What is the evidence 1tth;x c7o fp 6jhd,ot/42hnx that sound travels as a wave?

What is the evidence that sound is a r/;e,riq si+oform of energy?

Children sometimes play with a homemade w 8bwg(q1*y rhoix9 e0“telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child yxgh1r8 o( e q9ibw*w0speaks 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 air in6ns(3b+gsvp+ 2zmc w qto water, do you expect the frequency or wavelength tob+swqnc2s+ ( 3 z6pmgv change?

What evidence can you give that the speed of sound in air /ff4f ,p1ic d6- )pe)y7+oosjc kcahkid ur (.does not depend significantly dk+ e-6foj.suf,i ca)dr 7 4ycc hf/ipo(k) p1on frequency?

The voice of a person who has inhale l;hvwk+krc/:nrm 3 8gd helium sounds very high-pitched. Why?

How will the air temperature in a room affeh hejnn( 3e /)h hnjk4a:r0g6yct the pitch of organ pipes?

Explain how a tube might be used qmny( or1-9d kas a filter to reduce the amplitude of sounds in various frequency ranges. (An examy-m 9oqnd(r1k ple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movejz:wy*gft - tn+ pkt/, up the fingerbo:tw+y* ,k /fztn-pgt jard toward the bridge?

A noisy truck approaches you from behind a buiy0 qry 1rwpbee44x :u (r23yrrlding. 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 high-frequency noisere rb4pe(312rq 0xyuy4ry:wr. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due vx wya+htxg u;u-1(tnb/.z ++:q fcxp to “interference in space,” whereas beats can be said to be due to “interference in time.” Expla1t;hb+ /u ugcxn-: v xta+q y+wp.z(xfin.

In Fig. 12–16, if the frequency of the speakers were ln ptav;io*w -3,bei/e/qis(bowered, would the points D and C (whpv/nq *bewo3/ iist(i,e-ba; ere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the,tt 2ili,f3vx 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 relativ it,tvxl3fi2 ,ely 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 thoughnsz+vu:hakmy .phn. 3rr8)g b1r4e9nt of as a superposition of two sound waves with slightly di38 eh.s+9z rb:un1mrn.k arny)pg hv4 fferent frequencies, as in Fig. 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 move in the s1ok n ++ xp gmxsok(d2iqyul*af 6.-6hame direction, with the same velocp++axf-.s( 61lg o 62* hodkxnmqkuyiity? Explain.

If a wind is blowing, will tvg g ch7tw--ywytvci);0b)7tu3w5 o zhis alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity co37 yvb)uyw- -7w tgzg )0cc;vtih w5thanged?

