What is the evidence t26 kv+z)rvof4k (vj odhat sound travels as a wave?

What is the evidence that sound is a formhmm3s ;r :kg;g eet2m, of energy?

Children sometimes play with a homemade “telephone” by attaching at qd1(sif*9ks 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 cle1q(ti9fds*k sarly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wavg*j+:mc:atp e*psq8 78s jv gkel t:p vgc*p*:ajjm sg7esk8q+8 ength to change?

What evidence can you give that the speed of or.sw i80,(va1qtzme sound in air does not depend significv0e i.qwm8o(tz 1sr,aantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitchei l0j:ku;)x-0otz v-qguqzuh- :twb3d. Why?

How will the air temperature in a room affect the pitch beoau88bvesj b+id6o b9;4l9 of organ pipes?

Explain how a tube might be used as a filter to reduce the amplit 83zg mu5nwy;aude of sounds in various frequency ranges. (An example is a car mum8za wn;3 g5uyffler.)

Why are the frets on a guitar (Fi *4o vl90l5,i ,fdc bq:e *i(fvysqjqhg. 12–30) spaced closer together as you move up tvb*f oi:q,jh,9y4*0 (eqd 5 silcfvlqhe fingerboard toward the bridge?

A noisy truck approache dx/+yz 0yx6xyv1ij16ctbx w1s you from behind a building. Initially you hear it but cannot see it. When iwyjdxy+v 1 tcbxz x16y1i6x0/t 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 diffraction.]

Standing waves can be said to be due to “interference in spac14um n 6z4sowno by5mdz( )fn,e,” whereas beats can bnzomwn4yn m6o4s)u5d( b1 , zfe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredduej -ain9ck :1cgn2hj 1 l (vi42rmx7, would the points D and C (where destructive and constructive interference occur) md7xk9l1 i(m :2-1cnn rvag iuhje2cj4ove farther apart or closer together?

Traditional methods of protecting the hearing of people who+bzju-f-g 7jbvm(lx m3i7yo( : oa9wf work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not - g fovml3bb7-a(u zw fx:jo97ij+m y(block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a :1 tb oi9lj )rl;af qhk9cdh26superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), ao;6liacrhkj92:dh 1b 9 ) qtlfre the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer 7 t :u6x h4/azq3x gvu;6nbz+aild lm)move in the same direction, with the sam l4i6xqvh 7ngxz)umz :+ d3;alt6au/ be velocity? Explain.

If a wind is blowing, will this alt)8+k.j-5ltton4qzgkep91 ej aqo*lm er the frequency of the sound heard by a person at rest with reso4q.q1 elj+5tm t jo-kkl8 e) p9gnza*pect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various posib,x l32y-ul,a) tz 7k svb)aadtions of a child 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? lkul a,ba2ta)b-dx,)ys 7 3zv Explain your reasoning.

