What is the evidence that sounnh5o2 ;yvf 4tgd travels as a wave?

What is the evidence that sound is a form of eneyl 1p 7w)/nftdrgy?

Children sometimes play with a homemade “telephd3c wk ;:vixgk)s ;e;xone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one 3s;deg: kxc x;w v)i;kcup to the other.

When a sound wave passes from aiyign ;62hz xse6,elquu70p5td1 2cpdr into water, do you expect the frequency or wavelength to chpt,l6hyu206;eud7xinz gspcq2 e5 1 dange?

What evidence can you give that the speed of sound in air does r y 6vknlw cft: q3*z47kkma3(not depend significantly on frequenmwyqk 3k6anc4l3f(7 k: tvr z*cy?

The voice of a person who has inhaled helium sounds very high-pitched. Whwkqt,b. v jqnw+02co1y?

How will the air temperature in a room affect the pit xa87s ojsc /h*wo-jd;ch of organ pipes?

Explain how a tube might be used as a filter t+ +exi nd;xtk*o reduce the amplitude of sounds in various frequency ranges. ( e*;n++ dkxtixAn example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move cykgif-ul2+67-qsh dup the fingerboard toward t2- i7 dusq6chg lykf-+he bridge?

A noisy truck approaches you from behi;fl bw8.far)n u ;5 x0vh8uqydnd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explainnb ryv08w hx.8;fuu;d 5)lf qa. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wher6f,na7ve ahu6 eas beats can b,f7vh6 a a6eune said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,8bckp+f0 tq*nin /w32gb)qop would the points D and C (where destructive and constructive interference occur) move fan* +2b w )o/3fpbc tkgn0pqqi8rther apart or closer together?

Traditional methods of pgx/h iiyyo,a0bhh f1p2 i-;(n rotecting the hearing of people who 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 block the ambient noise. Instead, a device is used giay1xb;p/i-(,foh2h y0ni hwhich 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 thr k 3.q, ol47h9opow*mo exq1uought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the who4q uo7 3okw xmr 19qo.le*,paves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift ,u, qye/in4jpwo+cbt7h,sy 5if the source and observer move in the same direction, with the y,,epq yu75 ctjh,wo+nb/i4 ssame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hear* ut5zaeh +yvq 0dc9u7d by a person at rest with respz9 y0a*57+vhu cde tquect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A vmgm /d1wg3e.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 frequencm3 / 1vg.gdwmey for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout *os 6mtz 8+ymyreflected by a cliff at the far end of the lake. She hears the echo 8mozs+y tym 6*2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. yv ub d +g;5drf2booi(as:mpjppcu2v:* ,*/sHe hears the echo of the sound reflected from the ocean floor direcudvgoyduso p+,*p* b(fai2 b5: r2:/m; jscvptly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavc:-h;n i)t 6izysuf+z elengths in 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 juste 9bqwt,e6. rh6kfyku()pc l7 d4gswoo2(q/p above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Howk4,h lg7o6ppr(btcwek/9e2 oy( qw.)f sq6ud 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 striking th,w45iug7y h fo7h6q8(rjxr e b ),7u/wmp nrbme water bel/uo8b hxqrimnfw w5j7 77 m6herb r,4,pu(y)gow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ghe9j brvcbczhb: 5.) .round, sees a huge stone strike the concrete pavement. A moment later two .zh vhb59 : bcj).cerbsounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-se 6digm (njvf+s/h)7eycond rule” for estimating tvhyd+(m s 7g6 ifje/)nhe 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 tah/fw, b lqnvq q 3(;-f/ lswr.h:ckj5he 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 whosebh(d )vx:2fj q intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultazdq k/lu/,b .pneously at a certain place, what will be the sound pzuk/d, qlb /.level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dic pu,dv+l:u*yl5 uj )astance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on puc l+yu l*u ,a:5vdj)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-to-noise ratio of 58 dB, whc o8 v)8cg+tmwoa.i.wereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac. cov88g+twcaw.i )om h device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounm.2q4wqm(,bq re clq :d from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere: e,cqmw l2qmbq 4(.qr 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 eag)pps,5ss)f bt fd*2c -ofp, qrdrum 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, poq b+)i:sx, csr+u, l4vuwa,while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker r:caxul ,i,s vpo us+w,)+b4qconnected 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 pc:r6q1 ghiu:aw1 9lxulaced 2.8 m in front of a loudspeauuigx r 11hcql9:6:waker 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 d5hbdcv c4luqkqr7112ifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose lcdcubq 71h5qklvr241 evels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wi5 ck mifs.thn6iudx9k)kzm+2hj951v ll the intensiuk 9khmd jxi.f6ni c1s52m )9z tvh5k+ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one h5l(*dqm mqj6 ias twice the frequency of the other. What is the 6 lmqqd* m(ji5ratio of their intensities?   

