What is the evidence that sound travel u 9:dm grm9:j1v43bfg3 nxsfos as a wave?

What is the evidence that sound ts,a.bz+4a,w;kh k; l,vfptqis a form of energy?

Children sometimes play with a homemade 0ch,wnf2+0 n 2qwefaruy+df;“telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can b2d a ++qy,fr;ufwhfc20n0en we heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o0vs, 2gy 8kfz 9-v e;hirvtw0qr wavh9v ,wirgzfs02ek-y vvq0;8telength to change?

What evidence can you give that the speed of sound in air does notf9j9,xtzy qp/:s 4ncu v ))znd depend significantly on frequf: nzdqcy )us)tvzjpx,49/ 9n ency?

The voice of a person who has inhaled helium sou x0;poa4m rwbha25g95lh d(yhnds very high-pitched. Why?

How will the air temperature inw ce1q2c2:tjrv 2384n ikb gnh a room affect the pitch of organ pipes?

Explain how a tube mighttbg5iit )i(9x be used as a filter to reduce the amplitude of sounds int(95 g itibxi) various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mo z-s iysu)sek)4b jy/.ve up the fingerbo4s beus)/k -).sy jyziard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it bfx)l, e8fs ,lqut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Exp e8,llfq ,sfx)lain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats28sqhhktqty47o j 64 y can be said to be due to “interference in time.” Expy hkqj o s72tqt464hy8lain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points g8 7big3 y(5i agt/c3qhp w-o,gwt j2lD and C (where destructive and constructive interference occur) move farther ap iy 7 w38g-cq,hg tlb 5ti(g/pwo3gj2aart or closer together?

Traditional methods of protecting the hearing of people acqw,eej w0u* /61eoguzqg-e e 40s+cwho work in areas with very high noise levels have consisted mainly o*,+0quqeewzjac 0g/wgo64 ec e-u se1f efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Ea w isiv7u2kgm;e+agk+/ga2* e ch wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies fam+ 2a2 *g+wa /igve;sguekki 7rther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift 0t 9q7lk.qy) czjd-ojif the source and observer move in the same direction, with the same velocity? Explain. t-d.qc yq70zjo l9jk)

If a wind is blowingu uo0u9diu 1s-, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chdu0ou19 -uiusanged?

Figure 12–32 shows various positz/q :cxub3fl* w0em i cxm,1x7 xtiz8+ions of a child in motion on a swing. A monitor is blowing a whistle in fr7 m,i*xzu3i+m:c8x l1 tc/qw0f exbzxont of the child on the ground. At which 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 -a pta 4 kw2kvrnk7ks8a w36m)the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimws 4) r v2a8n37kkta6akwp-kmate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hear;txt, )lm,tyid k )bm3s the echo of the sound reflected from the ocean flmmx3itl ,k;ttbd ,)y) oor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at c68gujraj 2mjm) 7l/5hpbko9 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 abovr y 0:kf5y-.(r poywaa( wn3*gqk, tzqe a school of tuna on a foggy day. Without warning, an engine backfir-a*tpwqa0y.r(,r n kk:f(y y5gqow3ze occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The6yi(v/a 6n;dxohbmo siwd8 i 36vvk38 splash it makes when striking the water below iyoibh 63d/(8mvv k8ii6asvd3 n 6w;ox s heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone sod fpkly)*vofh: 0(:ztrike the concrete pavement. A momen klozy*:fpod 0v(f):ht later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dist*wxz (u05+etpb ngrz2 ance by the “5-second rule” for e z+z nu0gbtw(2*p 5rxestimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atg9b8 gjc 1c5v1vfzq, v 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 souuwv0aaiyt q8 e/n0y )4nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired s c6 cpg;mi 1davsct()2imultaneously at a certa6c 2da(mcvst) i;pgc1 in place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain q wc)oo9gnnlf;203l 5l) kdn udistance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level ngo)c u2l5lf lnd03;9)oqk nw would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 p: o .rcl6ecole2/gkwz+c39i dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgroun/e+eo :zi 6 rl9k2 .pclwcgc3od noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spea 83jpxt2nz4,2 q+ ce ykorp3r.n+so qbking in normal conversation. Use Table 12–2. Assume the sound spreads roughltz +3 4osnqjpn q2r.y8erp+ 3b2k,xco y 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 whoeu3ap dab8jp5 ;zb :n.e*a5qdse 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 250 W, while m(m -/qme ;jhs/0m //pxpazs rthe 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 connectmrzmx;qmjs me p/ /p0-a/h(s/ed 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 register f02x.l dorzen7qg/h1ed 130 dB when placed 2.8 m in front of a loudspeaker 2gq/or1zdxh7f . e 0lnon 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 di)/ww7 t6sy+b nf rkon.fference in sound level of 2.0 dB. What is the r )6swrnytwofkb n .7+/atio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the kx4d- os iqq6u( in,y4)tgz-cintensity increase? Increase by --cng itu4ozykxi q(s )q d,46a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa*oc4 hego1zj6cement amplitudes, but one has twice the frequency of the other. What is toz 4co*je61 hghe ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave i/bn n 4x p4ki7/is3oocn air that corresponds to a displacement s3xnk / cpn74ibooi/ 4amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudy;+ 6cd.z7 pfp2lokf p as a 100-Hz tone that has a 50-dB sound level? (See Fig.pl;. kcfd o+z2y7fp p6 12–6.)    dB