  A hiker determines tvw;p :q+5:qv o/y9 8seyl/aet4yxxt8e7os fn he length 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 t: o7+wy8 8 vxsq4vyato/n9fs: leee/5tx;qy phe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of*ds+v -wpjz)k his ship just below the waterline. 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 nop-+j)k*wds zv t vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air att: *wpbcjd:dr c-o- (p 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 rux- cs-l)g cls.g4acs9ul /b .ue/uod13(kr drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away b-xla(.)usg/uks1 urg-us9ec43 d.rlcl / c o (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 w df7 n5- x4kasa8 v j*w;z(oiy:iow)jchen striking the wateswiv ;jk8(4 xz )af ooijdy*-nc 7w:a5r below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hu1 agg.s de qbuxjk ;:ktv-16c(ge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in: -vxsb k;6k.eug jq1da tg(c1 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 distancebf;x ;tnqzrmb;yz71 3 rv8:rh/ sf*xc2vgb/o by the “5-second rule” for estimating the s/tgx1cby/b8rq:ovvrrb; hzn32 m*zff;;7x distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le u.7 ic6xb0p fmb(q,1x 2u7,qfrcc jzyvel 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 inx ck. jjs2+ q,egs)p5xlom:q9tensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult0 sh/v(;cxky)p n8ro paneously at a certcvk0)8n prphy x;/o (sain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with qc;:3 qpdhx *-k(mesw8 spq4u four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person exped3s8: hspuw *4p qm c(qqk;e-xrience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nois.mc9+ b.kbb jwch,8fae ratio of 58 dB, whereas for a CD player it is 95 dB. What i9 ,w bm8fb+ .hajbckc.s 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 sound from a person spea-qzm2o h9nfp ,3i2kjpking in normal conversation. Use Table 3jph,-2o qz mkp92nfi 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 strikmp1cyk;t+m )o2gj 9bcydt 64x es an 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, while the more modest amplifier B is ra 6;1qp5zu5+af3qhpagfr ,nam ted at 40 W. (a) Estimate the sound level in decibels you would expect at a;q, 1 zrmh5q 5aapg6fua+n fp3 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 d(rp rj.)ehq3wr/)zf when placed 2.8 m in front of a loudspeaker on the st3 e (r/q)pfzrjwr.h d)age.
(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 sou917p j w-l0w m qv.yf0j.uiduond level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectu17 j0-jwdilyo09w.f q.pu mvion 11–9.]$\approx$   

  If the amplitude of a sounfgzgew pnf;z 3.387:s 7rjjckv1 d2zud wave is tripled, (a) by what factor will the intensity increase? Increase by a ;gpzffkej7v3 :1 szn7 gj2r38duc.wz factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplib -i d- t/0uloco:cqi5tudes, but one has twice the frequency of the other. What is the ratio of t -oi/5l:c0dou tb -qciheir intensities?   

  What would be the sound level (in dB) of a sound wave in air that cx pfpclnz s863hh84y s q;k8/rorresponds to a displacementchs84pzh38p8x 6qflr ykn /;s amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sou2 5rotv/q8 u*acedqf/nd level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (S25cqd /o8/uvr*ea qftee Fig. 12–6.)    dB

What are the lowest and highest frequenci g/ndv;:yhs0mmto l + 1+xgc9tes that an ear can detect when the sound level is 30 dB? (See Figy;t1tchm/onml:9g d s+ 0g+xv. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.aor1 wi i9yv7n7-ax .j What is the ratio of ina7a.yxr-v 9owij17 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 lengthk4m4ro9 /)zm,agx gl, jckb if8.x jl( of the vibrating portion klmk j4(/gbcaz.8gjm)r, l ,xx9 iof4is 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 fundameijnp cl* b.)b8 ekz3r:ntal and first three audible overtones if the pipe ii8zb l.pckrb ejn ):*3s
(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 er s+v-me- :vxfrom blowing across the top of an empty sodarx+smvee -:-v bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of hum x64v+6*db its wo+lbuan hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requdl64 o* +s6w vitb+bxuired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. -gw1 nlih2-stnrh+s17vq c/ s What will be its 1s/n-sci nh wgsv1r l7 2th+-qfundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middleo 3 efxps ,ld,2v-iy s,tj q*7tgnlmz*+ 1ic-w C (330 Hz).l,ms7yt , l-,f z+2tdvs*q- pjogie ic3*1w xn
(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 pif0tq.gtnn0f y2 x -s:tpe that emits middle C (262 Hz) when the temperature is ft2gqx.s0-0 ftt n :yn21 $^{\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 28zk:3; 6y q 3zp4vz1yyscio.ciy 8jrt 0 $^{\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 th,u5n ljojs5 i(at must be uncovered js,5nl5(o ijuto play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate ate7:q:a,2yzbcepaag )5jh l8l 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an oap c :ae,5g jhy)azq:b 2le7l8pen 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 op rw ex9*x 9z2zm0uif n77h;byuen at both ends. It resonates at two successive harmonics of freqixe*; yz7w z rx92 uubh07f9nmuencies 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 5;urpkr 7x9yq$^{\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 within6 pv4tiizbuug pm6. *0 .sqco (-wk.b4 3wqdyk the audible range for a 2.14-m-long organ pipe at ui 0mqu6 bp*o zvi(4gty k d.bw.63c-q sk.wp420 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is ak1vn s0g qai20pproximately 2.5 cm long. It is open to the outside and is closed at tas00 1kg nq2ivhe other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of 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 evea .5p ux.ez -*bqze*tt*t c)bxry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency isec.ztu-t.*ebt*5 x *zx b) apq the other string? ±    Hz