Figure 12–32 shows various positions 9 7g , jkwqn0b4*cz3hznm(ropof a 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 ,kr mnzh*( g3oqc07wbj4z9pnE, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a l p7* 9fc 1ebgabg(-wmaihwj;1qlo*4 aake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She h-l7ocjw* fa ;1ah 4ba1pe* gqmb9wig(ears 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. He hea) 1wo sq +f.38kycnvnbrs the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and doev.)1koyqc+w8bs nf3 ns not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a. xio sd)u;0oet 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 rexth)3x hjvu7dhy;tq)4fk/7 uv)+c x0ed/hdrifting just above a school 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;j4 kv3d+)h q e7c0)hhu)fr/xu7 / xhxtty edv elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Thiqx l-u2.ble+ yymz ,7e splash it makes when striking the waterl+b-zyu 2xe lm7,yq.i below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, se0pqi h+j4l.hh gscoe 4,9oxv(es a huge stone strike the concrete pavement. A moment later two sounds are heard from the impacqcgi9 ov.xs ,o+(hplh44e0 hjt: 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 distance by the “5-se bt9k)z, yht mx,-dh0 a6j4jsecond rule” for estimating the distance from a lightning stt4zmdx0 b,tjh hjays, 6)e9-krike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pmyt-)nw l0u k:ain 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 ofc4bcdn(+ 8)7ei3t alf;s yplu a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound q5qzcmg3u php-),a/f level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: qcugf/pmqahp3 - ,z)5 Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equall(g *)8wosgd 8qn,xta) r4 arcpy noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captai()nd,wc8 q atp84)xrg s*or gan shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio on 7hil5fi z;l vmhq7 tk.24d9bf 58 dB, whereas for a CD player it is 95 dB. What is the ratio .fz9knvdb5 7lm7qt hi2ih 4;l of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output cgtbm6fr)o/.m-tp/ w of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughw-p)ogc tfrt6/.mm/bly 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 earjo;()epgl vch:qpv r:u 84xh( drum 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 rm 3 ek*)a3egb0 co*.zuwbjje2d;c1 kkated 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 a point 3.5 m from a loudspeaker connec e*3.2keabkecdg k jo3) 0*1jb;cmzwuted 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+tsf4x5 efr( e meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the srs+ fe(xt5 4eftage.
(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 deted1wri w2- qup2pejh 4-yl p,d6ct a difference in sound level of 2.0 dB. What is the ratio of q4rw l ,ij -6uepy-2wh2d1ppdthe amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trhn 4as.f/l0i0mhuz :i ipled, (a) by what factor will the intensity increase? Increase by a faclfn h:ma.h0z0u/si i4tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal ep-.; 4h-f(b q :pdt g,zwwudedisplacement amplitudes, but one has twice the frequency of the other. What is the ratio p4 dwp.qzt(:bd-we,u-g ;e fhof their intensities?   

  What would be the sound level (in dB) of a sound wave in air 5sroa3p4 tkgp*5aqw .y v(8f vthat corresponds to a displacement amplitude ofrk s(woga 3q5yvp4vfp.8 5*a t vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loude,swv4qm: d *yx4:wbx as a 100-Hz tone that has a 50-dB sound level? (Sx myv:e,: qwbs44xw *dee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soup/ ketn2 t:x(jfmkuc m -4j;8gnd level is 30 dB? (Seu;8 n(e-xmk/ pmc42f gtjk t:je Fig. 12–6.)

  Your auditory system can accommodate a huge range of soz /52heydtj bd2 1)wjfund levels. What is the ratio of highest/dj y2 h)fdj 1ebtw2z5 to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a viol)v ,nho f m:xv;lick.8in has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass ;8 k.xclnvv:ih m)fo,of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 gt;4 ++wic8gyfx ryhta7mait+3ct +7cm long. What are the fundamental and first three audible overtones if a7;itxy whamfg++tct 4rt8+ gcy7+3ithe 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 blowing across the top of ra s:u1o5aj4opv72*+qy q8 lcc: ryop2rh c)ban empty soda bottle that is 18 cm deep, c2+qr*q87 s :y)h1ur5 abo:ao rlcocv42j pypif 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 *g tyfi(9 3exwpipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the (x*tge9iwf 3 yrange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What wi,hmu-lc*-b udxs;;ov5 u7)z bfep, wvll be its fundamental frequency if it is fingered at a length of only 60% of its original length? ;d-lbp,), ;sczb v-fvx hum57woueu *   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abojvgemf:8 s.n8 ve middle C (j8vf.g: es8m n330 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 orga53xqws 4f k3 noetfn79n pipe that emits middle C (262 Hz) when t35fw xsf7kon4e t nq39he 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 (x e5bmt+7l(ke b5t qr20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of t2cuv(*3llywb-8ni d) g6 c nfjhe flute in Example 12–10 should the hole be that must be uncovered to play D above middle C ayc3c)vjb dl 68ngwl( 2n f*u-it 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,f 3)+r1dv glf f/hr+y04p pnwj but not at any other frequencies in between. (a) Show why this is an open or a vgfrn/ffpw d +3l )0p41rjyh +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 end.7vvff5 kee*n s. It resonates at two successive harm5 vv k.7nfeef*onics of frequencies 275 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 ar )46e:)oma q 3dccbt$^{\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 presensnis; +;8vs okt within the audible range for a 2.14-m-long organ pip;kvs +s8 ios;ne at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximaosqgq yem/1- 8 g;ok1ptely 2.5 cm long. It is open to the outside and is eq18ko 1/-gog;ysmq pclosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust th8s/;cj h k2cv48fy hry qr59awo strings, one of which is sounding 440 Hz. How far of;h2 qj/ar8c49ks8h y f5vchryf in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (26z(z,e+) : .2-rjpmd;cqmu+mqocy oj u2 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 (brand X) bvz-i0tg8fym f( f*5 uoperates 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 simultaneob f0 fu-8(f*mytigz 5vusly, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 bea9w:w ;ypjg6ayts/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 frequency of the string? Explain your rwaywg6;j 9py: easoning.    Hz

