What is the evidence that sou +ijp.fv/xp;: ba vxy 4cnyj7nrv 39/und travels as a wave?

What is the evidence that sound is a form wdm:jpq f;1rhpny ;2)of energy?

Children sometimes play with a homemadh(w7q+z4lmel :z9d xte “telephone” by attaching a string to the bottoms o9zt:x7 w4mq+d el h(lzf 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 cup to the other.

When a sound wave passes from air into water, do you e en vyx6qqyn.;+1u kx+r7i1pseqw-, expect the frequency or wavel vyy ;+ iw,q 1x+xuqepe1qn r7-.6snekength to change?

What evidence can you give that the speed of soundgzh (,rfu9 ;ik in air does not depend significantly on frz(kr f,g; 9hiuequency?

The voice of a person wh zluf,d .xy85mm2(gr lo has inhaled helium sounds very high-pitched. Why?

How will the air temperature z9v3 jayq0v, fuh+ kv-f1t(hf in a room affect the pitch of organ pipes?

Explain how a tube might be used zb*ts* yvs 0:wir2 *ymas a filter to reduce the amplitude of sounds in various fr* ybs2y0zrw : ti*m*vsequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mvjoz fyj ccv *0ea*r7; i2y3)gqyy5p0ove up the fing2** y ;epa7jr0z3y5ycqfo0cv yv)g ijerboard toward the bridge?

A noisy truck approaches you from behind a h +g7ig7ufs:effj, ejf93o d +building. Initially you hear it but cannot see it. When it emerges and you do see io+:seu gh f+,ff77d9 gfj3eijt, 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 benr6ni ,xl;e6;zd ;qd-mjlk e9 due to “interference in space,” whereas beats can be said te n6d; e6k- r; jlil9,xz;ndmqo be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowlfp8iq 7f i+6aered, would the points D and C (where destructive and consa fpii8+q l67ftructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peop(njr .up bds3:le 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 th:3.p djr(sn ubat do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can buu/yt;m50q493k l frhp.e b/fss)u dme thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farthe pebs/qmffur9u ;h3)usyt/ mlk d 40.5r apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directi unjpaou y):3*1gszwd*gf8 ,mabm c*3on, with the smw 3bgau s: *1jou)p,adz3fmg* ycn8 *ame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a per6qi 0) fwb;4t*dai0wtvkbyb cw9r 3l.(j4gs fson at rest with iw cb lgqaf;trbd*v4 3tw 0ws( j b).y40fk9i6respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motionx(qq soc8,qacx7 fv+a mn58x4 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 hqxv8 am48 ,qfa xcn(5o7xs+ qcear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of e( u7y tx3rec66x9rljhk/0 a dher shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the len6erh07yae /c dxj( k xut6l39rgth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below th87.kpp49nn ubk;c,4kuq ube r e waterline. He hears the echo of the sound reflected from the unuc 98p ekpkqu,4bk7r.b4n;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 not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at snbq2-.8 cd:m:ferkbe 4 mt;t20 $^{\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 abovolh3 igbw9 z;i spzw)061,gooe a school of tuna on a foggy day. Without warning, an ezgwiw0lpg 13 bioh;6s)9o , zongine 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 f5/4oaw/:nl 9x oo)oby)m tw*c *bdc efrom the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff/ xobc * )fbl cy9o*4em5w)td o/awn:o?    m

  A person, with his ear to the ground, sees a huge stone st4n7 vlc.go,9po zwe/tv9 ;j ifrike the concrete pavement. A moment later two sounds are heaw79l.te v9gp, covi;z jnof 4/rd 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 ez)/nol6z0p g*at )mwmile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a6en 0t z mzl/)gop*)aw) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le3tzzn0d98nt ; s difn5vel 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 intensity is iltq) k ;6i7me;7ii cy$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when7z ckf) mz)lz(h,n wlkz f;l.8 fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitiellf;.,7fk)n )zw8lzk (zmz hcs, not dB’s.]    dB

