What is the evidence that sound travels ax:h: 8pukd sb*m(zddikf ec t0*,;*lds a wave?

What is the evidence that sound is a form of energy8d cln) bhp) v4j8*re k70ludy?

Children sometimes play with a homem0nih(x- kaae y/w9 y9zade “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 be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels fayzhk 9i /(eyxn9a0-wrom one cup to the other.

When a sound wave passes from air into water, do yrms)h ft9dfeksaab.+0 x(/i *ou expect the frequency or wavelength f. bih/skd*xf+r)09ta s a(meto change?

What evidence can you give that the speed of sound in air does 7d*+o hzazag7afs c4x8ix +4zj 1s1rxnot depend significantly on frjai+d71ha xgr14 8*af7xz xzo s+4s czequency?

The voice of a person who has inh)rpud a7 b7eh;5r5 lrdaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ p o. 3ma qm04bei:6p1pxw59v e cr8tqodipes?

Explain how a tube might be used as a filter t9qs9 ;q qu1ms)8 s8- j isy,wv,yedsyeo reduce the amplitude of sounds in various frequency ranges. (An example is a 9)i;y-dm1 8sssvyus,y 8q ,seewq9jq car muffler.)

Why are the frets on a guitar (Fig. 1,lwsr*a nn 3 l ev4+4jcb 3bi:wvkf-(p2–30) spaced closer together as you move up the +fbl44cvw,p-sna3e3(* wkrjlbn v i:fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it bh 6q 1eldb/:wx.v5edhut cannot see it. When it emerges and you do see it, its sound 1.lehxdv q:eh /db w56is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” neq0buvds9w: ybk2 kc* )/x+swhereas beats can be said to be due to “interference in time.” Explabcn/e+ xs:wb y)kv0kdq*9s2uin.

In Fig. 12–16, if the frequency of the speakers were lowered, wo ;x c/ evhhz( t)hl3g68u9/d ytzh:wvruld the points D and C (where destructive and constructive interference occur) move farther apart or closer toge/xr6gzehvct ;zwhdu) :h39 vhly8/ t(ther?

Traditional methods of protecting the hearing ouc6 jtb0sd29l f people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise 0l6tc 9 s2jubdlevels. 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– p8 o,c0rpd/hj31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as inop/d hc08r,pj 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 a:21r4sd f mpumove in the same direction, with the du4p1sfm 2r:a same velocity? Explain.

If a wind is blowing, will this alter the frequency o8pocnu1 97x*m jath8tf the sound heard by a person at rest with respect to the source? Is the wavelength or velocit*uxtp9m7t8cn81 jh ao y changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monwd59flusnenq6)h rh o+- -o5f itor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the higheq+ohnhe)wr9u5 s6fd5- lf- nost frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the v re k1:gv3 ta.aa1zes-s5g m8length of a lake by listening 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 of the lake. a a.5gev-s v1re8tz3kma:gs 1$\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the e.82ua2bs xii )dorl+5wumz/3 vejw o6cho 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 s ao)zdobv. iw ew2xj3 r/86+lmusu5 2ieawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths 56 jap ,tdlk yds085fiin air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school)v lqmz f7: fya49m)oi of tuna on a foggy day. Without warning, an engine my:47 mo v)zq)ff9alibackfire 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. The splash it makes when strnun3xcxace *) ;++1etz ohcz9iking the wauh*cx +ox 3n1zce z;+n at)ce9ter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete p.-vru s;rhj 1eavement. A moment later two sounds are heard from the impact: one trarjushv. -r1;e vels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-s. hsuoyp/l442errr33b -sku tecond rule” for estimating the distance from a lightning strike -44h23rusty 3pou/brs e.l k rif the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thezrg4y cql5n/a 9+bt9iojl ; e0+7bd op;1lduz 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 of0 z.z rn6gp/hq,nd4p x6q 1vjs a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers p0r v eoqx3;ia-roduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitiesa-irv0;e x3qo, not dB’s.]    dB

