What is the evidence that 0 e rw6*9 ionyutl6+umkws1,x sound travels as a wave?

What is the evidence that sod8ehn.b 6odr .qol2,ound is a form of energy?

Children sometimes play with a homemade “t v7nyi gu0e w:xn)coa7oi +-0eelephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a chilee0: y-c)aio g+o077ixunvnw d 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 frcu;/m b/tr+q4yzq5wxom air into water, do you expect the frequency or wavelength to cha qcm /r5 qu4xw/y+;tzbnge?

What evidence can you give that the speed of sound in air does nkygrgfs(/ c 67ip xd82ot depend significantly ongc8y6pk(2xid srf7g / frequency?

The voice of a person sv0g, wsuk gbe:a/-)p who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the piy5p n57 .ztio5l wa:9liklf: ytch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of souf:z8).g wkbmby ,ak o:nds in various frequency ranges. (An exampl k :.k,zab :m8wf)gyboe is a car muffler.)

Why are the frets on a guitarq n-wy1cocij90o955 2zbwgp)ex c8x h (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridbcohcoew2z p8x 5ig-cqw1 9j0n 5x)y9ge?

A noisy truck approaches you from behind a building. Initially you hear it butmz+c68b pn. v refz3t ,p2p(s1qd4m+ z g6poxj 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 11–15 on diffractioo6x p1 z(4dzmspe6ct+8z2p rmb,p.f3gq +jvn n.]

Standing waves can be said to be due to “interference in space,” whec9x*wnh ly* zc;:ax 2kreas beats can be said to be due to “interfhc* ;w9k x*a2x:ynlzcerence in time.” Explain.

In Fig. 12–16, if the fa+ 0o6s4-2w.excmrg :/ bcvg4l vvbwnrequency of the speakers were lowered, would the points D and C (whb.owv 4v+x6-r:lws/04e cnagg m2v cbere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in* t8n*:tzmew-fnn vr7 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. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in a*nn*t-n7zfmr e8 :wvtddition 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* qggyj3 d0nc.ch wave can be thought of as a superposition of two . qny0 cgdj3g*sound waves with 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 direction81ds)y (yx*gho+p ynpos2 lt7 , n t*1ops 27y)yg( hopd 8syx+lwith the same velocity? Explain.

If a wind is blowing, will this alter the frex0382bj.ojpn b c3e ya(mej *jquency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity 32j3pnxb. j*e8cbmajy0o(e j changed?

Figure 12–32 shows various position;kmr: lrwy2zi)(p p 8ms of a child in motion on a swing. A monitor is blowing a whistle inm )( imywk;: pr8z2plr 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? Explain your reasoning.

  A hiker determines the length of a lake by listenid lrrz34+bh/ aj /jtl+4u bt.ong for 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. Estimate the length of4j+rt4l j3/ +dabzbru.h / tlo the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hsmm )53b buz7qis ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. Hm5bzubsqm) 73 ow 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 arm/(*pdk oa/ /;tu)ijeant* v4 4jwkp 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 fogr 2km*ey7cj/raa(kk jn2(2awn hc5a 9gy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a)rackkw a/ja2ankmr 2(2h 5e*n 9 yc(j7 by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clii19;p cgx/boiqeb0. gfa s43mff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff? 3g /.9g p fqbxs0a;c1iemb io4   m

  A person, with his ear to the ground, sees a huge stone strik1yk7-v)zecz ll7; vai9 3 zjzpe the concrete pavementvvz7)7;y9a e licj1 z lzkp-3z. 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 apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mihn6 )av;fkul.le of distance by the “5-second rule” for estimating the distance from a lightning strike if the tempe;v fl6)kn hua.rature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensityh0k h2xdu5i) 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 whose g4e )nio 9g-mpintensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9ylo8+ k ux2zs*5 dB when fired simultaneously at a certain place, what will be the sound level if only one is explody*k8 z+xus2 loed? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane ho7) -,nxe9medb87szipz6 mqwith four equally noisy jet engmsod8i, z )p9nhee77zbq 6x-mines 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, not dB’s.]    dB

  A cassette player is said to havep98 zng6. zsi;/hl,e gfbm-yo a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and tof9p gge n8z ,s;ybl.-zh/mi6he background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from wy1m9-p (ap h* u s.kbs6e;kwaa person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mo apk-s9a*.(; wmuwkpe16bys h uth. $\approx$    $ \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 anv; ibac1 st4by +(mc7p eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, wh6pk(ty)y j4smile the more modest amplifier B is rated at 40 km4 t ()6jyspyW. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m u1zdv.jxjng2huckux 2 ch8m+mp6+7( in front of a loudspgup(2+8x1 vmmzx+ j2u u.hdjcc 76hkneaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically det v,-(2aedhq yaect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hid-ahy vq,ea 2(nt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factol j 74f*z5getir will the intensity increase? Increase by a factt i*g4 75lzjfeor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicex7+7ymkr:q fl the frequency of the other. What is therlfq+mk : 7y7x ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tovza)zm;i eb 2) a displacement amplitude of vibrating air molecul2ibm; ev zza))es 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 tone luip o;5/sa0dg61nf lthat has a 50-0opl/s51n6 gdl afiu;dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequenciesg pvz,k /d ;jl2upnfy1(m(2yp 0 goci5 that an ear can detect when the sound level is 30;/yj2v 0plucgn(d5po k2 pi(,mgzy1 f dB? (See Fig. 12–6.)