  Two violin strings are tuned to the sam igr*bm rb 6e3pkb(ij,,i p,s1e frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequepb3(gs 61b *irike,j,imb, prncy heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mvg d +u *3s1neinus0ct 7og6.uv/;xyjiddle C (262 Hz), but one is at 5.0°C and the otu d0seiguv ;1 u v*/yxjsnog.6c3n7 t+her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whsjyt c-zq6( 6nj6-adken A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are soundnyda-cqtj j(-ksz6 66ed 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 3.0y4o:y q9 ux:jqkqde1p:x -,ys0 m from one speaker and 3.50 m from the otheqj9e-y y,1:xsxo:: kqp d y4qur.
(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 h)t.;x4li ut.ts .8jlnjl5s brears three beats every 2.0 s when they are playe5l8bn .s)rj. jt;s 4 uilxtt.ld 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 wavelengt3 n zh;a2gelb63y/g db 3aqly2hs 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T;2 blz y dha6b/a3qy32 ggln3e = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain c1gu1iewf*da3nb .h e;, dm/ yfire engine’s siren is 1550 Hz when at rest. What frequency do you detect iw* n uf1ed,bmi gcy e3ha1./d;f 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 k0lojvy2inymdc2 o 1lq*1/r3fire engine whose siren emits at 1550 Hz movc /*yyr3donqv212l l10i mj koes 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 souki54z t,nqm-:qymym)yv. ) o2 mj4zjurce is moving toward you at 15 m/s versus y:itvmzqj))25m y4ym -knqz4m ouy,j.ou moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whek,e*)ttip*kon8 d: -67sew -y refbynn one is at rest and *be r7 os6ykte-n kf,y*i-d8: ntpe )wthe other 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 at 50.0 kHz and r0 ded-: pyiai9ut 4zmosm2qs,o :e7/ eeceives them returned from an object moving directly away from it at 25 m/s What is the receiv:eusetp i-,dm sy4z07aoq2 e9o i:/dm ed sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 6)wri+clgt*ec 8 b9fv5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in t+ *lgcew8 )trbi9 c6vfhe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments,/j:c re*bc,fg3 ) obc+i*mkoi 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 heard if the train car approached the stati oo+fkbi)j **m:g /bccre,3cion at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to ho r,gjem1d(9measure 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 expec1rj9,( deghomted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wave m8ufmt9a vn ywt3t+4cfow.b*+9wn7ls 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 velocittlr3; wwm-ih) y is 12 m/s fr)rhwlmwi ;3t-om the north, what frequency will 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 on land if its speed at 2 maozajl2;sc r e8r2yj 1p;g6/0 $^{\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 isrqykgtk(av4 .5b :1ew 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motbk vg5 :ey 4a.1(wtrkqion?    $^{\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 ea zas+ ;whsfru cg,02fn1k 6ev2s9f) thin atmosphere of a planet where the speed of sound is only about 35 m/s evncr60s;1+k zw uhf22e 9s fsgaa) f,
(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 strik26mzl gku /zza 9b/:vfes the ocean. Determine the shock wave angle it l9 a :mgfz/6 kbz2u/zvproduces
(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 /r1,e.ea if5t2na4vl0oc r b1z0(eyz qvm8f r $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a fc1rg t oxmcqt; .l .f-v::rj6plane exactly 1.5 km above the ground flying faster thao -1..fr ftj;v6xt: :mlcqrgc n 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 soue/6xut jdc/tx 5 xf34s9ic9ghnd pulses downward from9c5x3j6ietx u/9/ cgfs4h dtx the bottom of the boat, and then detects echoes. 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 octave6zrx zj4 k;vp+s are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of m6vkag5x()n dd 2pp3+okktv6 jany plastic pipes of va)jkv+(ppv 6dd kt2nak3g 6xo5rious 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 threshold of 1ztddf 0j 0rk1human hearing (0 dB0tkjdr01z d 1f). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sounczl2*-yol p9m d level when an 82-dB sound and an 87-dB sound are healopm zl2*- cy9rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dcevr88x yoj67B. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direcy6je87c voxr8tions?    W