  A person standing a certain distance from an airplane with fod cs,9fg*ih 21 ydzt.xur equally noisy jet engines is experiencing a sound lev2xgiz9 tcdshdy , *1f.el 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 have a signal-tb2u6hsoa( mz3 o-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signhs3 uo6zbam (2al and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conj1nuehdk p (lo(xwqaw(tnr1 :9x h.3v *q1qh3versation. Use Tablkqa:xuh v3t w1q9h3 qne x.(pd1(r h wnljo1(*e 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is/v/ o 0xe( wlyvi(-8ciym2k bv $5 \times10^{ -5} m^2$ (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 more ;j oed - ;6tr(hie 4k)ixr;xhtmodest 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 connected in turn to exthd;hejei(6i4t; r k-or; )xach 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 mem*cw t2 z.shzk 96wcj(ter registered 130 dB when placed 2.8 m in front of a louds2 zkjs.c*96mch tww( zpeaker 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 detect a difference in sound level m.td h8cz0hb*sg7 hzqd9ev :1 of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.sedcz8 hhh tb *dqg9 m:17.0vz]$\approx$   

  If the amplitude of a souar 800/+fa owxv+ b*cjcxsv3*jx yl,i nd wave is tripled, (a) by what factor will the intensity increase? Increase by a factor as*x*+0j/cox0ifx,cv 8wvy rb3jla+ of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementxi*jos,t8c+-m qwa igx-r n4- amplitudes, but one has twice the frequency of the othcr taq -8xox-m4-,+gji in*swer. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corv(9dm 6or8u d)lu gc5d./ ecrgresponds to a displacement amplitude of vibrating air molecules )r.ol (d/d59gudc e86rgmu v cof 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to35ex6d1xccy9 rc -p nc seem as loud as a 100-Hz tone that has yccrpc6n-xd 9e1x 3 c5a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the s3 w+ggf33 jgx-v 7to m/kivzr7ound level is 30 dB? (See mv3 k+jz 7g/ 3g gfrw-vox3t7iFig. 12–6.)

  Your auditory system can accosz*uqxwej e +2b4 89svmmodate a huge range of sound levels. What is the ratio+qew b9xseujvzs*2 4 8 of 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 lc2,t r ykui*w-lz+rbbd1q3* qength of the vibrating portionwuc q-1bdyi, 2rqtl k3r*b+z* 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 fundameneq91e67;gj snlrvho2 tal and first three audible overtones if seqrh vo2 96nj1l ;7egthe 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 freqm j*a c+c2m(oo:5;yr6r pqnwjuency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wa6y(52q ; +jwro*mr njcoma:cps 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-tubew0p8x0x g efy -jnnpooc,u 62; pipes spanning the range of human hearing (20 Hz to 20 kHz), what wg 0j6nxen-cfpx; u0 ooy,2p8would 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 harmonm*lhiy tu 1fo9ogwd7 )mv5 t05ic. What will be its fundamental frequency if it isthu19idl* o y5mt)f v7w0o mg5 fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mivbnay*2 v jep3j h9o4,ddle C (330 Hz).v2 jna3p*,bovej9hy 4
(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 (26fir+ h+nv7:lf2 Hz) when the temperature isrlhf:inf +7 +v 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 ab44w;dy) zzw-3vwr5 tcnwq-oo -na,zt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be tahn4;tjc 7j )mhat must be uncovered to play D above middle4t ;c)h ja7jmn 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, an0s7 -yd smcfwu6kp*bsh q5z5:d 616 Hz, but not at any other frequencies in between. (a) Show why t7-zh 5swm6c s:0k5syqu f* dbphis 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 resonates at tw+;6rxexje,pj j1dro/ u(-q0wq a p3iko successive harmonics of frequencies 27xr ix01 kro-wjea 6p;d(uq3ej/p,qj +5 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 k298qibpae6; e/)as ijsiw- hi)sfj:$^{\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 n xc ak tn2mq6o4/i:r9within the audible range for a 2.14-m-long organ pip6tnr 2o4nm :cqak9/x ie at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 6zdq.*sepu k8wpf 5) g2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencieswq8*defzu 6k5gpp) .s (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one byy3* 9mdle l-ieat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the o-dy 39e*miyl lther string? ±    Hz