  Your auditory system can accommod0f30bhwrywo-/ rs 9dq9, ttpaate a huge range of sound levels. What is the ratio of higr3st,y0o a /bh-pfwrw9d9t q0hest 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 fundxnnon8k j69d+/a* dryamental frequency of 440 Hz. The length of the vibrating po6knadjn 8+*nd/yrx9ortion 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 longm99/b ddxof4l. What are the fundamental and first three audible overtones if the pipe49om9d f/ldxb is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the tovdu elp t6 j44i4qs+d7oin* s,p-qe3sp of an empty soda bottle that is 18 cm deep, ipe*i,4t oq7lss nq sdej4v-6i p+3d4uf 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-tube pipes spanning the rangeqg2sih4 6rzv /sa7j(w of human heajh7arqs/w4siz( v6g 2ring (20 Hz to 20 kHz), 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 third har ;qeh;n4r 8nu 7nxnwy6monic. What will be its frn7 un8nwh yxn6;4 q;eundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73w +.z 42answsf m long and is tuned to play E above middle C (3z+n s s4a2.wfw30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) 1zah.8bd. +74(ao m lgbpe kigwhen th .l71i+gdeoba.g ah4pmz(8bke temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at ,9z s4zh(ztemrbdwb4 prg.:( -v wn5 e20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examplevuq*le0mwlo./ c9ey.o 0u -gr 12–10 should the hole be that must be uncovered to play D above middle C/qo.c9e 0 ol*evwg. lu-u r0ym 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:c74 jj m5 7juanf.qzt Hz, 440 Hz, and 616 Hz, but not at any oj.ufq:m4j c jt57zn7 ather frequencies 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 ooq9a+6qr 1yr.n ;rjzapen at both ends. It resonates at two successive harmonjro.;az6yn9 r+ qarq1 ics 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 bsggb h )un1-r 8j6ff6$^{\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 pr-zu dmp*: sdg6esent within the audible range for a 2.14-m-long organ 6uzs* d: m-pdgpipe 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 the outside anno/ bw7s w8-ryd is closed at the other end by the eardrum. Estimate the frequencies (in the audible ow7bw8-y/sr nrange) 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 nqm w/(cc; prm9 yv87zmr zv94beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other r9rmvw7v(m m4 zc /8cyz q;9pnstring? ±    Hz

  What is the beat frequency if middle C (262 n/q2+ 04ol j-yk dhihiHz) 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 anoth io5- edl0+u3hh ul+hcer (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played sep lh0+-hihdcu l5eu +3oarately, 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 when sounded with a 350-Hz tuning fork and xkpe.o q okbsra pwq 15e700.59 beats/s when sounded wisq5po7 wekop abx0.5e r0q.k 1th a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the s g9g)d h(we(xc w*z-esame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What wilwhxsd)e9e*g-cg(z (wl 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 identicar 3ka 8qh9+cz s89 .4jf5 ykx)nlrspfeb (4kopl flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 4 sop+ y3xfks54 ar9 lr(jh9pkk).nq8ebzc8 f25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. ,r dt,-h 5eqfx.fll7ku tk;0fFork 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 freque7 ,lkfuqf kh.r5 ted-0t,;flx ncies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker an+/uw,cq etrw jgg,u,*d 3.50 m from the other. qwu/u,r*gtj+w ,ce,g
(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 supposedbqp98e p*6 rbt to be vibrating at 132 Hz, but a piano tuner hears three beats evrbtp86p*e q b9ery 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 wavelengths 2.6d7jv(ysrkmwqp9 )si0d1 7* ad 4 m and 2.76 m in air. How many beats per second will be heard?*0js7wv 1(dd9qap rk 7dmiy)s (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a gy6.rt2 u n1 lrmwl,xy51,pmm certain fire engine’s siren is 1550 Hz when at rest.11y 5r,mux,gl l6mpwnt. mry2 What frequency 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. What frequency do you detect if a fire engid2t7t39i ko +gra 8r+yjdl*rlne whose sire o*3y9+k 2i+rrdlagtj 8t d7lrn 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 frequ f)m wzll7/z(aency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frw /lz7fm la)z(equencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency hort4x l zcvwhqzio* + hk6j(4::vn. 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 the horns emit? Assume T =z:+cq 4kh4z*ij ov6htv (:wlx 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz a8lr4 1husltugpk)2v )nd receives them returned from an objectu)rvl uk 8h4g)tlp2s1 moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits anm dggofk goqe508y:m.ei rdel0iy;0*.6g0 pu ultrasonic sound wave with fddq8m gyfiol:p5e0ee0k0 * g 6.;.rygmgoiu0requency 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 mo 9tkpty tdsz8:7*;osuving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the stationty;:t p 8 s7s*zku9dto at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoundl5h+ew;ujuiq; / zp9p waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human ti u ;pjie9pq;h5zu +wl/ssue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves/ zwpk;*a1ms*6 eme5h8ec h4yf:ydgi 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 frequencx,q -h gyrs,75uol0rk y 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will o,q0so -lr hx5u7,g ykrbservers 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 objec)yae+ t (ekb/gt moving on land if its 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.hh9ri xi7;*vy uvs b(/9mwln/3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directisi;hr(mwnl u/hv /*99b i7vy xon 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 o9 1lvcqsa 95oh-:lru : hhk-ppf a planet where the speed of sound is only abou rh:s:lp 95hhako9u qv--p1c lt 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 the shock wave ang,c0-k.cx2v nz b9mi laleb in .0lxkm cz29-vac, it produces
(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 y9go02two0 wf1py a)p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plk3ra: ;nc j0j ,bgtbqe3yq, *2u*xonzane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic xajr g3ykz:t *, qe,oj n; c*buqnb203boom, 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 doo8m8* ( wim, rvrv7samhg5t2hwnward 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 frei5*o, m78wshth mg vrva2(8mr sh water)?    s

