What is the evidence that s2,mquc30(gr5 zrx jz tound travels as a wave?

What is the evidence th a,7)z7pelb2/nn )l89ykjkji; otf ioat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to t0+ j8ppqikelb7v ge.z)9 0ruehe bottoms of two paper cups. When the string is stretchedpz9 . ek8)ee 0luv7q+0grpji b 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 fro0(g8ybdifhw7c/ki zd4:ibh8 (1e;u 4v n jibgm air into water, do you expect the frequency or wavelengthiw0:he1g(u (h ji48bc4vk/ibgb; d87y nidf z to change?

What evidence can you give that the speed of sound in air does not depenia3wyr28vi xg-rrs8v5 08e,u qg hj2f d significan ig2uri8qr 0 f32hw5 -vxsy,88rjvegatly on frequency?

The voice of a person who has inhxf6sgieu96cg .u x5c ;o2wri 54+jphsaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the piw jwitwb8fwu-qz1s n1 fb2 +-(tch of organ pipes?

Explain how a tube might be used as a kbu spyjn 1 5 1ge(2zegy6:kq,filter to reduce the amplitude of sounds in various frequency ranges. (An exampy p5qe61 (ygkj12 z:ungb sk,ele is a car muffler.)

Why are the frets on a guiyd6b(3g+grb*zx 3d9 d(o0ugqhy:bpk tar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge? yz 3kg(*6 +hd3q: bb0upgog ryb(xdd 9

A noisy truck approaches you from behind a building. Initially you hear i57w 58t5kedx bqrvh,l t but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section k5hq,tvb8x r5l5we7d11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas b;00zatmuz -dveats can be said to be dudma -t0zu;0z ve to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wedpo9d fb1 1l1nsiv/ot0ikf+. re lowered, would the points D and C (where destructive andv0io o k9s ntpb+ffd /1i1.dl1 constructive interference occur) move farther apart or closer together?

Traditional methods of protecting thee5orq 8h: *oey hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. oyreh *q eo58: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 showuq a m*8cwjr++f6 q1k3vv2q pjn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig8cj1pmu*fq q26vqw+r 3k j +va. 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 sou zao),x 0dtpw4. 4tngacxy/i 4rce and observer move in the same direction, with the same velocity? Explain./ ax zcgia wp)ntxd4,440yt.o

If a wind is blowing, will this alter the frequency of the sound he49i,2rvfta)yk0,n(j+wl o s 3p fsdhoard by a person atfjyo ,2(sa0t4nwo )kivd3sf lr,+9hp rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monijm 7q*1*xj hyitor 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 whisj*y 7*ihj xq1mtle? Explain your reasoning.

  A hiker determines the length of a lakexpo9*nvf xw:2 he j7 uhg;k3p4 by listening for the echo of her shout reflected by a cliff at the far end of the p9fxk:v3 7h4e2;*ojgnx uhw p lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.5zxx(u hnvw 92 He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantxw( h x9un5z2vly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelende5u.r 5pirzlp8s6nda 72f 5x gths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a a m 1bb;s*qsc/i: )wcts/.uxvfoggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–3cws msbtu/c :/b1).v ;i*sa qx3). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whtw:6d q ylsb.oea/e 6er.r 2s,en striking the water below is heard 3.5 s al /yo. er2b 66sree.wd: q,tslater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone st7fjj 8 s,(oi4 qp3gjjcrike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s ifcqjp ,4jg o8(3j j7sapart. 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-seco w7to :lmy9hb*q;zh*ynd rule” for estimating t z :t9y7bw yhh*mo;*qlhe distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lenncnmgb86z88a ni 326.wxtn mvel 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 levr,a v:ri0( dg q)tdvv959hpxh el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously j cc* 2+siaq gm2heu.gly+n 91at a certain place, what will be the sound level if only onjc9u*2ahqng+. 1cei2 +gsm l ye is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from q7ac3 ;9p 2tkb nb)- mji,getran airplane with four equally noisy jet engines is experiencing 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, nota;it 9nberm3ckp 2,)-q7bgtj dB’s.]    dB