What are the lowest and highest frequencies that an epb7i7cn o,iz :ar can detect when the sound level 7 pnb o7ciz:i,is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is t;+ l xcmku;+irhe ratio ofiukm+;lr+;x c highest 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 a fundamental frequency of 440 Hz. The length of the+ psy+s:jj+g4n;fp tytjef:+ g np;4+ sjp+se vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental an ;;-p0gxyhtskge*u; rd+ay i0 d first three audible ov;dp0h-xgty r k*igy; uea;s 0+ertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across t. cocf)( 8uo2 y2jc is(llrq .t;gmn)hhe top of an empty soda bottle that is 18 cm deep, uir m2jfly.c.coqt) 8(h2ogsl c(n;) if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tu)1l: 1upn chxi;mulc ;be pipes spanning the range of human hearing (20 Hz to 20 kHz), ilh xc1m;c u;1:lnpu)what 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 thiru:ue qj 6.r50q l/f/nqiak/ ihd harmonic. What will be its fundamental frequency if it is fingered at a lengt a :l0jiqq/erh6k5n./qiuuf /h of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pla2c 8(lk +wmodlp4t0cl y E above middle C (+lckod l4ltpmcw( 802330 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 emiv3ch jdm*c4c6o v: d,tts middle C (262 Hz) when the tempeh*ocjc:m634 vct dd ,vrature 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 gx c+6pa;s)e3x grwf*20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthp-px8icnku y +)iece of the flute in Example 12–10 should the hole be that must be uncovered to play D ab i8)-p kx+ncuyove 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 Hz, 440 Hz, and 616 Hzv x:ima-*phr -, but not at any other frequ*irhpv m ax--:encies 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 long is open at both ends. It r+wn7c1 rjnxb *esonates at two successr7+ nxwjbnc1* ive 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 eqd2lj qxo.e5kjf4gd0y 7ix*(o(ac 0$^{\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 wi( 6)vawt a+ e)7o3)bthm /drxlpnzek *thin the audible range for a 2.14-m-long organ pe */ )temo)a)avt6 d (bw3phln7x z+rkipe at 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 th7qer6,w8s i ufe outside and is closed 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 youesq 78wiu6 r,fr 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 adjt vb* nv2o2m72tu;uun:e i2me*+ hx wjust two strings, one of which is sounding 440 Hz. How far off in frequency is t;:uv ovtuj2m2ue7 bxwi2 m2t *neh*+n he other string? ±    Hz

  What is the beat frequenc xz2.*ux in w+q)h sszx/1,xzwts;2b94y qlr vy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another /ydazzvu(nuv -qy hh(m01q2 - q3 plp)(brand X) operates at an unknown frequency. If neither whistle can be heard by hvqu) 3q(lh(dpy z0yn2 a1v-uqh-/pzmumans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whel p ca1zgs.k3np n- n/:tg:+wy igf*-xn sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the/in czf +px3gg n*w--pt1:gna:s .kyl vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to t2y1oyq6 vt(20(s qof czn;esdhe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be 2( y6vctyz0nqfd2e( ;oo ss1q the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard /6p*koxlqw+k9h4 nbd if two identical flutes each try to play middle C (262 Hz), but one*ndo9/pxlw b6q khk+4 is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Foranlny fr, /pr7s63y(ek 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 ryyn nrl6 (3eas,7pf/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 apai2l8tx9hmfmw no hmia0c; cbt)-:5. lrt. A person stands 3.00 m from one speaker and 3.50 m fr-imlc0tl)ih :5 f.;htac2nwmxom8 9 bom 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 ar4a y usee:q5 v:for6w*i*qb:be supposed to be vibrating at 132 Hz, but a piano tuner hear*ebayi4frs:b vuqo: 56*e:wqs 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 ?   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 wavelengtkwyv(aejz1mf,mbq w-6u: x 3,hs 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume w,wz3,-f6 ujy xmmvqk1a:e(bT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s y: .rj j41q g8bwfyfs5siren is 1550 Hz when at rest. What frequency do bf5.qgjrjw f814y:s y you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sireeovky) sc/f+ o b,mn50 k +)b ,om5sfenvy0o/cn emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcj5lz/n) bgl)ppla g:* e is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly theg pjb)/all*zp 5:g n)l 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 freqsmjvvun-v 5tm+:u)spt16n .x uency horn. When one is at rest and the other is moving toward the first at 15 msmjvtx v vs6.mpt nuu+1)-:n5/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 wave ipx) h:l.b yw1zb(;ces at 50.0 kHz and receives them returned from an object moving directly away from we1 yz)ixb.clp; b:(hit 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/snmu+q )vpvd593b 5 bzrpkb dh;x0/zv4 As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency q 5xh43nvdz05)puk9 bp v/ +zbm;rbdvdoes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplzgvezwr)0 b+c*6tvz bo. 1t dx b35qb4er experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played th1g .z+04e5o3vtv) bb6qwc x*dbzbzrt e 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 wavew0 bwlcl9wb9 -;7sivks to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arte99v-isbww; w7kc b0llries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavebj rv1j v18c7rs 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 windmnt(3 z 1l0zxv velocity is 12 m/s from the north, what frequency will observers h(n zx0t3zmlv 1ear 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 i;mq -,ni1w ckjts speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sj7mp;)yom(3.t: cut l2 m emltound is 310 m/s (a) What is the angle the sllmme ;jy)t.o2 7 t:pmuc (3mthock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the s1e11k.ysd j3fni+)prw jv+ jspeed of sound is of) 1j3.krejy npiss+1+ vjdw1 nly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine te)g82* umnhes he shock wave angle it produ)e h*emugns82 ces
(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 ip1zgtc8yq, th; x zl,4rsaq: mi)0 h;$/theta$ 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 gr(5*hl- ybgtxgvii0* s b0mgu+ound flying faster than the speed *y vuhgb0 0g+l* s bm(itg5xi-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 downwar 5:l19iyhu 7zcnz+7( tltlj x6m2bsihd from 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 hjyibnz7 m9 c i6xtl(z7t ls125h:+ luwater)?    s