  What would be the souwx (j7jl j1f1tnd level (in dB) of a sound wave in air that corresponds to a displacemenxw(lj11jj7 tft amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whnlru p;xd6 (0n/r17rn jyvndg ()d9xikmd+q8 at sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. gdvyn)0drr(x;n+ q79ddp/nx 1j( n k6ul 8mri12–6.)    dB

What are the lowest and highest frequencu 2k,e1++t co, p+d5 nopoqp pmzvv9r9ies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.5n ,kv+pmr 1vdz t uq9,epo+o+9oppc2)

  Your auditory system can accommodate a huge rank *1bnhx*wd(x,7 oxts 4dvi+xge of sound levels. What is the ratio of highest to lowest in( +iv bo1,4xkxn*wxddx*t s7htensity 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. Thowgqnsp;w(lj 0)zv ) 1:0 tt-nxbvm-le length of the vibrat0nqox jmwws pt0: l1 bg(vl-- );)nzvting portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenb:3tw 1j khrm*s,nru,tal and first three audible overt su, ,3*m hr:wnj1krtbones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across n1fxhn a7i7 97pbpgt, the top of an empty soda bottle that is ip9 x1 ,bfgn 7n7a7tph18 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 s5wt3os ht:md 62 w9bxdpanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths hm s:62td 3b9 x5owwtdof pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as jy 3btlc2,xd65;vb6 whwsmi/ its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orig ;,vjd y2bm/w 3tc5 6bwsil6hxinal length?   Hz

  An unfingered guitar string is 0.73mr)rkm)sevz v p7qr5k+3+dp + m long and is tuned to play E above middle C (330 Hz)k7s3r+p z r)+md5 rmv+) evpkq.
(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 (2( qe 6cp2thxvg:2clq;62 Hz) when the temp2;c6h c (vxgqt2qp el:erature 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 f 4g5s :cs7xo:i:4kf3fm rsdwat 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 E9 bc spr,217sv -c.nu0xghdu wxample 12–10 should the hole be that must be uncovered to1 hg 02cvpsn7bxs, 9 -r.duucw 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 at 264 Hz, 440 Hz, and 0pp,f.xb8gnf:a r 5kh616 Hz, but not at any other frequexb,0khp.nfp f8a:r5g ncies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at b:euahnv 0zl6;oth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hzn 06lvea :;uhz. 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 /qkqf,zv *rs ) f8 pvn/m2uhk9$^{\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 presenttk (egzp/z (6i within the audible range for a 2.14-m-long organ p/(eg6tpz (i kzipe 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 kbbbs 5klc+2ah 4j- 6xto the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing wavsx5b+2c6 k4 khbbajl- es in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0o32j8 q 4tfq0h,xeblo4 +d fbt s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stringt+x q,ofj3 4t0o4fel qb8hd2b ? ±    Hz

  What is the beat frequency if middle C (262 H;nah n9 ll5lp51i u;wiz) 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 op)wa+t*n0d3q g0aei suerates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of fa*+agiw0tnus0d)e 3 qrequency 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 sum mjlbgs5 (u;yo-2)350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fr)s- ujo2umbsl5;my(gequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same i*vd2wbao *uhi 9l.qz 7,8+jmws ym5ifrequency, 294 Hz. The tension in one stringow7+.wsv*iu*ql2j9 bmhyd,5zia m 8i is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hearpzgcw+y4 sn bx( 7h(r/d if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and theg/7pwbh (nxr4zs+ cy ( other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forkftdhybi :xn5;g,15h07 gq re6hnt8m fs, A, B, and C. Fork 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 p;h1bh08y ,xni fhfet5g:m n65d rq7 gtossible 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 aparq 6y.2w- qsqb v9g/maqt. A person stands 3.00 m from one speaker and 3.50 m from the ot6-m swvq/yg9 q .aqb2qher.
(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 wzhybz t0; x,,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, whahwtzz,, b; y0xt 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 2.64 m apt)u cr*uv fn /co6.ri*d5y)and 2.76 m in air. How many beats per second will b*apond )ut f5c)6uvc. r/*yir e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequs(f g0yt+e px4p:b,gsency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move withgt e4,+p ypsfbsx( :g0 a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wh: 5mz jq;yn2cbmzg4t-at frequency do you detect if a fire engine whose siren emits at 1550 Hz monb;qzmtmjy- 5c:g4z2 ves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency oic yd4 ;3.p qvl6xk6dif a 2000-Hz source 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 the ; k663i4.dlyovqdpcx y 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 the8r dt) -yr;otg1f o red9e8lc -upbg2te9y8:p same single frequency horn. 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 frequenc)-8c rlbrf ;de9p- uggdeto : o2t198eyrpty8 y the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrashy4*tda5 yu)jcvh 1a)onic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequencyd*h j1 ah5t4a)yuc) vy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed o ffa;:b (a,bbf:s3 mz2 qmpyi3f 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequ,myf pbzf 3q2: bb:3(asa;fmiency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moc akkh.j4 5kf e*dc*eu *bbm06ving flat train car at a frequency of 75 Hz, and a second idec0bm kfh6au jb.ek* d*k 4c5e*ntical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses uo 9enfl *;s/ 9hpaw(bfhj))pwjybx8*ltrasound waves to measure blood-flow speeds. Suppose thewj)*an;pel9)j shp* hb9x 8 f(yfbw/o device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freque1wyy ge7 r9a0pk3id)q ncy $2.25 \times10^{ 6}$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(f4fdk; in mw/ dq7qynsxt;81 sound of frequency 570 Hz. When the wind velocity is 12 m/s (;7iyx; nms/k1d4q tnfwq f8dfrom the north, what frequency 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 itst jf)+(r5xmje9-utuw 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 Machxvhnf1ef4 )xpr1+ih :zw/:jt 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion?+p:jiwtrh1): xz/1 hf f4envx    $^{\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 cw0w vfo- v3o+planet where the speed of sound is only about 3 owcw3vo- fv+05 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. Dq. hs5- 1,sxo7wrjxv qetermine the shock wave angle it prodj. vh5wx qsr-sx,q o17uces
(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 xla3n 5:k8pq0.f+e(lb hh gyy$/theta$ 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 exactlfnj / h 4;gz0chupe5.vy 1.5 km above the ground flying faster tha pch/;fgn hze0jv5 u.4n 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 device that send6hl argq,f6hm3//2 pruigzp3 s 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If tu,g p/m 6ar36 /iqhpf2rlzh3ghe maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hua2qu6:pvo cf ;man audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of man b;k x n3:7a-u+aw( dghqlpzu0p,p lm1y plastic pipes of v( na 0lp:bmhlp1-3 u 7;u dg,xpa+zkqwarious 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 pb-gm55r-xk:o0 hip* i xk9 pbterson makes a sound close to the threshold of humabixk 0hxk: t5orp-ib5m*9p-g n hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hea/k2uo; na kumd sc94a2rd simultaneousl4n u2s2;ca/akod9mk uy?    dB