  A cassette player is sapz7n ipj8.w t 0(h:2su uqqal;id to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is 8.nwjl paps; qu z7ih0 2tu(:qthe ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outputbp(r g 5 fx-ix.il4 va43f9yfn of sound from a person speaking in normal conversation. Use Table 12–2. f4f ygl.vbnf(4 -ai3p95 rixxAssume the sound spreads 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 aretglndza q3(m*-b d+4za 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 250 5-y p ook:po(jb2jv;b W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you woulobkp-ob(vj jopy2; :5d 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 dabb);7*x bu)g veb; nqfyoew,l1vwp7: 0 +ns sB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on y7q0 , :ebu+wnb7ba;)g pv )fvwlb1 nssx;*oethe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. p7qq ;3 w*(nen+nddvgWhat is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectindvpn +gnq3(*d w;7e qon 11–9.]$\approx$   

  If the amplitude of a sound ljuw)jl9 95t ;l;df kva/o fw-wave is tripled, (a) by what factor will the intensity incref - ;jl9av9 llkt5wo) /udj;fwase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have ,/sbj--r i(jow (2/dl6xk1w wtm jwal equal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of th2j wswdj1 w(k/j-lml(a,/ox-6 riwtb eir intensities?   

  What would be the sound level (in dB) of a sound wave in air tva )4b9efhi1+ h 7mkdp+q )ygso3v + lq78zsuihat corresponds to a displacement amplitude of 9bq7zas)1pq+kovh)fs4 h v7mi8 3ly u i+e+dgvibrating 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 tonngi*m8 h ) ohdhw65gc1s9 :yxne that has a 50-8o w9hhni6sgcn) mx*h 1gdy5:dB sound level? (See Fig. 12–6.)    dB

What are the lowest and hewaw x p(b(;w*h d dje-;o6k,bighest frequencies that an ear can detect when the sound level is 30 d;j 6xd-(;we w,(oabekbp*hd wB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soub /r9f* ngnsy-fmc/t.nd levels. What is the ratio of higheg/ffn/s*mt9r -y cb .nst to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has aiwv(m: hi7cg9 c7l 8hc fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 87l(7hiw cchm i :g9vc0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are tx/3nbg 7xqfc9-,wy1o r:xggkhe fundamental and first three audible overtones if thec 1 o fr7wb:9y3x/xgng,k qx-g 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 wopbwwp 1ar 7 hn+pgzdw3 8bb;w2uyp:97uld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube? 7pgh 2nbrpw1bw ;wp 9p:awb 3 +yu87dz   Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning l h*s(w9;c oja2 d;)lsw)izrbthe range of human hearing (20 Hz to 20 kHz), 2ha;li cjs;rd(9w))o*bl z wswhat would be the range 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 wm axe:r tj19xvd8h(n, ill be its fundamental frequency i ,v :nd1hr9mxxje(t8a f it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle c +a;/d zm9xt 3cybxi29lh9 fuC (t2 z/iblc9x+99u;dm hx3f yac330 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 4cw,)due28y ,jpzugf an open organ pipe that emits middle C (262 Hz) when the temperature , 8,u2zy4f)dwgpceju 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 at3bd*q7w f v/dg 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 h r 3nw19wp2p3 nj:lmqbole be that must be uncovw p :rn2w3 bj3nmlp19qered to play 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 resonate at 264 rjm *q/o)qwv6mz ey;9Hz, 440 Hz, and 616 Hz, but not at any other frequenc 6m;qw9zq*o vyj/m)er ies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m-hd2 o5y.;m4hjaez5pojdq*p long is open at both ends. It resonates at two succe- ;5jh4.y5*m2d dopoaqj p hzessive harmonics 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 ha fdtm8m66,xo5 q)u ,u-r7y ;dzqy pq$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14cfxdj3rj ; y j*uk:j14-m-long organ pipe ac; j:j1rjxd*k34yjuf t 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 open to 6j0ha mztrl q4 ;aqk45(;im mbthe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible rangemm qi (q5z ;jb4htamlrk60a;4) 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 e p-bmxp/-r g9hvery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. Hog9mph x /b--prw far off in frequency is the other string? ±    Hz

