What is the evidence vh0/fagb l ya38eoc 8 czz7q**that sound travels as a wave?

What is the evidence that sound is a form of energy q*r p9: rki casq x33iox)obv2xyz*+:?

Children sometimes play with a homemade “telephone” by attaching a strx 8ypzm tk/0t b37+ldging to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, t7k0ypxltz/dm t+3 gb8he 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 ,tauv8y,a 4dbfrom air into water, do you expect the frequency or wavey,ab, uv8 td4alength to change?

What evidence can you give that the speed of sound in air does not depenlnum 32ppvq1h z 9;8a h;u84rghelc2bd significantly831vzcg92n uulm lhh;284re;bq hp pa on frequency?

The voice of a person who has inhaled helium sounds very high-pitched.x :7uk)vwjuk (.wrs4i(z by: r Why?

How will the air temperature in a room affect the pitch of organ pipero g d(6l:(d y-by9zwhs?

Explain how a tube might be used as a filter to reduce the amplitude of sounds a y2pma3y3w7 pin various frequency ranges. ypam3y 3pwa 27(An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you ryxhvk1x 8j ,4move up the fiy vhk,jr18 xx4ngerboard toward the bridge?

A noisy truck approacheq:i9wc1w7c*me x r;kfe7od, us you from behind 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. Explain. [Hint: See Section 11–15 on diffraction.]q;eidc :1worex u m9w,7 *7cfk

Standing waves can be said tym n(4v/ tt -g- *pgkosdqm/y8o be due to “interference in space,” whereas beats can bek *g-otd8g (s-n/mpy/ q mvy4t said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredlo0m5 xn8z1 +ze l)or7w;ffvi, would the points D and C (w fl+zrm 7 vw1zo0)lx 8fni;o5ehere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopi *nt8scc0 er4le 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 which detect4cc8* ie0 nstrs the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a ( ckemfn3)1(ujzv6 em 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 com(jem1 e)3ufnk z(6 vmcponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same:i6 zsngp),dwr;tda i p;m6j: direction, with the same velocity? Explaidi ra :t,z;6jnmd6)s:pp iw;g n.

If a wind is blowing, will this alt5kzqaf7* oc y d+9ym5px*jl +ter the frequency of the sound heard by a person at rest with respect to tfk+* xzmcjptyodl7y + 55q 9*ahe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positiows9b wzd , 5zhyjd+/of*,w,wens of a child in motion on a swing. A monitor is blowing f zewz/wsd w 5d9 ,,ybw+,jho*a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengtwoy wwb(o0;z 6ya(nua17;ow mh of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengyw ya wz;nmuo 0;oao7(1bw(w6th of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thei*vmi: ahjv-a;s52 c x echo of the sound reflected fxm*ic jv 5 ;2-:sviaahrom the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength ugsf/5lq dy)m(rti: jn30ka,s 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 i13 8)( 6mivjofrum;w wkfyr0ns drifting just above a school of tuna on a foggy day. Without wanm6o8;( 1v ) rfym3jkfu0wriwrning, 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 from the top of a cliff. The splash it maken.9g5-e 1z:bsw 5wlftkfan/+ qlv d (fs when striking the water below is heard 3.5 s later. How hiq(nv1l5a f e 9lw d5w:-fb+n/t.fzgskgh is the cliff?    m