  What is the beat freque:2b*a+m ))- gcptqgisdf7k vg* 1wmujncy 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) operates at bpkj7 ,(xj nw7py9w4s ;tso 5van unknown frequency. If neither whistle can be7vs;j 9 pk5wsnpx o 7,4yjwb(t heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whqwi v::wt0n( hen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vw(vn:i whqt0:ibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frezae a+8n exk1.9f7 wsbquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the be8a9beaxke w71s +nz .fat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicr.az4p+)z ciy:gom 5vbl6r8hal flutes each try to play middle C (262 Hz)r o 8z5ypvbhl:64cz.a mi+ rg), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has ls+n wzaa/y;f h16 uupd -7e2za 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 n+- 1zp2s6efluuh7dyaa/wz; 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 stanyhx+c 4p) b3j s/j4k94gmq fjr0y 4lehds 3.00 m from one speaker and 3.50 m from +br msec/3fqhjjx44 4g 4kh0) yj9pyl 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 suppbrp1dt0.trtgv8 z -gu )tj5 3cosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other 0.zt8b tg-)p5u 3c 1gdr trjtv?   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 2.64 m and 2.76 m dac (gc4 3xij)in air. How many beats per second will be heard3xc)4jc( a dgi? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren -cgvi*(x ap ) .c0phdtis 1550 Hz when at rest. What frequency do you detect c0vcapx*)h-(i.dt g pif 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 frequencrt5e*yo ipr55 y do you detect if a fire engine whose siren emits at 1550 Hz mo5pte55 oiyrr *ves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourd kcff*:x +jyt7np fdsj)q,bu, y+2 (sce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they clo+dkj cy bjf2f sxfy(q7 td p,sn+u*,:)se? $f'_{source\,movine}$    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 horn. When one iefh ath*hvh*. oz3(r9s 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 emit39.ehrh h(v*fa*t hzo ? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ud(t pj(-sj4a cu )lio01qcch 7ltrasonic sound waves at 50.0 kHz and receives them returned from an object moving directlysjp oc(aqi-c1 u h74ct )ldj0( 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 v)ej)f90rafaqj3zd9k 6 an.hof 5 m/s As it flies, the bat emits an ultrask jdazv afr69jf).q)9na0 3h eonic sound wave with 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 w3wgrd ,:j9,t*vhv +jtj hv)dyas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone whil jh*gw r),:hdv+v, j3tt 9vjdye 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 measure blood-flow spem5 m;5-affbud1qql;r eds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is takeb -;af fu5q;m15 qdlrmn 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 u8ku+5 n oovki1ltrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When :3ep .lpzk4aul7jo-y the wind velocity is 12 m/s from the north, what frequency will observers hearzyja-klp 3 l:.ueo74 p 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 ifynewqn7- 7 c4whs iq+( 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 2.3 where the speed of so1iitdy3og orv k )a wn,19te pf*d+:h-und is 310 m/s (a) What is the angle theaod1 :*-e)+wfit rodg yp3t inh9k1v , shock 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 planetw b-)xb1kco ;mvd e. fl0)68a;yfxxyb where the speed of sound is only about 35 m/s bexba 10xxkc8b lyywov ;-dm6))f. f;
(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 )n*m19tfxdj +q ysqo: shock wave angle i q)ms+y f:t1nq*9oxjd t 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 +bvl:mz7z) zi $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and sg x,-zwcfc: 7xee a plane exactly 1.5 km above the ground flying fas7x cxz:,fw-cgter than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar devicy .*j1q7h sqr5hop-)k rywp.v cgf.r/e that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed y.1rpykr.h )/j.v f5 coqwqr -*7ghs pto work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible4fmz5g 56 +q(eaxi vjz range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists okd ef+(mdhca24s/y w7f many plae/d4syw m7(ak f+ hdc2stic 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 from a person malv+k vc5 ,p( tf1;d,vq p/tpmzkes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 10001ktc;/ (pfq5vm vzldt,v+p p, such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound - wm0il;ofn4+q kw y(mf5rkx/are heard simultane n+ m(mlww40if/q;y f-kkxor5ously?    dB

