What is the evidence that sound tovp-1d1+igul ravels as a wave?

What is the evidence th*tun.b/q( c lms c-bbw(,tje k+-ot; oat sound is a form of energy?

Children sometimes play with a homemade “te+779i teae xggsx p8q(lephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the otheeiq8+ a7sx extg7 g9(pr.

When a sound wave passes from air into water, do you expect the frequency(l jy8;1wi)m 9u3gsovyv x d p0.h;gqt or wavelength to chang 9mv3su;g. 8(jygw v0tl 1p;ixhq)dyoe?

What evidence can you give that the speed of sound in air does not dej*8* ,r6c. f1ahjnm,bd g foqapend significantlyd1 8qg.cr*6jfnbo ,ahf jm*a , on frequency?

The voice of a person who has inhaled helium sounds very high-pitcazfn5s j l.. ig50jnk/hed. Why?

How will the air temperature in a room affect the pitch 69 qf1v ,wu+goi6 xcbqof organ pipes?

Explain how a tube might be used as a filter to reduc 0v; ,ik;1+u ctxttcvce the amplitude of sounds in various frequency ruitv;c; v1,+0tkcxc tanges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you moveg49bb9rf 6imqwol .- a up the fingerboard toward the a g6bw.o4ql fr-i9m 9bbridge?

A noisy truck approaches you from behind a building. Initially y twd: m,qdllk(jgm967,(yf;g z pw(nrou 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 noise. Explain. [Hint: See wydzr(d,9 wkfm mlpq j ,g:ltg (;76(nSection 11–15 on diffraction.]

Standing waves can be said to be due to “interf8ee8 9+jeov*cn jqo5z, c oj:ebx*f 2ference in space,” whereas beats can be said to be due to “interference i58n+qbfv:e2j ,oo 8jf e9 ceecj**oxzn time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would t6osrurtbgr7wd5b8j.d k*4n k( 0hp;vhe points D and C (where destructive and constructive interferen 8thdrgdbjr b wrp n7k(4*o6uk;5.s0vce occur) move farther apart or closer together?

Traditional methods of protecting the he8j ey(oao:9nnaring of people who work in areas with very high noise levels have consisted mainly of efoyoe8a (nn9 :jforts 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 Fiig/jk 9zx()p ig. 12–31. Each wave can be thought of as a superposition of two sound waves wi 9/p)zjk( xigith slightly different 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 same direction, n 9h7nm8rr(cr-s80zredh ; xu with ( mhr unr9n8x7 ehc;8rr0 -zdsthe same velocity? Explain.

If a wind is blowing, will this alter the frequency of th,.tv4ny7li :kxool2 kk 6s +uce sound heard by a person at rest with respect to the source? Is the wavelength or k+o7yv o.knk t6,cu xs4i:l2lvelocity changed?

Figure 12–32 shows various positions of a cr s9 vla,fr, sg0xyv+-hild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explas9, y+vs x-gr,0 alfvrin your reasoning.

  A hiker determines the lennydes 4 9r 5,xcya)9cbgth of a lake by listening for the echo of her shout rye5n sdb),rcac49x9yeflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wa 2uw*250bqpsz, ip4in)bgn gg h/ptl9terline. 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 significanbnw2qb 9,g*z ugs0i igp2 4ht5pnp/l)tly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a w7.dqtd p6da;t 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 foggalbjcq;i/ bjx4 lh 3,x 9r;ke4y day. Without warning, an rqchxb 49a/lk j,;xi bej;34lengine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fro7 3zs76c rsvuo1m.h/aeog r1 rm the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the ce1ao/z6c hr.7vs1ro gur 37m sliff?    m

