What is the evidence that sound trav.pi);ar7 yh eedcv,a; els as a wave?

What is the evidence that sound is a form of en, kntt iy:jz)0ergy?

Children sometimes play with a homemade “telephone” by attaching a string 7nv:qber1 :j:bjtht4to 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 so j rebhqj:v::ttn417bund wave travels from one cup to the other.

When a sound wave passes from air into water, do yownrc/4 .coxa. id8ki; )uf oh2u expect the frequency or wavkhrwn/ .axi;8c .24io )udfocelength to change?

What evidence can you give that the speed of sound in air does not hlv))8il(ias depend significav( h ila)lsi8)ntly on frequency?

The voice of a person who has inhaled helium sounds very hon/7 .wejzz l,a; m3gjkh-e b4igh-pitched. Why?

How will the air temperature in a room affectgqtsp j. e*94/og1ugnudx )l *8jwd;rs7b c0j the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ams*.yp qmka::),sxaf hplitude of sounds in various frequency ranges. (An example is a car afy p a,q*sms):.:hkxmuffler.)

Why are the frets on gor*(q(xfoz kv,r80 ca guitar (Fig. 12–30) spaced closer together as you move up the fingerxqg0c ((f8,*v okroz rboard toward the bridge?

A noisy truck approaches you from behind a building. Initiar;ot wlke g 0g4b(r;;wv8cw*pen1*b n lly 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. Explain. [Hint: See Section 11–15 on difk8 vwb;gew01rewcr;g *(n nlo ;bt*4pfraction.]

Standing waves can be said to be due to “in hbi,u; )n5;.60wqkh dtlz oshterference in space,” whereas beats can be said to be due to “interfer.tdlho;,qu) s5hhi0nk wbz ; 6ence in time.” Explain.

In Fig. 12–16, if thezqfd mb2,j 7dappfp *f45i2mp/ck )3f frequency of the speakers were lowered, would the points D and C (where destructive and constructive ifi*fp qd 2m)mfp5d ,/p3j fpak 72cbz4nterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing ofq m9okuo b,6seq:(8r kq6ru 1w 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. Insteadk b69rrm1q8uus6,o(wq o:qe k , 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 offe 97ve7byml : as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b)y9f 77 mvee:lb, are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if s:n*aly, xaarn8ibb o rs04v9 +5o.di the source and observer move in the same direction, with the s,r+nbxb r aii458aoad :sv* .9l0soyname velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hex9mo+vp3- s5it x * xm6z-;ykhwutp0eard by a person at rest wih5ou6pe s-y3xx 9mpi;-k+z xmt 0v*twth respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chil1y al5. zl ctotqq(, 5us1(bovd in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At wo1zl caq5.qtol(su,yb v1(t 5 hich position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeninff gh,-7t n +2epykvs 2/iwp,bg for the echo of her shout r+wf y2hptvfs ei/-7,bnkp2g,eflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side oft mlnx12 vifqx3bl +* c133/ziut7gm m 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*vmll xbqzg3c2n 7+3/131 utfmi tix m–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at .vd x j8k f)qsg)(ef++qguol -20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of,s( vwj:e6rt0 o wthf2 tuna on a foggy day. Witjs 6w,veo t2(:0hfrwthout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fromotm 4b 4,t27 p-ynldsp the top of a cliff. The splash it makes when striking the watebm4o-,n l 4ptpy7sd 2tr below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grou (sk3xx uota).nd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard(atx.o u )kxs3 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 madevbh,uttn)8 (d,5 5rb(z 5bu h+xzh opv over one mile of distance by the “5-second rule” for estimating the distance from z t ,5b,bhh ) ovu(d+r8u( 5zvhnpbxt5a 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 levelh-vm9/vwh 7pf;h3p; l. e.tzdnnks7d 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 intensito+ 25zv07pdebne3 do fy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level h(c7zt atnc3 ggjs:sx zl ),3.of 95 dB when fired simultaneously at a certain place, :j.cg7( ac)z 3t3xgt, sznslhwhat 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 cz kwldasoehz b,c4/2crgt77;2kd2 (four equally noisy jet engines is experienco/eg wrch;z (2ks2bzc adk2d,4lc7t 7ing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said1z0)(qw)l() qfwtfpk( v wz fh to have a signal-to-noise ratio of 58 dB, whereas for a CD playe vz zwqw0l() p)qft(fh(1wk f)r it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of soy*ld8rqslbm, fpcy,y ;pz o5jf 9+6rfwi6 (r+und from a person speaking in normal conversat5 dsy9*68(yf,cop;jbfrmyr,lf+iqz lp 6+rw ion. Use Table 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 ar1( r5q/vx1 eic)t3zya j hgfy-ea 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 amplifix s5xk3 (xnn,u hbs4y hj. j2,f5myb0rer B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poh5 (3nry,h sf. xx0m,jukybs4j2nxb5int 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when pla/gs4 8ylvd dj76og:6xtt(v rsced 2.8 m in front of a loudspeaker ost74r /tvdo 8v ygj:l66x(sdgn 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 of 2.0 dB. What isi/j ws3emxo4fd59sbg )(lu x 5 the ratio of the ampl fmsx(5w 9eldo/js5 )ibxg 4u3itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) e2x k27wz1vrjpf k3lcht/ 32yby what factor will the intensit1fx 3 7h evyrztl2cj2w23p /kky increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenxy :yvvb*2i7i/myrb,69e h q vt amplitudes, but one has twice the frequency oyv72b,x:v6 9r ie*yqh m ibyv/f the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound tu;m7) ho8zggwave in air that corresponds to a displacemt8o7 hmg; zug)ent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone tha8/mrng0 s79q hanch; ot has a 50-dB sound levelmg8sn;0 /n7oahchq 9r? (See Fig. 12–6.)    dB