  A stereo amplifier is rated at 150 W ou 9ozm1i2 yh+ yk*wfzr)tput at 1000 Hz. The power output drops by zy z1yof+wr*m 9hk) i210 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thety qw:h3 5zi 19vej*ifir ears. Assume that the sound level of a jet airpla3* yevt: qzfi1i59h wjne 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 systems, the gain, v* lpfe5zw0+chf6 )was9w k n4$\beta$ 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 alzko +8z2f mmm f3dtv5e01l1 k 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 btp27lh ;f*7lm wgu po.etween fixed points with a fundamental frequency of 440 Hz and a maspflp*tu7ho .mg7w ;l2s 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 tub4ytu zgqw-) vm5q+sj3e 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 wiuqy+43mw-z gs t5qvj) th 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 is open axns-pzjpzry,zezjz 7, z 85 u9eg4m*2t 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 harmonic in th2g7p54u xpzz zjm9ee n,, jzyz *8srz-e tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lool4d5fl5 qjn s wmt71i4p ($\frac{1}{2}\lambda$) 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 tj 04a:b9tb 6-qs dtrfghe 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound levbr d690t :qbsa tfj-g4el 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 whist9fd9q9)hs n mtk 21bymles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other traimkqd92bm )hsnf1 t9y9n approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you ismekukdd iji ;2+:h 5,q 538 Hz. After it passes you, its frequency is measured as 486;d, e+5: kik2 iquhjmd Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can esu rgg *)f;j7wftimate the speed of cars 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 ; *j rwug)ff7ggoes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beatwa2 :sfcn rd (qpng.64 frequency of 11 Hz. The shorter one is 2.40 m long. How long wnaqd2ngsr6.c fp:(4 is the other?    m

Two loudspeakers are at opposite ends of tt6j e4* hi4wma railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (bhwtmie*t46j4 ) 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 ps0)k+ krf:uk mhb4g6 in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directrks0m )+6p4hbg : ukkfed 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 mothi(dq(-h 2g for9jd h/u 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 wave reflects off the mhru 29dhq/d(fji(o - goth?    kHz

  A bat emits a series of high freque0zyrk(ay86fqns)96rt( fr x fncy sound pulses as it approaches a moth. The pulses are approximatr) (kzr 6 sy(86xntafyq0f9frely 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was oiw .(bpg 4sq6ru lb)vth 5,u*qh uu4+once used to send signals from one Alpine village to another. Since lohq ,hbso6ruv g uq*bpw4l+i 4t)5u(. uwer frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listlxylg5zi( bd+k4 m l7-ening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m widm+ld-( k gz7l5lb4iyxe, 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 ax5 vl dt9u/wlrr2jp,5 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 be made jtdl59vu/r5pw2r x,lto “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 frequency of abb7qii7k wet47 out 100qkiei w47 tb770 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 obs*9q*t+osx q deerver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planxe *o*d t+9qqse’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isf 6a* x-.bdjdl 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