  A person, with his ear to thq*hxk6a qwvt v 72gw60 ra 6hbbz(mx*+e ground, sees a huge stone strike the concrete pavement. A moment later2h6vz6rkh xwx a 7mb+*gt qbvwq*(06a 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 oviey+*dn qo86yer one mile of distance by the “5-second rule” for estimating the distance from a lightninoq 8y+dy n6ie*g strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitw2r 5,qpc9vtsy)xki w2 - dty/y of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose0+utmzre v5zou 2wx4- intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sibflshjv 91+, /onh 6,f0 i (c 3ud/rbgxzqgi*tmultaneously at a certain place, hb/b ijnug* fz+ 13fgh xso,t i/q0r,6d9c(lv what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain disg djwp)rsxm0- ,eu (3 :q:ylhttance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience i u jmd( qex )h::ywl,gtpr3s0-f 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-nois lmyw6lw*9(awfnaj( fz t;5c1e ratio of 58 dB, whereas for a CD playe6m1c;(tyw wzjlffa a(n*l9w5 r it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of souq ssp) e956;4f bl(uppijon,ze lep9-nd from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centep6en;9 qpl49sflp)e5os j ue p,(-izbred 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 area is 9qthe;igo f ul.t 0)c;x s((nf$5 \times10^{ -5} m^2$ (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 the m6m a9 clj2k -hfet+pe.tb mo+ 4x3swk7ore modest amplifier B is rated at 40 W. (a) Estimate the sound levj9.+ttsw k2xp - 4b kf3m aco7mh+6eleel in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB(ew cp muz2d+t6slm0 5(a )teb when placed 2.8 m in front of a loudspeaker on the stag6ztw (t b(e5d0mlp+e mua)2s ce.
(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 dBs+uo(oex :n4f8suomv6v7qm8 . What is the ratiofx s:vu omou8v(7 6qs4m8e +on of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sounn1+ko6 kuimc-d wave is tripled, (a) by what factor will the intensity increase? Increase by a fac mon6-+u1kic ktor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one x :h:kh:ww0b/zkht f* has twice the frequehhh/z: w*0f t xw:kb:kncy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that7be8al e(b j4u corresponds to a displacement amplitude of vibrating air molecules of 0.138l4jabb uee7( mm at 300 Hz?    dB

  A 6000-Hz tone must have what sj3h;mk11i0, khxwe b gound level to seem as loud as a 100-Hz tone that has a 50-dB soueg xw,1b0khim ;h 3j1knd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cansuke; 6tjri ; s8a79jp 0dkohw)tmt2: detect when the sound level is 30 d h2mwrs )itdjk:; e0u jpkt7os69a;t8B? (See Fig. 12–6.)

  Your auditory system can accommodate a huge r8hl-8y kn*ebtange of sound levels. What is the ratio of highest to lowest inten*y eblk88nth- sity 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 fun -iviba/sl;xg rr mcs73j0yld 5/ 0en3damental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensilg-vdeixa 0 /3 mr ny;jcbr7i0/s5l3s on must the string be placed?    N

  An organ pipe is 112 cm long. Wha*6pl ,dz53- mzwwp9 j4cjza*k; x ddkct are the fundamental and first three audible overtones if the dk- x*,wkc djp*63 wpd5z4cz9 lmzj;apipe 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 freqs6sxw 2oei re3zbh7k (bg0**lkz u.0 tuency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assu.ez*72eso(*l b k 3guki6tz0wxsr bh0 med 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-tube pipes spanning the ran; xy k(m8(px5;qgo icuico.1hge of human hearing (20 Hz to 20 kHz), wha p.mkuqh;;x( (g iix5c1ocyo8t 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 freq( onw2-uavjowfr 60 0quency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingeredr( uo0jqwf an6-wvo0 2 at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 mm,b) xjw t8dr)yd);s(xhkwj3 o:o - wr long and is tuned to play E above middle C (330 Hz). b)w t kxy)( r;om -w,)jxohs:r8w3djd
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits midu tthsn d+y8puu4hb c33(g82xdle C (262 Hz) when the t u34hcsb3d+x2 n8g(8 htuty puemperature 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 bu ;tzc,hdemv8.rm /( 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofjspf;5c 2 bei( the flute in Example 12–10 should the hole be that must be uncovered to play D above c j5fb pe2(s;imiddle 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 piwoxz zie c62xes,6c/*pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed p,zwccoz6x*e 2is6x/e ipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m lon4.n cqll-k5 v)oiymh r9q b(dh c8o6,bg is open at both ends. It resonates at two successive harmonics of f4 8n)hd.kc( yb6olhq o9 5br,i lq-cvmrequencies 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 -gir-l1jq5 :r ry1eca$^{\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 audibld )twhe+ .+ns47whg hye range for a 2.14-m-long organ pipe at 20 d+ wh) g7yw+hht4.ens$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apprxd/ kf;zs0tuiim c f-n4.en3;oximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing knfe;4i ;-cnxiz/fms3. u0dt 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 adjumnvaw2jz )h 9)st two strings, one of which is sounding 440 Hz. How far off in frev))hzjwam9 n 2quency is the other string? ±    Hz