  What is the beat frequenvr,b n3la) /iycy 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 (brand X) operatez-elhd ua88 (rs at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operati-(l de 88zhuarng frequency of brand X.    kHz

  A guitar string produces 4 vog-gp74kjd0q)hg 7zbeats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? g- 4g7k0oghv )pdzq7j Explain your reasoning.    Hz

  Two violin strings are tuned to the x j8e9wqvcyn0 h5 ,:bssame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat freqxwq h:0c589besjnv , yuency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identis0s1 d7; +6 redpgwlxjcal flutes each try to play middle C (262 Hz), but one is at 5 gsjpsw 7e+dx0r;dl61.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bt(wl 4f b/(ss/kcw3 nd has a frequency of 441 Hz; when A and B are sounded toget dfw3ckb4 s(t(sn//wl her, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A 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 st1jnh :us9m xa w9 u-89vdn zg*hde1i/peaker and 3.50 m from the other. :z8mha1 9h9u*9dwseg udn tvnjix1-/
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hts aex22jw-nwo,a+h - ears three beats every 2.0 s when they are played hase-xw+ao2- nj w2t ,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 wavelengths9jd)jqe( i0ky 2.64 m and 2.76 m in air. How many beats per second will9ek0(jjy iq)d be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550(fhrypt, ie7(sr d+. j Hz when at rest. What frequens (7h r,r( jf.eip+tdycy 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 frequenico76ta .oj)db. z:hrcy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of o )cdh:rb7z.6ait.jo32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency7f-z) duy:ye t if a 2000-Hz source is moving toward you at 15 m/s versus you mdufz t y)-:y7eoving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same sing*5 uxepijw2c15qc w o.le frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rex5jcw i o.qpu1c* 5e2wst 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 wavej)/5c u0jn9t gkwnpc.s at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received s )nuwj.jp 5k /t0g9nccound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s Aeum+ yh6 *h:sws it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frey6e*s h+mwhu:quency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp/0azh,ngkf4f ler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same,zh fnk4af/ 0g 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 ultzvv cqzl+7w nlzv+6/*rasound waves to measure blood-flow speeds. Suppose the device emqv++ z ll/c7zv*zvn6wits 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 arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequengvzprk1o bp a)vc( .(v;.j2flcy $2.25 \times10^{ 6}$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 fre1kyoq *vg1 84rli8 dsuquency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency v8o1i *8dy4g us1klqr will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed 35fo qloffm +.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 whpxf zz72)4g g+,2vmt jcdibo7ere the speed of sound is 310 m/s (a) What is the angle the shozi mdp7gcb7jgfxt42,v z+ )o2ck 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 speed oer 53tl5bmw2n f sound is bl5r2wt3enm 5only 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 ocedrk5mf 4 bh5;ah9nfg,an. Determine the shock wave angle it pro,m bknhr5fh ga;5fd94duces
(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 7.:hernehbe6 jkx)m. $/theta$ 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 exac 8qbkos 2ewzm))vi3s -b9r+;5pa qntttly 1.5 km above the ground flying faster than the speed of sound. B3m+r9e2 qoq8btp -s; zvswtn5)i)baky 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+l;humw 2 ca3x downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200axwmc lu;h+32 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range? 8o(l5p hrryg3wv, lnp(f0yu*e(( lkp: e6 suh$\approx$    octaves (Round to the nearest integer)