  Approximately how many v/dwfpuot4r7lf1 ( /. j(atzgoctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called h: /i) hq 4pvd3 qnf1hs;sxr (top,tp8a sewer pipe symphony. It consists of many plastic pipes of various lengths, wh tht s1s;,r4xdq(pi3nfh8 qp) ohv:p /ich 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 soun,svi 3cl ujr-2d close to the threshold of human hearing (0 dB). What will be the sound lev3urlsi2jc , -vel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound a hose4royxyc30 w /-x;re heard simultaneously?y/ h wxxos -co0ye;4r3    dB

  The sound level 12.0 m from a lojupn0yvz k +edk9+3e(udspeaker, placed in the open, is 105 dB. What is the acoustic ek93+npj k vde 0+y(uzpower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outphp96c;(sdur/g .s kdi ut at 1000 Hz. The power output drops by 10 dB at 15 kHh 6s. c;u9s/ddgprk i(z. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectix /gu)f/ dy*lvve 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 unprotecteu dfy/*gx l)v/d ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, *ayq9 q k 8a 3obiw5mww 2e,ws3pjl+e3the 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 ti-*os h xhpv0,e5 d5.fe gfir:5r*xkko 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 fuph;vi6/som-yvpqp+y+. zz* wndamental frequency of 440 Hz and a mass per unit length ofp;phq-wz/v.6+py s y imv*+ zo $6.1 \times10^{-4 }$ 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 wzzl+ jrg 8p,9mith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in th r,9 p+gzjlz8me 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 of mass 2.10 g is near a tube that is opexpkd g w;v+icze;5+tk43p k6xn at one end and also 75 cm long. How much tension should be in the string if it is to prkxic6;v+kp z5 3 ;+ d4txepgwkoduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop q6) b+hrdsod0 ($\frac{1}{2}\lambda$) 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.mi13p wm:;;x gb wegs–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.3g b m;ps:xm .;g1wewi34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on theeo*zoj(h tx.h bs.k,wr1 m(9i w.o6xr stationary train hears a 3.0-Hz beat frequenc .om.rr( ,k9o(.6ei1xwth zhsjowx*b y 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. Afm1umnjcwixp+) ix)pm61q )a* (c3wz gter it pamq+ ugwx (13*acc) n pm m)jwz6pi1i)xsses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of 68w2lsm1 bu gb2yxcx 5cars just by listening to the difference in pitch of the eng68bsxm12xgy25wu lb cine 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 straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding e7 8upd nk5b)fnzr 1ubriw .,(together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the otuf. )nbubr perd(57i8 n1,wzkher?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s 9vrt0(ubbb 9b vvyk3-tationary 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 frequencrv v3-9kbt9b0by (v uby heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in theyhcxwkl82n5zh l-d x;chq v7b4 /q8k- aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blod ;c/8 vk zh5 xy7x-q nl-bc4klh2h8wqod 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 whileu,lt: t c0/iq -r+odam 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 fre-at0 ,tql io:uc+ dmr/quency 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)/ wl; ru krlnh7r)/ss it approaches 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 detected by the bat so that the echo from one chirp returns before the next chirp is) r /lhrun ks/7w;l)rs emitted?    m

The “alpenhorn” (Fig.wt9 c,+psxcld1zo.v7z9m s/j 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenwzxs c,jmlos9t.cd 97/z+1p vhorn 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 5ol sm,/hi( 2o6fvn qgpresence of standing waves, which can cause acoustic “dead s56fsnoi,lvh(2 qmog/pots” 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 rjwzjz+,haysrwp ;4n xu+4ys rr 49-: rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the r;+zypsw wnuh s y:9r4-4+4r zajjx,rrod 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 :r7 l ea a2*ovecu8ja*ear at a frequency of abou 7*:aa* v erc2a8oluejt 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on thev(1d3y ypnzvlh 0i8c+ ground hears the sonic boom 1.(vzy pci8v01l dn3yh+5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 (wy0ffco99ys9 d z *s1 .oquxw$^{\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