  What is the beat frequenfi/n n-yr-; -/wwd- x/:ly wbilsy8qrcy 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 (aeho2fj 5 7+fcbrand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequenc+haffeo57j c 2y 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when souv1la-w.f ooe0k aknj(zx)n 2 :nded with a 350-Hz tuning fork and 9 beats/s when so.0o a ovl:-fxw za2kk1e)(jnnunded with a 355-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. Thedy;j l0jhsy lxxf 8si;v)v/,2p o,g8 i tension in one string is ;0l;8 2siiogs8h/,yvxpljxy) ,d jfv 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 rhpj mad rsw*..m9,sh73j*za if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°7r.*wh,z jdp9smm*3.a jh sarC and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of k me:,8/zgn34o kqexndsake t*. 3 jj(441 Hz; when A and B are sounded together, a beat frequency of 3 Hztogzk.n 3 :8 k(qsje4kmne3/d*ax j,e is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m f0b(wlzf q*y3 ) ndtnc1 ,pz.juxzq* 5mrom one speaker and 3.50 m nmjqzpwq3, 5yu*(dnfx tc lb*z.z)1 0from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are suppok rp35 z.rpra,g0 t b9 hykv*b8c3lou-sed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played tryl30prgbcra v593z t8p-k h.b* u ,koogether. (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 ofho iu7 kkm40d9 wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Auohd90i4k 7mk ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rahp znr*u a;+vm)i17v8bnze 8est. What frequpizh7 88ranumz; n av v*b+e1)ency do 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. 0 +lpeb3o9s hb)9amjyWhat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed3asp l )mbe+o0bh y99j of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shiftr y0 epc rvqaenik6 -/95u8by9p*wlr / in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/sqp*errkl0arv6 wci9/y-8b9un/ y pe 5 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 sing v. k)qvk/,lmy8pi8v e.u t(ngle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the drmqkv.gpt u(nl8 /.y , i)8vevkiver 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 wavy2 0 ysmp9 zywx+kz/-kes at 50.0 kHz and receives them returned from an objeskwy z0 z/9mxp+kyy-2 ct moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of,o9p81fge:p ,pbbo2rdz*pu. dleq.1ntr .dv 5 m/s As it flies, the bat emits an ultrasonic sound wave d rdz,. f.g9po b e pn2o1 p8t*pb:1,ldur.evqwith frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat tuqmp9)o 59wlxgjp .6qrain car at a frequency of 75 Hj9 qop9 mqu6x pl.wg)5z, 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 station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measu4r zjt3 jdn29fu)neq:g 1e z9b,qq2iure 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 flowing9d42b 3 g9tizjqe1ju)2,n enfur:qzq in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ost/p x,xhng20m t8p+ pf 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 emik+;9 ol78a hnwiz, ejmts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who ar8lhoj a;kz9 n+w7i,em e 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 2f28s3so4m cdz0 $^{\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 speg,c 3gqkror;4 ed of sound is 310 m/s (a) What is the angle the shock wa groqc3;rk,4 gve 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 soundi/w/met , 3 +kn)moghg is only abeh 3wmt+om/k, )i/ggn out 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikeh.c l.vnoww tdoyj); wf6.ct rw4fhb(23c2 ;ns the ocean. Determine the shock wave angle it produ w cc cf6b.h)l2jv4wh;wnyd t. o nf.3w2t;or(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 yjvam 1 +t txyfc-22o($/theta$ 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 jrq xn5/i*wl; ground flying faster than the speed of sound. By the time you hear the sonic boom, the pl;xwirn / qj5*lane 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 sendstl0yc*i-*4fkh5 bt h k 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, whatilhf4cby** -0tt hkk5 is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ra55wfhs j+)qwggk,noo4 lb 51xvd:va *nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of ma * d)rv(kzl1jzny plasti dr k*(z1)jzvlc pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m fr rrw)vy1o lffg+;;76arco -qkom a person makes a sound close to the threshold of human hearing (0 dB). What will; g-f7y r)olq cv oa1wrfr;6k+ be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sol s4 y-(fpjbz)jm;x )gund and an 87-dB sound are heard simul(-b) lzgjx y;js4)mfptaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in tn*ey9(q m 6z2a)ij :h rfut(ithe open, is 105 dB. What is the acous:j9 * i i6ft(u 2qhntz(mrye)atic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rat jozz2s8y g)zyr,1s)q ed at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz.yq y2jz r)o,8s 1zgsz) What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protect qldtoc * 5;k/h6uo*clive 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 unprotected ear at a distance of 30 m from a jet airplane engine?l/* tlc6ohodq uc *5k;    W