  A science museum has a display call9 pjg82 xs5o6q3 srcqqed a sewer pipe symphony. It consists of many plastic pipes of various le2qj9sr8 xp5 63ocsq gqngths, 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 5.06.nqi mrvu1)q m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level 1in quv 6m.)qrof 1000 such mosquitoes?    dB

  What is the resultant sound level wheq*;m0ien j*dsn an 82-dB sound and an 87-dB sound are heard simultaneousliejq **d;0 snmy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opwxo45crw1 6niwqoz:hd1 dvv s ,+z 9/pen, is 105 dB. What is the acoustizwp/5nrcd sd h461+iz9,1 :xv vowwq oc power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power 3)fov3c 1kguo output drops by 1 kc 31o3oug)vf0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their zfl) :hy4m3cxs3a9;:6 sbpub8mh d*rw kgw8u ears. Assume that the sound level ofm3szwuus3yph ;b6dbgxarf8w4 k :):m c hl89* 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?    W

  In audio and communicatio 2clzmifg qcn(ys3mb3 4(w8shr/4 ye2 ns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin*ls6o( 1xxf3gxzf b* k is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm lfo*dg)s v5xa;,od pg.u5-ovdong between fixed points with a fundamental frequency of 440 Hz av )dvdad;5oous.gpfxg5-*, ond a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a ver)5vumpmkyv1q1m/3 ep tical 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 i/y)vu m3 1vq5k ppme1ms 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 57uy-iua1 -g -snl;e 1bgk7xufdww7 y 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 resonance (if u;- i d7ky-e ua-u5wlwg1 yb1gnsx77n its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonadh(uexgw1g 3 ; og/9jl5gb1 kty2m h6ite 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 from two sources. The+ 7(wvk2:h43pfuj 0ylcpty oi 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 0.34 m farther from one source than the 7hwlutof+j 3v4 pyi:2 (yp c0kother. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trci)19 ,mr uf8zduhyh 6ain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed o98h16m,izr hycduf u)f the moving train?   m/s

  The frequency of a steam train whistleiheb 0h4n(*j7s/yl g j as it approaches you is 538 Hz. After it passes you, its frequency is l h0n/jyjh 7egbsi*4 (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 cars just bz zuu5db yg6of801; u-.v , l(a.cxjl7gfjbduy 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 halvb lzg8c(;0uzg-ld,b uaju.65dfuvj of xy.7 1ed) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat fkb*+y pxs;krv+- wh* frequency of 11 Hz. The shorter one is 2.+hf-;xrp*v yk+ ks*w b40 m long. How long is the other?    m

Two loudspeakers are at opposite ends o q6cpo:gew;+xf a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from +pogewq ;6cx: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 nl cz bz(h :i7/*) gnf.yifj:pzg*w6k sormally 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 blood cells? A./(zf7n*b z*gw cf)sjigkyhpz::6 ilssume 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 wm)ufmf2essj j(9 k3 e+j8a;rnhile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.3f )+ 8r(saue; fk23se9njjj mm5 kHz. What is the 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 approachwhaoap17z61p)unbwure))r wk 6(9 o fes 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 ecz( )7fo1ukuh)oapb9)r waw6e 1np6r who from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once us.kybuef r) . .6ac;cdoed 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 alpenhorn must b)cuc..rfd baeo 6;y .ke 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 compromi,i2sdjaw7c870 x:pu+ bigeh ased by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m xi:e87 0ad,+7gajp i wuc 2shbhigh. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratio qf-g,pi, ar/qi.ij*o.w nq :rn, called “singing 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 rod can be made to “sing,” or emit a clear, loud,wqig-f / :i,pj.* ,oqa.rinqr 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 hearingt7dto 6ng1 p)j for the human ear at a frequency of about 1000 Hz isptt jg1o6 7d)n $I_0$ = $1 \times10^{12 } W / m^2$ 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 obserp8- yp2xt5aetd35xr rver on the ground hears the sonic boom 1.5 mi5r3eyr28 5xttpp-a d xn after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboamk/ g4/q3n oq.pyifb5t 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