  A person standing a cer srhhua)( 7b,ra1bh6lujv,8 ftain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound lev, v86hr1hfbha7sra )b( julu,el 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-ts 5 x8)sqbua80ly w;olo-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal ansxyba8 w)ouslq;58l 0d the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversanzbtz,rzo3v 1 umi6 mstx99 3(tion. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on t1iz3 6r9z39x sztn mm,tu (vobhe 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 strike jggtjl0/7+q ks 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*mc:(h nziup f50i5 hg, 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 lou(c5f0p huh 5g:im iz*ndspeaker 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 mete o 9x;pm tql.l3qhon1/ xp6x2tr registered 130 dB when placed 2.8 m in front of a loudspeaker on the sta tx1pqqohl m/o39x xl2n;6.ptge.
(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 typical8 l*qs6cfl+ ogly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: s6l *+qf8locgSee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,ljd 4s+*xv2 ns (a) by what factor will the intensity increas4 j*xdvs2+nsle? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal din7(5x+m sslz qncd) 0y;ps;k ssplacement amplitudes, but one has twice the frequen7s0qlpcz5k dsyn;s+x; ()ms n cy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wubt g: 0.af8vfn r2.9 d41utdadnjs5gave in air that corresponds to a displacement amplitude of vibrating air molecu4 21dgnutu.jsf frgnta0bv5ad9. 8 d:les of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud dbxneftzhr4*u0;xxm i(/8 q4 as a 100-Hz tone that has a 50-dB sound level? (See (exu/bn mtz4xx*d80 4fqhr;iFig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wh:w5,grvh v 3 /whiat rui*s*w-en the sound level is 30 dB? (See Fig. 12–*/h,ga uvwrvwhi-:t ws r*5 3i6.)

  Your auditory system can accommodate a huge range of sound levels. What is the yw) 71lq)ako ajww:;d ratio of highest to lowest iq):wjda olkay;71 w)wntensity 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 w aolt.7c/*d )fxcny4of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under w)t/o.7cnfld*4a xc y what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental acqaij .8meo; (ys/zy 3x-sq1, okczy+nd first three audible overtones if /-zkscy q+ ,;a1si.x8o3zoc( mjey yqthe 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 the top of an :qf kcbt;*(wa empty soda bottle that* c(wf tkqab;: 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-tbatj1,ewb)i 43iccjn8lh30b ube pipes spanning the range of human hearing (20 Hb03b n1cw4 hc ti,j aj38b)liez to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequen derw* *chgy ,z,-hl9k .px8vscy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originalx.8dey- gz, hs*kh wcr *vlp9, length?   Hz