  Approximately how many octaves are there in the human audk5u81o i5cphvjk( lk -ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displadhh4whwo8 e)ud 58j8a y called a sewer pipe symphony. It consists of many plastic pipes of various 84 h5dad 8w jeh)hu8owlengths, 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 o9kft5ipjkm* soy:33close to the threshold of human hearing (0 dB). What will be the sound kfk5om* p:93tyi 3soj level of 1000 such mosquitoes?    dB

  What is the resultant soy+e7gnr 38wgwep(l)w und level when an 82-dB sound and an 87-dB sound are heard eelwy 8 (r3w7ggn+)pwsimultaneously?    dB

  The sound level 12.0 m from a loudsp;gj r+:hpvw)( lw7aj((l ho4navx9 r jeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, asjo:a( ;xl((rvap wwgh7vr)ln +h9 jj4suming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1l jjnfkeau2v4 l3:5l6 000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watlf n le :v52lju643kajts at 15 kHz?    dB

  Workers around jet aircraft typically wear prot bxfm+maf5 *k8ective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 fbkam*+xf5 8mdB, 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 sys * kp0l 6-tnumafiou9k58-de gtems, 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 tu9 djxup6*ogb2q8bn ts(.a)v p ned 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 violin is 32 cm long between fixed points with a fundamf(kd6 kj6, f4kzk3ehkental frequency of 440 Hz and a mass per ud4f6j( kf63he, kkzkk nit 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 violz ;iy.z5mz+ bration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, y;5 +m.z lizozthe air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water 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 og* yim l)m*t*0r /ndz:+dcm i)dlj *naf mass 2.10 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 reson /l)+l**ac rzdnm*dm 0tjyidn) i:mg *ance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatqm 1om.8, srl b28stxse 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 to(ep z2*hd0 7665,iflwbkrpq4q otwnnne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the ftfl06 p7qd nepinz, (*qr2o 4h6wwbk5requency 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. Orf9 f8r e7u4xlne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is 9r 7 ff8elurx4the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is gg4 p0t0ofe*e -ch;lg 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant veloci-00lh4*g ;tgfepecg oty)?    m/s

  At a race track, you can estimate the sx;e ;rw qed,5apeed 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 bwre x5; aq;,edy a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, shk +r -g6gvt+z,ggin7+ e ia,hounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. H gtgahi++7 h,ri,+zvg kg-en 6ow long is the other?    m

Two loudspeakers are at opposite ends of a rail 9s0s2pi0rf qstuk0b )road 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,2f0sk0p bsu0tiq9r )s in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abos*jqn.83z j/ sw gf7xeth1nh;4x0d ujut 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrastdg8 wnxunh3/js;js4 0qjx7e*z f h 1.ound 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 towarwjmnhzbx)0b3a0 x7q/o rv v2q(:nqw )d 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 refleva)x0zqqw7jnqhb(b2/0)xn:3rv o mwcts off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth v 44aezzs5o7a. The aa4 svze74z5opulses are approximately 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 once used to send signals from one Alp-19lgv9 atxzmp n7 u* h(meq3kine village to another. Since lower freeq9ga3t z m*pu -vkhnxlm79 1(quency 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 listening can be compromised by the prese nru4dv 77:vzj5/ v:b0drleth nce of standing waves, which clz :trd4j:0 n7dv/be5 7uv rvhan cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long,m x:4rrlb 1f(x 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 to “sing,” or emit a clear, lou(4:brxl1 xfm rd, 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 ab9isvl jv+trlh9h, vhb+78m 9 bout 1000 Hz,ls rb+b9v9hth+ 9vhj v8m7il is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on ;a8p9 psf/j.fk hp;uj v)z-ufthe ground hears the sonic boom 1.5 min after /ahp8pj f9k .vfp-)j;f sz; uuthe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo.w9f;n 6 4o +gw g67bhzizkkwpat 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