  The sound level 12.0 m froe* .fp:kqz0*bbh y a+sm a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all df*:y0s bq.a* bhp+zke irections?    W

  A stereo amplifier is ravm(2b z wkp x+gt8*zojqi.41 gted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpugbtz* xz1mwq. 8 ij4(2okvp+gt in watts at 15 kHz?    dB

  Workers around jet aircrafsplc-cf/j , 7kt typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engc ,lcf 7k/ps-jine?    W

  In audio and communications systems, the (fz2 fud:w ra83cs*dy ze)r)ngain, $\beta$ 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 tun rr9nn8 zo qj91ll/vh)61jf rred to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental fwrz6vrr)w :z0requency of 440 Hz and a6r:rzrw0 v )wz 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 vertical ope9 tw3sk/b aal)n 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 from the tube opening to the water level is 0.125 m and again at 0.395 m. What is s/k9a a)wblt3the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.ciad 2(b:n/b yk(l+x:qit d (v10 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 v(t2(xn(ki:+abldd :y/qcb iresonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonxe rs3mjdj m4 w60+2fnate 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*nd3za)t b j7k 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 f dn*b za)3jkt7rom 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 n lyz5-5y2shlthe stationary train hears a 3.0-Hz behzlyny5-2 5lsat frequency 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 zpi/ug88mp3ws 6 ov: sis 538 Hz. After it passes you, its frequency is measured as 486 Hz. Hospi6:v/go 8 pw3s8umzw 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 t.:,y0g9dw7doflus jm he difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a fudf 79w,mdju0 slg: oy.ll octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce arl:lykg15l b .k 1dnws(0b8u x beat frequency of 11 Hz. The shortnluykb50l 1k1lgs 8.wd :(br xer one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad m;s ycs(s/y i).nrl5 mcar 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 fr5msnsi.c)s /; mrlyy(ont 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 aor2:9un ay ;6 dhlfb+9acc 7ofdrta is normally about 0.32 m/s what beat frequencb7lfa:cfn od9 r;yh26d cau9+y would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flykt8 ahj 7bqvc.o/ )e)(cxyb n/ing toward the bat at speed 5 m/s The bat emits a sound wab/kcajn.7)v8 t(c eqoy) b hx/ve of 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 high frequency sound pulses as it ap8e.d bo m j 0kavfl 6+;edertdf93s5b,q7x 9ycproaches a moth. The pu.f r qbyb9stme+j 0xle, 85dkeof;dva d39c6 7lses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wasz/f vn/0 o;yto 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 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.) Modefv/zto 0y/no;l as an open tube.

  Room acoustics for sterkd ((d x5/3jmon:9lee tralw 9eo listening can be compromised by the presence of standing waves, which eok:e9(l3m5dn r wtja9/l x(dcan cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called qqv ,3r.jvmrqr l;*m9“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, ringing sound. For a 90-cm-long rod,3mq,*qm r;r v9qljv.r
(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 healo4vz63p(8hqtz3xu f(: x hazring for the human ear at a frequency of aboutzz lv x3 hz(6(h3at4u:qx fop8 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 the g.d;go/5x .*h)fm0 ciumsi g /0bxwlifround hears the sonic boom 1.5 min after the plane passes directldb fcmg/5s h*;gimx ixwoui 0l /.f0).y overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo-h imzw:;cf0q at is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h