What is the evidence that sound travels as a (gkk3j4 l-vgovcw s(nr ha/22 wave?

What is the evidence that sound is a form oftu9mk o66ga j(5xag scg6t,:n energy?

Children sometimes play wih 0 4 8y*huc,iskbmoy,th a homemade “telephone” by attaching a string to the bottomsuh cso4 8kby*y,i ,h0m of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from,o;v9 pof3 g9k1dfk3 q gwqpm/ air into water, do you expect the frequency or wavo 1k93k3 ,go9pf/gvqw qmdp ;felength to change?

What evidence can you give that the /fa .pwqf5vfz.kl *-v speed of sound in air does not depend significv wfkp.5f* l/.-av fzqantly on frequency?

The voice of a person who hasoom-d*p z9 jy4 inhaled helium sounds very high-pitched. Why?

How will the air tempe nklr7n4;d4 fm5m *+ cd+sxirtrature in a room affect the pitch of organ pipes?

Explain how a tube might be ffiie0zfhon/sf6) *: used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is:n )foszef06fif h*/i a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethermhdfsui ztvhwisa; ;0 +f)8 /3 as you move up /a;hihv su )imw0 s;fz+t8d3fthe fingerboard toward the bridge?

A noisy truck approaches you8zoessy u.ll 5f *;iz)os 0(up5 3mkko s3k3zc from behind a building. Initially 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 hi3uu0kps c(z.353se *of5s) ykmollsozki8z; gh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can b qblp1 dyt3;c2e said to be due to “interference in space,” whereas beats can be said to t;2 p1ql3bcydbe due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowere, zjsg-0ja/9 3dgefo dd, would the points D and C (where destrufs9z 3j/eoj- gda,dg0ctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearin u rwu- 8qce4w2o3ri.qu03 mcsg of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a re3w c 2cr.sqoum03urieu84-wq latively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be ..sskwijkm1 k ,mgg2 51uzeucz88e1xthought of as a superposition of two sound waves with slightly different frequencies, as in Fig.cge81 812mk,x wzkeijzug5.1 su .smk 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer ,.51ii aeh/z 283fkxll oddsomove in the same direction, with the samell,d.sifz53 1 2d8xe kohoi/a velocity? Explain.

If a wind is blowing, will this alter the frequency of thexh/3huiye)0tuiv) :x sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed?ih/3x y)):iuhev tu0x

Figure 12–32 shows various posirnmihk1mb .562 qcydm3y* j (wtions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At whichq1y5nmdb . 6ihm cjmw*3yr2(k position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shougjioo/4:uedp *mzq 68kum. 8v g7:jvgt reflected by a cliff at the far end of tjkg*v8ij:m eq/o :u 768 .pz4dg umgvohe 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 *c;/ r bevk.w-.a+j m.kqjuntship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s lau*r-e+/ vk mjj.abt. wnkq;c. ter. 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 ino0/:g wh0 e,ifd asn.(v3abegb v 5*bh 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 of4cluz jpat:2,uf /of; tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapsesao:l; uu4/f, fzp 2tjc before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff0i/ 6:q hy.gp0-u *cecqve mvp/x x3mo. The splash it makes when striking the water below is heard 3.5 s late u. cyvhmxoqc 0eg0p3/*m - 6pveiq/:xr. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concre b nx4ikrc5a1;a*r o3ite pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrex a niocirak5 *4b3r;1te, 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 ov,iv/ razi:c1rer one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (arr:1i ,/izvc a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun;u4bs*4 ga -xkq )kafgd at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a souu cjk d42w) yyo (4ee.ws182dbg8cmb bnd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a7i o6j6y x-26jppqnw j sound level of 95 dB when fired simultaneously at -j6qwjp2yn66xpo7 ija certain 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 wiry24(t l rot3+xo b.fa4 m-egs rj5wvf);1qdb th four equally noisy jet engines is experiencing a sound level bordering on pain, 12tt2.)fx+q 5 b4 grr1d -(bj rm3w; soao4lfvey0 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 xh5gk.h )rgzj +smg1*to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is *sg +hx.r1kjgh) m5gzthe 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 frz0zit md hxn.2vgi+y)m/ds3qyb 2, ,dc) m; hlom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ovv+zbt)dmg3,0nyi2/.m2 hmdq)lh ,d ; cxyz iser 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 jf,ps)ef /vi* rgs (u,whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 2ykd5qm,r;co+ ;v wv u150 W, while the more modest amplifier B is rated at 40 rkv5c; vo +,mq1;ywduW. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registeree (j9 ya;a4fut a8b+-cswvh 0ad 130 dB when placed 2.8 m in front of a louds +4a- ( 0vcea;at9fsbwhaujy8 peaker on 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 ovxcp8n w(ip g735-gd jf 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sec( -nx3pvgj5g8ipcd7 wtion 11–9.]$\approx$   