  What is the beat freqn4am0 d i*rvb1fbnzk1i w 2r:m;h-.q euency 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 t zuq. *ev1l.boperates 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 o1.. zel*tv ubqccurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whewhj0mxiev:z 3 lv8(f9 n sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 3550j v(zew:ifxmv3 89hl -Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensiokbz/nfe* o cu6hfr14c*w i 17rn in one strinkrco/ * ebcf hi*u16174fw rnzg is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each trpr1lu2 i8v 2p(hfa ydt3pq+ xu93l5 i p-i+mrny to play middle C (262 Hz), but one is at 5.0°C and the o+(- n8vpfitu +rphdua325 291pyi m3liplq rxther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning:(tb;duv 4n1n1eo f pk forks, A, B, and C. Fork 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 possible when A anu1e:1 ( f vd;tbpkno4nd C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80npvb,q,-k wh6 blh50c 8cqsv; m apart. A person stands 3.00 m from one speaker and 3.50 m from l;8n p -vsc6 h5q ,h0c,bqwbkvthe 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 vtb(yxypb+u:m v. g9b v3/,,4ovhgxi cx7 vn.i ibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must begmvn4: y/ viv7ig bb9ub(.x.3,vhx +,ctyx op 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 z9h4rl uqnc rd;86*mewavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Asshcqe 48zlmr;r9*d6n u ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenu-*sd6mu1hm ,zew 6v scy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detecuzws,vmdms1 - e*u66 ht 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 freu (krrs m50q8wmn46jld 0hbd*quency do you detect if a fire engine whose siren emits at 1550 Hz moves at ank(0lb 8m*mru 5 rs6jhd40dwq speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 200 hbw-s69hz m) ogm*s/o0-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two b-m9gh*h6ss oz/) omwfrequencies 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 fra)3uh2y* ge vboz/2 igequency horn. When one is at rest and the 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)*2 ai2yzveu gh gb3o/ the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoni f3pa, s): g8crrnwjpr+mva8+c sound waves at 50.0 kHz and receives them returned from an object moving directly awwa +nr)gv3arm88cs :pfjr, +p ay 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 A c7x4v saci 3,.)k2wyu ivfr0ns it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fre2 c4,i .va wf0siu y7vrkc)n3xquency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expericcnq bz0w0cxx+iy xc9(6 r *fse oxs6-)xt3, yments, 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 xw-9 fc x3 r+yn0zxxcobyscs *xq,6)(te6 i0ccar approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-fll i1r.4iordt 1bpd0tc +,xjp*ow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing ipo tijt1p,*4+ r.0ld 1rdx bcin large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonil)5k,c gek z/qc 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 s 56f,i ; ba6fyd*aj 4hlty9pr5y 2ujqkound of frequency 570 Hz. When the wind velocity is 12 m/s from the north,yfjabp; ra y 2k5tyhiqd9,f4 56ju6*l 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 l.. fen2q2 ,i:uxs jpyat 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 sp 5mcag t1sov53ct26 xfeed of sound is 310 m/s (a) What is the angle the shock 6535cv1sgafcx t 2mt owave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soujvfu)3f g -dyk/p(yp 8nd is only about 35 ujgd - fyy83p p(/fk)vm/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave angl .(;3 q1kc8 e gtp8hqf4lxhjcwwo9f*ae it produceahww8g.k1*f xq3oh ;l ecp (9c8q4fj ts
(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 5.5kt edv14f u4dmcom$/theta$ 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 flc seh./3ve e*h7grv* mying faster than the speed of sound. By the time you hear the sonic boom, the plane has travele *erc3h*vv/h msge7.ed 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 15oxu dmo3y:oiv0fn ;ps7 oc. device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designedp:1 c0yo.7ov3o;xmou d5 f nis to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audjt)8k 9pn x*rnkm; sk;ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display caly)qo :q ;+aewcx)54phh/ xvjoled a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bothoe)p: q 4o/ )hcxjyhvaq;w5x+ 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 thenq2sao;ys btbe7*4 jkc y86o+ threshold of human hearing (0 dB). What will be the sound level ose2o6bt jksc8+* qnayy;7ob 4f 1000 such mosquitoes?    dB