  An unfingered guitar string is 0.73 5es9otn 39bjhc v:; q *fvop6c h+:fvqm long and is tuned to play E above middle C (33no tv5 9o:;:sj fh3b*+ hqefvq9v 6pcc0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open oe7l+ ;peq .bjtrgan pipe that emits middle C (262 Hz) when the tempep7+;e qlbt .jerature 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 a tq6l-nq*sh u4puc 41gn(s kc)t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hol dm511tdc;sqao,ek a4nh2o d.e be that muac .4;hds,ndmeao15dk 1 to2qst be uncovered to 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, ztzft:*ev9wka1) f/ 0np g6kld.*v kz440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show n k1a9lf*:/gvztkw)v 6z 0 ezkpd*tf.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 both ends. It resonates at two s-wgpl86 a9 )(/y/g 0p xfotyhkynu xl*uccessive harmonics of frequencies 275 Hz any(kun8*-0owpa gplx9yg 6 ft/)hxl / yd 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 f :t/;dcrwxw( $^{\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 within the audible range for y2lstpf,-/wpxq8k3 rysg v6ek6 -.nja 2.14-m-long organ pipe at 2 yk 6.p-3j wl y-ts2k/rep,vn8sgqxf60 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 20 t+hgvh p9 v-k3(xfsd.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 to the inf3- +k sp0 g(xhfvvth9dormation 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 trying to adjll* :3t hd2afbust two strings, one of which is sounding 440 Hz. How far off indal3lb2t* :f h frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and eg9d l 2uvtyyk9jl4+;qgm8 l/$C^＃$ (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-*gw6+s :w wqky7 -a / .ofxmrv(g6odgo;lhpwerates 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 o of(/ *.l+ oryxd-6v;:q6ww woh 7s-mgg akpgwf frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 l3utt8m:ny4w)c pdfz6ju hjzk*2r *7z zl85lbeats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of th j8pct32 6z7lyzmj*wk zt hn):4z ufd8rlu5*le string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz.(85p t;bt0ays.jsbkf lzrx;* The tension in one string is then decf* s5(k0xat.pl;s 8btb;zy jrreased 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 hear 0 g(*(ool:v 7xyhry/kl2xyerd if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other *o xkleyrlhy2 vx o(r/( g:y07at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning le:gp4ww+r3ltqkhf 5 2los o5 9o(h(xforks, 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 possible frequencies of ltww4fs o :e5hlk395 ogo2 (lhpq r(+xA and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker a tnw9cu/5b5 5nz(z xcqnd 3.5w z(n qbn95 cuc5x5/tz0 m 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 vibrating at 132 Hz, but3m: n;kk/ii ugosj.r* a piano tuner hears three beats every 2.0 s when they are played trji;g3oimk:ku / * n.sogether. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beatgch amb 1twrv/pkyrik0- 94-3s per second will be heag314-ihkrbc0ma /-y v pt9k rwrd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren h,:rh gabz,1 o/a8 mneis 1550 Hz when at rest. What frequency do you detect if you move with a speed oh e r,,ma:1a g8/obnhzf 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 whk d5b t0(ds-c0cjm z.nose siren emits at t0k zc-bmc(d5 sd nj0.1550 Hz moves 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 source is moving towys m: pk-k i(xgwr2.gk.tf3m0ard you at 15 m/s verx y.mmkp-.k s:g( rk0g2fit 3wsus you 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 fw0lw7 ot e4 k2(a1sy;vbn1 foorequency 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 frl 0v 2wbtkfy;snow(e7ao 411oequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 jf6h tk4g1h kpxe:g*4 kHz and receives them returned from an object moving directly away from it at 25 m *kgjh144t:xepg 6hf k/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bsuck;l9b- :orq( 8kk bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thborku bk:9 q( l-cs8;ke reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, al6wgv(:qp6.f 1 q icsf tuba was played on a moving flat train car at a frequency of 75 Hz, and a ses:1 ( pcvf gl6qfq6i.wcond identical 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 ultrasound waves tl9bi:xdk)3aa u/ u :uqo measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is tha:au kd)lx/3b9uiuq: e 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 wxuyib 30-j0 zoaves 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 the wiud.vy a9c8eiv1hew 4/nd velocity is 12 m/s from the north, what frequency will observers hear who are located, athy.uce1/ v4v8e d9awi rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its)*vyr(9hn wvi 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 whe 1.y xyp6bjn9 vr4vg*qpvk:)*p wuk+hre the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the4p)*vuv1r:* vx6pgyjyk bpn +9.qhkw 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 plan:du,3 f;m.- mzbkp k7*qppsqcet where the speed of sound is onm cd :7;kp-.bs qzqupf3m,*pkly 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 wave angi mxlv mnjm9*/qca(:qcr;6 coac;z )8le it produc6c/;)( a:mnjrc v l 9iaxo*mcmc8;qqz es
(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 njx+od1zhtupde9v:o7qsbc6q : 1p2 4$/theta$ 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.xasw456n5otu 5 km above the ground flying faster 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. Detostx uwn 4a556ermine
(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 pdb,::af rg09,wo0fbb-ym cf device 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 to work is 200 m, what is the minimp cb9ya ogf-00frdbm : fbw,,:um time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the h-e ;slzxeq8:scsy0 1 mj/nz4o uman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphozzstk8(36 p/oj1egxg ny. It consists of many plastic pipes of various l3 tzp(g1 o e8s6xk/gjzengths, 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 makes a skv.zq7wer- kt*h78 xi ound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?r7hxk 7 tkvi. 8*q-zew    dB