  If the amplitude of a sound wave is trips)ww6wg 5ij/o+ 1ttmpled, (a) by what factor will the intensity increase? Incrw+wgi t1 )jmo 5t/wsp6ease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, buttvytr. jo m7.vz54iw86q1ogd one has twice the frequency of the other. What is thyo74 ovwm1iqtg..vzt56r jd 8e ratio of their intensities?   

  What would be the souzo6o ib5r t31ond level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating bzot351ri6oo 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 to6l+xq5t 7ttjrn jh(u, ne that has a 50-dB sound level? (See Fig. 12rl ju,t6(tt+ qj5 nxh7–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the / rkwog;,1vhb28iyb i sound level is 30 dB? (See Figy1iogw2 ;8vrb /b,ikh. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What avwd:6ki q l/ 44hn gq.xah)wsg5 j,2uis the ratio of highest to lowest intensilk26 g ,qju hia: ndw4x.g)aw s/q4v5hty 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 qg*c :4i,dn c) khrceij02 ;ogHz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be plaj:eochgcq, r) 2c 4n0 ;i*gikdced?    N

  An organ pipe is 112 cm long. What are the fundamentah7;4 .ubn w 6ip)e lcwajgxwsp52y2. pl and first three audible overtones ei4 n7wgpbp;y6chu 2).x. 2w ajlp5sw 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 frofs1muqi:y ke2o .g*y3m blowing across the top of an empty soda bottle that s eyko3:u1*gm fy2. qiis 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 withrs.z)lps5 -d qh+c g7z open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of thlcr - hgsdqsz 5p)+.7ze 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 itsbag i0iz:-i(qn 2xn7u third harmonic. What will be its fundamental frequency if it is fingered at a length7 biigu:ax2 i(0q-znn of only 60% of its original length?   Hz

  An unfingered guitar string y,m sbw+kru*9z)hu 1 f lg97lais 0.73 m long and is tuned to play E above middle Clgf r+ z,by9whsul1)m u*k97a (330 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 (w 3icp9x4knb:vj2u /k6tw4 fw262 Hz) when the temkv3w9c/4fikn2 jpx4 wt buw: 6perature 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 ag87k qta.,yv xt 20 $^{\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 biw8ebpm-bcblb 8tq7969s izp ) u*)k ye that must be uncovered to play D above midd*q-s8y9)6k7imwb bl8 )bepb9 zpt iuc le C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but nfl8vvfczw7*jn.. wj;.i wu *3vxf5i zzij7)not at any other frequencies in between. (a) Show why this is an opi cwfvz.xj* f7nijvf5 zjnv w8);3i z.l.w7*uen 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 en/q pdvyaq9r7sw*zn4 j0la b2a 39lqebkj.- m)ds. It resonates at two successive harmonics of frequencies 2blw l q) k v2/jn0r esdb3y*aq p74azaj-9q.m975 Hz and 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 3+ehz ygzja83$^{\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 aree-n w)c 7b hmc)o2orxj*5o. j*clwv9a present within the audible range for a 2.14-m-long organ pipe *lac95hjo. 7 wjo oe b2 wrcx-)*)mcvnat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is opehc*7 )/b1q9uaigcf x 72xfww xus/* npn to the outside and is closed at the n c7 f/*7wgqfx*u9xh1) uci ba/sp2wxother end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 kn d9 ,07/ hj/e(uwljyiofct8x*ko7as when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the 8hjanielu dk 0c7k,y7t *(o/jx/fw9 oother string? ±    Hz