What are the lowest andlmz0 -).4gnruez jh6zyvs4/r highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) )gry6 ze4r0m znjvlu4/s hz-.

  Your auditory system can accommodate a huge range of sountvh6yzar6e,+tj y8sgh7 j9 ox*ho.e .d levels. What is the ratio of highest to lowest i67 6oj *ez+hth s.yj8h. ra,e xovgt9yntensity 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 fuhlns/ b2+ vo t4/ v(bgs38ahwundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. +4hl(8v sba3 /tnohs2vw bg/uUnder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thrkjyyt;;av+ q (ee audible overtones if the pv (; k;yyjqa+tipe 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 exsl:i+9ly x,xv pect from blowing across the top of an empty soda bottle that is 18 cm d vsxli9x,:y+ leep, 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 ghpt9 )36u cmwpipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipesumg36)tc phw9 required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hasuw5jp 6s*f sy/oahz(v - e4g4t a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of itseyjwsp64vu*s ht/4f( 5oga z- original length?   Hz

  An unfingered guitar string is 0- p3) +casc3wd ws:m7luwhr 49e xswu ebg):6z.73 m long and is tuned to play E above middle C ( bs:4+73hwc:w )rzc l9-weg x6uedwa ss)p3mu330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length sn2xhu y jvk2*j30l)0dxj j+tof an open organ pipe that emits middle C (262 Hz) when the temperature iss nx)x 0jk3u22yjj dljt hv*0+ 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 +4 (xw66smaqrdk2g+qd-pgs b$^{\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 zmrpboyl65h6 o92 l7c hole be that must be uncovered to729y6 o5czl phm lr6bo 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, anaqz ptf,5lh:v udf26 z1-rflkl- h,bxj-/. efd 616 Hz, but not at any other frequencies in between. (a) Show why thbu pk-- lf1ar5zh,.e, 6jffxdqzv2t/flhl -: is 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-4rz7ehpwi pv7 c2 mq4 both ends. It resonates at two successive harmonics of frequencies 27q4hr-p vmp2w77i4 cez 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 yf0 )vi*:l)vut lpo (j$^{\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 wi.r rq3-+b8,4 u flltyji 5oupfthin the audible range for a 2.14-m-long organ pipl 4o f8 rb+ui -ft,.u5prlj3qye at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.i)czy* w-ak(iur2pd8 t.(dl e 5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer cdr e8(.iikw( pzt2 l)*d -yauto the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when te1k 6xdhgn238gleu: )f+b wta rying to adjust two strings, one of which is sounding 440 Hz. How far off in3e d 1ufh8glxa2ew6t+bk:gn) frequency is the other string? ±    Hz