  What is the resultant sound level when an 8lg c9q4r8hn *e2-dB sound and an 87-dB sound are heard si98 cqrn *4eglhmultaneously?    dB

  The sound level 12.0 m from a louhm336g1r-wkkc si(ji dspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assumic 6-iji kmg1h3 ks3rw(ng it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power 92(fmk uo-ayloutput drops by 10 dB at 15 kHz. What is the power outoamk(fl2 -9 uyput in watts at 15 kHz?    dB

  Workers around jet aircraf0wl jsun -(usx qdg(94x 36sdvt 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. W gqu3 udjsxx( (n49-wssv60ldhat 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 swe89w9fise2ia(7 v s xki:g8mqc; +mjystems, 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 a kzf:y)v-8 cj0n;rv p0 .l bksffrequency 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 ps(m8km(v 8 pnpg91hx0mmi 7s points with a fundamental frequency of 440 Hz a7 ig8 s psh(nxm(0pm8k 1v9mpmnd 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 tube fho. (m5trx/vzilled with water (Fig. 12–35). The water level is allowedmr5( htvz/xo . 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 the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g isl 3.*igo0dqui near a tube that is open at one end and alqd0. iulio g3*so 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 in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as o 2z7gve:y 6dzo fwa;,dne 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 s33 vo0*dubowzk ;6 ysxources. 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 one so*dyb0oz3s; vko w 36uxurce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. 1auov4 f2rh4ig1i+ orOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the sp1vf 4orr oihu4i2 1ag+eed of the moving train?   m/s

  The frequency of a steam train whistle as x424bs s:oq k.zmsp 1xak.9 klit approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant2m skzx4sksax.q 4 l9ko1b:p. velocity)?    m/s

  At a race track, you can estimateppwc8re1-zwd2 2;wo4iw) ey l the speed of cars just by listening to the difference in pitch of the engine noise between approaching and recedip)we lp14o e;idc8zw 2 y-rww2ng 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 together, produce a beat frequency of 11 yvn*r qoaagr )h7g0n.64ga 2xHz. The shorter onr.qa0gn rh yxo*) 2gan7a4gv6 e is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite enx)y/ ynczflj66)nuy u mw, up6g/o6f ,ds of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b),uxu6no),yn 6y/fg/p wujz)6 ymfc6l 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 aboud s kqt9+t.ym11yxof /t 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflqxto1y.ystk+/fd1m 9 ected 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 towap:0mi w,3y5oeg w:ci srd the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave ri c3i :pmsg,0w:5yewoeflects off the moth?    kHz

  A bat emits a series of high f 1w(d:5 tcm0s10c moxgb 8:xgh2 sejghrequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How x 0xghgo2:d0 tc1(w 81hgss:m5 emjcbfar 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 used to send signals fro1 yet/p 3ijk.ym 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 T je.ky1/yi p3table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence o. p.m06lg5j gn8lrsenf standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m h 6e0j.lg8n.gpnl5s mrigh. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slenderuufc t n 69mq-cf36p4u 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 mad-q cf4 f3ucut6p6mn9ue 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 a frequenyhhf)ij(1 21e ycc88 htlc ha*cy of about 1000 Hz is e8ja c h8ilyf11 c ty2h(ch*)h$I_0$ = $1 \times10^{12 } W / m^2$ 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 2.0ji0zbbslbp1):.(9 b l nwd wj0b;6sib. An observer on the ground hears the sonic boom 1.5 min after the plane pajbd :lbi) jip(w.szs1 nl;0bbb 6w09bsses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1/mes9:itcz4kcv93y : jma ci2 5 $^{\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