  In audio and communications systems, thegc+3 f vw/(ij5 (yeybf4-u2qqqd0 crn gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequ;uree 8 xon5li. 2kw ziyx+v1(ency 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 b 02bl .sa 1-vx4p5w1mv kqaykmetween fixed points with a fundamental f 25- 1 kpqbm4a1 kxsvwy.mvla0requency 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 ijdi t6)e n*pl)nto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to res*)ld j )ei6ptnonate 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 of mass ( qc fy,:0w)yyeion3g2.10 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 t:f,oyncyq0g (3 )yeiwo produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatenf*f3 9pq2 j;aqm4 lqc as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming fromn pv4np)e6 7yl two sources. The sound is loudest at points equidistant from the two sou 64lpep7)nn vyrces. 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 w2x m/ua0 * /vfn0rjvsqhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frvfr s/nxu *q/v2a00 mjequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftnvs-ydq jkun.++nnli/+ pj6 +er it passes you, its s/ nvn-di6.n l+qjyj+n+k+u p frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimatei p330u/xue6cxyqs k - 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 goes by on the straightawxkup 6 yx-0c3iu3qse/ay. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequenf b*zre3z;/rdcy of 11 Hz. The shorter one* /z;brz3re fd is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppcc ;q,4c pnv:mosite 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 observervp cm; 4cn:,cq when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bel6) sfi uc wux8w.75msat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood celc8mi5 s uxlf.)7us6 wwls? 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/s3rv/+9 y bur ltfbq0p(-j3t di while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the bt/u93yj03p+i q f bd(r-vltr frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approay*4/v ve tq0w;ncji;w ches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be dete4 tnq;0ivy w;e*jw/vc cted 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 signa2r +paw/y r) ycp2o+tsls 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, and which overtone is close to F yc tya pw/s2)2r+ro +psharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by n9 /o45h g.x63cxmv6x xravfqthe 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 wi/ x fa6xxvcog6vhq5x9 34rnm.de, 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 rw.mg6da3oxfn7u f *g5 ods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked withg f noawu3df7.5g6* xm the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at thooohy k8da6b6dznk-(7 p lr4/q4i/ a frequency of about 1000 Hz is /op(dayqz46b kto8d-nr 7 o4h h/k6il$I_0$ = $1 \times10^{12 } W / m^2$ 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 the ground hears0r 72q7/bzmjvdmtb0x the sonic boom 1.5 min a/7qdb mz 7vjr0bx02m tfter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo 8qmcad9n5x.s at 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