  What is the beat frequency if m*pzq.5i g 5 2ly+3jvycu,du; t/ mcdfdiddle 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, whi8rwg5, ikvqc(uh9n9 c le another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whrnc(v k5 qiwcg899,uhine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4v1;dyc/ ie1:w rp ec*x beats/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 fr/;11v c cxeiw:dye*prequency of the string? Explain your reasoning.    Hz

  Two violin strings ar5+ qqx5z-2p q7xvd)cwp6sm 9rd dtl*we tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played todpc6 +d9v5* r sxmzxpwq5-wqt7)d ql2gether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to p3ye7aphs d9 xa 6fc.e+lay middle C (262 Hz), but one is at 5.0°C and the other at s9eh6ep+ f .x7a3y acd25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fry 0o/ye cn.tda8s c/o)equency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are ss.e ocdt8oyn//ay )0 counded 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 stando/bb.db-gj gza i82/o s 3.00 m from one speaker and 3.50 ob gg.o a/j2d/ ibb-z8m from 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 supposed to be vibratin2 8r+niqa gky*g at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If on 2yq8ka i*nrg+e is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76d,(k (jc,j(9qz wsju c m in air. How many beats perw((szc, j9c(j jqud ,k second will 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 155;2 +gs*g(;o3 wd ubzp qt1dzvlw1yq c,0 Hz when at rest. What frequencyt+cuq1 3(zb2sl , pow* w;;gdg1zdqyv do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose cs, f8zf5-0ddds uq d9siren emits at 1550 Hz moves at a speesdf-,sfu05dd9q 8z c dd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz souhi2sszg .b31sro.t+prce is moving toward you at 15 m/s versus g s2 h1r3+o pb.t.ssziyou moving 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 single frep56dud6 jc)kb a,le,n* n0ixfquency horn. When one is at rest and the other is moving toward the first at 15 m/s thlnfu*6dd)nbia cxj,5,06 kpe e driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soesv f(tbi 4estr3z43/ und waves at 50.0 kHz and receives them returned from ae4/f3 3eszs bvtr( it4n object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sqh 5/tiu :ykwoli 9fr -lk;:e)peed of 5 m/s As it flies, the bat emits an ultrasonic sound ruikf l:5t)oi hk;lq:w ye/9- 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 ))xf,m 5oj +lt02rdt q3n ao:+aalh yfexperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone wh 2o :qaoyxf )alfan5+dj,0t 3rtl m+h)ile 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 meas.-+ uc 9(u x5gln2nl 7+czef8krrjc7/slxpq jure blood-flow speeds. Suppose the device emits sound kzlfsj-5+u xn+u7rc.2cl 7j9p/(lc8gq e x nrat 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 frequ dsy dc/:lpg27c++x rpr6bp5xqv.* stency $2.25 \times10^{ 6}$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 the w6 5 5s ya5z-gdcxh4j+d1svlwuind velocity is 12 m/s from 65uwadl yc dsgz-+sjh1v545x 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/upn v9sg o.9d if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where th;kekm vaf )9d n-4cototr2 y/0t gp6h4e speed of sound is 310 m/s (a) What is the angle the shock wave make mkthe02)- k4ct49d/grfn6ytopo; av s 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 wheit;; pos-v2r3xbk2onre the speed of sound is o2i23o-o vk;t nxps; brnly 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 ocean. Determine the shock wku w op6*8mw2 )glz6heave angleomk )pluz 6wh2w6e8*g it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle v0-t.6n95bpyoi hj;am71ln bn b uu 4w$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the 8e e:g5r5pblf k6we41e u c,dhground flying faster than the speed of sound. By the time you hear :rebp5 hc l4ukg6we e1f5ed,8the 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 downwaky2 a1 59 bincqls4yp .dkq(-sc9s/qyrd from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the m4(q/kya-qcyscp 5ysl9k i 2b qd n.9s1inimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audi1 sw3 +k*rjapjble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe bl2t5k9;v *ndlqe.3.3vu l nc iblxw* symphony. It consists of many plastic pipes of various lengths, which are open on b*n *lv q3; cu59.bbl2.iv3le n lxdtkwoth ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sorrdgrv r jz g.iyu61wo3/;b2 *und close to the threshold of human hearing (0 dB). What wil uo32r rgr6bgwjdiy;rv 1* /z.l be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level weu4 (p;iwdz1y :brfn6hen an 82-dB sound and an 87-dB sound are heard simultanebnf;i reu 1wy 46(d:pzously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What idc or,jrn8(d0s the acoustic power output (W) of the speaker, assumino(jrrcnd 08 ,dg it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po8 2fxqqjyvve.6 zo2n8 *xk 2jywer output drops by 10 dB at 15 kHz. What isnv*y xq.2v8ko8 ejq2zx6y2 jf the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typic-w9b9 aorzb/*tryfh 9 ally 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 engino*9rrahzw/9b9yb t f-e?    W