  What is the resultant sound level when igfwc.;o6fp (an 82-dB sound and an 87-dB sound are heard simultan( f6 gfwoip.;ceously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whan tbzb00)b4nr-sdb2 gt is the acoust)b nz-gbstrd 0b20b4 nic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated atc-,wx -dzi 5 4s vpfuue1*ls8i 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? e1z d,cxs*5ufv4li 8ps - ui-w   dB

  Workers around jet airc45h*; evqil +z8tydvfraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unp qvedi58* h;tlvyz4+frotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatr.keimk0r0, /oa3t(l, kby seions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is 3z2dbddtr rv0vji)2 ky;z.z,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 violifu- euq k5-fh2fj1+0uubq9 t ln is 32 cm long between fixed points with a fundamental f5+ qjf91tkuql-bu- 0e u f2uhfrequency of 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 open tube filled with wa7+qai3 kw(,5 gwgz gjgp3od*tter (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 theo*5qzw+3a , t73pi wgdj gg(gk 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 ope i1 2p8v80+v0urwecxius* wjdn at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thirddiie8+0 p*u jur1c0v2x8 wwv s harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observ *hx5vqi/ozb0 ed 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 tone in;ngvl 44ybkp 46j7cub the 500–1000-Hz range coming from two sources. The sound is loudeslgbn4y;u6 bv4j k 7p4ct at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One traw-laa*)h .abv) t5xknt)c;ydin is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traitc) a;adynav.w5kh )-x)*l tbn?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aft o9qy h4wr)0ewd izxe4 g1,1d qv(zt.cer it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocitd) (hy4cqgz14 .o9,tr deiwxq1vwz e0y)?    m/s

  At a race track, you ce db95e.yr9ayan estimate 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) as9ary 59de.ye b it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz2c 5x u/inmv+b. The shorter one is 2.40 m long. How long isvcum5 b x/ni+2 the other?    m

Two loudspeakers are at oppositel-a,tht4 zl 4l 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 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 hearszh,-4latt l l4 the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally aboutwms*ija(4 zw; 0.32 m/s what beat frequency would you exp;j (wm4aws* ziect if 5.50-MHz ultrasound waves were directed 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 toward thelmju n+-s hb3*3 +* g3tdcufud bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What +d3b-fd cl3s+ *jn3u gtm*uhuis the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series 2g l(t2 7twfyvlj 0we4of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How fart7lv 2 0w2lfw4yj (gte 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 used to sec tuu(rf;1.rhi-m *asnd signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown 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, a .s(;-f*riahmcr 1 utund which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stant/gyb9d 66- ghzy r5evding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living - 96 rvg6 dzht5egbyy/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, a8 8d1 n7lxhoacalled “singing rods,” involves a long, slender aluminum rohdaaxno8 7 18ld 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 threshold o*cw4xl9psra a7v7fkhsv8,/ s f hearing for the human ear at a frequency of about 1000 Hz rwpas7s9*vk8 7 sx /hv4f a,clis $I_0$ = $1 \times10^{12 } W / m^2$ 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. Ankag e0h6heo hap 9a+e+;e6a3b observer on the ground hears the sonic boom 1.5 min after the plane passes directly overheha;6e e3 epkh+ 0ha9 aga6e+boad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 mli he:m /qw 5):t20y8xgcn esalw ,+y$^{\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