5rwg u5s;gncy of about 1000 Hz s585 wugr; rsgis $I_0$ = $1 \times10^{12 } W / m^2$ 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 dnqauj+a2p g/l8 l 8i6observer on the ground hears the sonic boom 1.5 min after the planu8p2laj/na q +68lgdi e passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 150g(efpb0 il / jdr7cf, $^{\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