  In audio and communications systems, thewbz5 b63jwy 6r 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 tu3 o j- h;xstptk-bqewwkt210. ned 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 fundam 9v n29a+/ylexkobdy) ental f /)2ln 9yox9ebdk+vy arequency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open to7ws5b rpn73 nd)5,csgyo6ni( 9suo9tp/h ybube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube aboio9g7onpn3 d79 y bhts/usb,(wy)ro6n pc55 sve the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at onesq v r9z3-g y,yx)vzl5 end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic i3z-vvlq 9,gy z5x )sryn the tube?    $ \times10^{ 2}$ N

A highway overpass was observ(ew0uw4 ic3n6n ap/p cfh6l(wed 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 500–1000-Hz range coming from two sources. df zhct 2p t*3 5e8dq.fd9pp4eThe sound is loudest at points equidip hqe.5 ct32 f8ddpfe* 4pdt9zstant 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 other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One tr1oc: 7zm l)dt3vkav9fain is stationary. The conductor on the stationary tra fv19z3mv:c7 lo dt)akin hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle aam-fpb5g11v8-a j79phel d his it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast wg1- 9ia7 p-vl hpdhej b51a8mfas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenin19n) k61yc**egx q6ordnjp mfg to the difference in pitch of the engine noise between approaching and receding cars. Suppose th6d*9pfxmryjnq11)ceo k6*n g e 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 together, produce a beat frequency of 11 yt;xw8 j+ 9ufmHz. The shorter one is 2.40 ;yjt f8ux mw9+m long. How long is the other?    m

Two loudspeakers are at opposite jzyruvmzh ;8fp-1 (6ehn-6uf ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–3u;z1f -huyp v6j-nhz fmr6(8e 7. 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, (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 n76f 0ina4yn-4w8y c hnkxc:s hormally about 0.32 m/s what beat frequency would youchyna 8wk 0fh:niyx-sc4 n467 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 whileu6 0im(wc(q eh the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequ(eh0w i c6umq(ency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequena:t b6c:lfcjzdyl)8r2 npq 04 cy sound pulses as it approaches a moth. The pulses 0ltda:zly4f28pb cqjr6:)cn 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) was oncu/ .mvoirt (6he 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, th o.mutirh/ v6(e 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 listening can be compromised by9*ide igs 2a0s1j9um x the presence of standing waves, which can cause acoustic “deaex2 mui 0ids1a9*sj g9d 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 demonstratio/o:ugez kurb oa/qnzq3p/74. n, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is 3/:on g qq4/kzpur/e.7ab ozu 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,
(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 hg,0du3v). juga)3 ohuxx lx2searing for the human ear at a frequency of about 1000 Hz 2 vd lu3oag)0 )xxx.hg ,su3juis $I_0$ = $1 \times10^{12 } W / m^2$ 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 o::7dk 0cjlpc ebserver on the ground hears the sonic boom 1.5 min after thekl c dj:e:c7p0 plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 w;og(n2 sb;qz u3y/kh$^{\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