  What is the beat frequency if middl vtd,bod;i6 9 7:oihjze 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, while another (bran9-hdkvd xoltbc w /4: wm::w-nd 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 t:v4 tdk-/:bwlnmw9x:h w-co dhey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunh-1m bdgjz ,z2ing fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is thebdj ,-12zhmgz vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 wj +u1( qezs7p 8ytxf5Hz. 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: Recal8z7s 1xqfet( +5p yjuwl Eq. 11–13.]    Hz

  How many beats will be heard 0h 7v x mrirti(rn,t5a36,lxdif two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25rntht6lmr i3r 0i5d,xvx a7,(.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; w/ 1dt-u0+qncpryr ,cohen A and B are sounded together, a beat fu1,pct ny r-c/0 r+dqorequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker tqka (:oukge d8yo ua+iyu -: 5du;-w)and 3.50 m fr)a-uoq edwu-gd8yy 5 ;t( +a:uu k:kioom 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 herf gw:z+gl7,2e s ez(pars three beats 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 ? zs :(wglree+f,2pg z7   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. How many b)e-dqane 8pd3eats per second will be heard? (Assume T = 2e q-8edp3)dna0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15w91auz*hhhdr3 j/j7v 43brl1wat- bv 50 Hz when at rest. What frequency do you bdhj1vbt-w4rala3zu3 w791 h*vrjh/ 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 engine x0:w*r2 uc de-p +)fho i3ifekwhose siren emits at 1550 Hz moves at a spee:2x c3u 0fw)opi-ek+ f her*idd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sou: sdqjjw.ely e/u)e 35vb,ez m 7mh,c9rce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the twomc 3e,v5d j)/eyje,qz9wheul:. 7b sm 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 asbx2:q5p d6ais at rest and the other is moving toward the first at 15 m/s the driver at rest hearsqp: 5b2ds6ax a a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ret* +lj445sogeb*lzb iq urned from 5olb gblq*ezsi+4j* 4an 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 of 5 m/s As it flies, the bat emits an u(0jqckm;wx 2d82le hsltrasonic sound wave wijs2hq2d(x e; 0cwl mk8th frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppd v ; ko1bz+2va, o9xdgrtg8o+nun9;dler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a sec,bo;n aorz2 xgdu;++9ngt8d9 vo 1dkvond 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppnjszcd :mq:(3ose 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 artqm: (3z sc:ndjeries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using kmth)x/twj k q*4z s9d 6qfa57ultrasonic 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 emitjdqoi+ b(4y2is sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, 4ioij + (bqdy2
(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 eg2 j+rwzp/3 hspeed 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 xgce5: vhgp w-;s s++hwhere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the air5ss g-c:+vwh;xh +pge plane’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 pla ldm)oss 55)wgnet where the speed of sound is only about 35 m/s ) s5s5gdm wol)
(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 strike. 3bv6s9 plevcil8 c-rs the ocean. Determine the shock wave angle it producel8brv c6 p93v. isel-cs
(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 cm9hdb *0d,n0jixmx 3$/theta$ 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 +s- ic;ktx ynt,-,sup exactly 1.5 km above the ground flying f-tsnis,-t;ky, xuc+ paster than the speed of sound. By 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 fr6omga17k 3h byom the bottom of the boat, and then detects em76 abgkoh13ychoes. 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 ther jybqv0-( kvuxuttzm;i9(8 8u e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displa5s oys5 fz47p.a 4udxly called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which ars.zx7dy l5p a5u4sfo 4e 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 m -ib ltpi(qr0cu; fy17c1g7p close to the threshold of human hearing (0 dB)ppy7b-q0m1 ut(1riic7g l ;fc. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound leo(toc.3psaz54bht ni 8etrk ap+) 6 :+a1ifglvel when an 82-dB sound and an 87-dB sound are heard simultaneouz6f3 + gt5tl h4a:sn18a(ptk+aooci p )reib.sly?    dB