  The sound level 12.0 m from a l308tfnf wd;al. vd)ck oudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it r.k8l03 ff;wvn )ddtc aadiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outd xj.t+ru7gj0 put at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is .xu0dr j+7tgj the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.9 ,y(e;k(o pyt1kgqu a Assume that the sound level of a jet aktq p1ue (oya9kg, y;(irplane 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 communications sem wg)w:y:s-yaixlewh.tb8z2c (+ p8ystems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to:kqf2z0:kyor 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 cmo o(j8t czn4q.w0sis 3 long between fixed points with a fundamental frequency of 440 Hz and a mass peoi4z3s (w0jq.s nt8 ocr 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 zhq: j)hh8:fp 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 resonate with the tuning fork when the distance from8j f hh:zqhp:) 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 )z gzs7hn9*,,vywu /.ny zagy 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 (in its fundamental mode) wiwzn)ghyy a/s 79 zg* v,.u,zynth the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obseraa;+opua2d k6le0v* zved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–100. xk.ajr: xtb*0-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 0.34 m farther from ox xbrakj.. *:tne source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductohv /w fglwo )6q+w5iw9r on the stationary train hears a 3.0-Hz beat frequency when thg) ov6 /wfww i9l+qhw5e other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trail7o1q )qb28zdd z,nq sn whistle as it approaches you is 538 Hz. After it passes you, its fre z2,s qd781bq zodnq)lquency 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 cars just by listening to the d3 krojj f:+v)g:4- px4/bzvrh8tctzb ifference in pitch of the engine noise between approachin 4 :kcrbbzjgttv34 + :j r)/pxhv-foz8g 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 togeth hj ,gy-6eo3lker, produce a beat frequency of 11 Hz. The shortjkgh,y6l3 e-oer one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a zuph/4ou7 fa .railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (bazhf 4pu7 o.u/) 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 be v 3o2vmp6edbp +8pq:e a5fbd-at frequency would you expect if 5.50-MHz ultrasound waves were directed aepdqpeom fv b:vd6352 8+-abp long the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the bax+ -qytg; -cafx/6i lgc go06at at speed 5 m/s The bat emits a sound wave oyoil-t/66gx x;cg0+f q-c gaaf 51.35 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 hi486zf ugk 1kupgh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is a48z1pkufg 6ku bout 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once us+xlm7ob+ 9axo k;0gdvy(hc( ded to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to creacmxo+k9vga ;bd0y+(l7x o ( dhte deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listeninb+ycv-) 3pm pwg can be compromised 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 +-v bw3y)mpcp, 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, calll k.f8tuhk o/3d/t(pled “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.8/fplhu ( 3t ktk/o.dl 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 5 dq-. .rrayoja frequency of about 100 ..j-qordar5 y0 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 the ground hears the soni1 g:p h+p5+qvx hsn1rec boom 1.5 min after the plane passes directly overhead. What is the psp1:en+qh v +rxh 5g1plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is7 k0:qgs .tkcd 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