  The sound level 12.0 m from a loudspea r)mjdni8du(x63s .p s3)qby gker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all d(.b8x)djm d6p q)3rn gs iusy3irections?    W

  A stereo amplifier is rated at 150 W outi3npf// ofet17 be twzc9e.x4put at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wa1/7ce btx 3 4.ni9fezf/e owtptts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviun8+q3h5x )ftaua 2 tdces over their ears. Assume that the sound level of a jet airplan 5naa) tdt2f+xhu38u qe engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy1/zutn e)rw( hstems, 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 t+)ugnl: - s0k/ rufp ie5n4luro 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 rmkwbo c5 *br,) n7vk432 cm long between fixed points with a fundamental frequency of 440 Hz and k wo45k* 7crrbvm)bn,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 tube filled r;39bw wn-ehcgwyik a +uq* +917y qsnwith 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 watni+u 79 gy k1awn;wc*w+qqsr-bye39her 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 2as t;;ruc a+j:.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 fundametrc:a ;a +j;suntal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obseru2 s b*-gfss-n0,. k 8scpo2rqmz+cjt ved to resonate 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 tonek1(jw.2 f0qy*+ dhaoyo3ca yf in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidis 3 a(yj1ch2a koy*q.+dfwfy0otant 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 other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train 4d rvznlnw68fyd ,.(r is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency wh wr nyn fdv6d4zl(8,.ren the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you uhb5;x1e 0x3:+h iwes ghi:vu is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fasb::ex+s13wxhuh; e i05ugi hv t was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listemuifk tclo1/1o ov+z74q i;v9ning 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 th7fqo oi4l / ou1v1v+t9c mzk;ie straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Theew5q)fg*5:lgh;mncazcm2d o m 1i)h) shorter one is 2.40 m long. How long is c mg)cgm5io2d nf1wa e*l)h m)5qz;h:the other?    m

Two loudspeakers are at opposite ends of a railroad c6q1(ny/+ri(t0xzor t2g: j 5 wg dqyeuar as it moves past a statin:yj t(uw0yeg qx/2it zqor56gd1r+ (onary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorpt6lk+,k ;a zbta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directedak,b t+lkp;z6 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 speeq2t 3-5s0dai5mh 8cak 8hpngvd 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wa 5c giathdhpn5s2-k308 vaq8mve reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches uf.ulkn suwz0 v3k p6z;wskj -+u6fa0 t w3b1;a moth. The pulses are approximately 70bank0. 0l6sz1k3wfu-pw s f u 63t;vukjzw;u+.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?    m

The “alpenhorn” (Fig. 12–38) was once - ,k*fuqidz my0pow+3used 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 alpenhornm uify,0zk p wd*3+qo- must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can) g8yqk8qcw(;kkp fy) be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations k) y)( k88wg;q qfckypof the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, yz wg 4uz+7y-gslender aluminum rodg4-gw 7uy+zyz held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or 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 thdkh)g +-1 g7bag,1 sthf 1jkzfjk;j kkzt5b 97reshold of hearing for the human ear at a frequency of about 1000 Hz b5jh;-1+kkg s7gfdhfjb1 a1 ,g j9zttz)kk7kis $I_0$ = $1 \times10^{12 } W / m^2$ 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 Ma 6jdedt 1unc,5m5t+8z fq1farch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is t5e5c,z6 t8a +n frdm1 dqft1juhe plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbkvff93a f8e*w rm*ox+ oat 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