  A person, with his ear to the ground, seeg8 0g 2bf ogt3q83)w 1rqjoyjvs a huge stone strike the concrete pavement. A moment later two sounds are heard from the goj)yt283j 0wg3b8o1qv rgfqimpact: 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 makn 7vro(0 -dgkde over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 3nkog-rd0v k (70 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? ly u.2+nrys7nfrrap tc8*hmqf8-k b6k 7m9m 6    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 socb0)j.1z ek 93vbptgw- u cyt-und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultanerv5 su 7i, ot5g*.snkq- 7rdwauqgu)8ously at a certain place, what will be the sound level if only uag7k5 7,v) uw-uo8q rsi n.dq5g*rst one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four trnh yql6 ., (ojs1wqy9j0ze.equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. , .9 (e1 lsjrhzjq0ty6qnwoy. 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, whereash1xipfz0y wso+m1jhp1x 5 f+3 awj052m (dqie for a CD player it is 95 dB. What is the ratio of intensities of the signal and the xi+x5h2+0(wy1 mpwqe0ism hozfa5jf31 d p j1background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of soui 17tfua/rx v1tov5i4nd from a person speaking in normal conversation. Use Table 12–2. Assume the sound trt5ufv1a/ xio1 4vi7 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 nmcm.,i3m m71 zeu w4peardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplpn)3wr x;6sge ifier B is rated at 40 W. (a) Estimates 3rpg)wnx ;e6 the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 25hugdmw:4t mw0 p; dh4dzhmt1v-++fu .8 m in front of a loudspeaker ohh +zg4;5d40dw- d+:tfmuuvphmw mt1 n 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 9b:m4to/4px3jd zh cg a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levelsgcoh dxpz4/b9tm3 j4: differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a stl5mmpthvi( az r8+dl3/vqa t)0c+ + oound wave is tripled, (a) by what factor will the intensity increase? Increas+tlr/viqa 5mhm z) (+3dla+ovt cpt80e by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemtkeq/e 6t4f j*95 bphment amplitudes, but one has twice the frequency of the other. What is the rk t5p6 f*ehjmqb 94/teatio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corhqlee q8y. o((l*rh9bresponds to a displacement b .h8req( *hq(oelly9amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wu7q m 2r5soux8*h7e *lg+bzvuhat sound level to seem as loud as a 100-Hz tone that has a 50-dB soue*+vz5ur8lgqu* so7 2 mb7uxh nd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tc7f;jfd 1qz(yhat an ear can detect when the sound level is 30 dB( ;qfj1 dzfy7c? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range n42xq-e,l xtesc87q a of sound levels. What is the ratio of hix8e2eq,7 s 4q x-tanclghest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has azvx,u xp;v*8m fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pla 8,v xumzp*v;xced?    N

  An organ pipe is 112 cm long. What are the fundamental and first three a onysm407o,1ex*+yv7tq rulfudible overtones if the1n*qs,o fl rxe 4outmy+v0 77y 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 expectrqi 6 (c6k)cvq from blowing across the top of an empty soda bottleq c6r(ivq )c6k that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build aak0:t( js 3,pezu h5eb pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of thepktbsj: 3 e50euh,( za lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thirdwkk5;7 m 4uf jgkp7ct3 harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% o;5pkmg7t kcw7u j3k 4ff its original length?   Hz

  An unfingered guitar string is 0dzzyd;+ duig y.d-3, r.73 m long and is tuned to play E above middle C ry+ -uzdi 3 zd.dd,g;y(330 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 opedq37cpaqc-b+ y0t*yd gtr 2am(p-e( qn organ pipe that emits middle C (262 Hz) when +0 (e b-cpay2d3tqtq-dpyr(a m* q7 gcthe temperature 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 wjw2u .n6k ahth4n4q-at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the hg jv7njdc*2p7o* lz2 flute in Example 12–10 should the hole be that must be uncovered tlg272 dc*nvhojj 7zp* o 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 pi0xhfof)fi1 r k*rw4n;pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wor*fhkix)w1 ; rf40fnhy 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 ends9+;9zhwexp uj d/ 3yawc;e, cyv-)vkm. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What 9d; h pcv3+-9ck);yv/ juzewme wayx,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 buy; l 7/t zje;00hto*tyt so6$^{\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 a vkorr5e0i3f yfy3 :79 uy,tkj 2.14-m-long organ pi0ry 9jry ,iyou5k v7:tf 33fekpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lon+q3t5kjf i30fyo iu-n g. 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 i-tujf5 ofinky+0 q33 waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every bx lwf-o1 d)7u2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far-7l u o)df1wbx off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andg4 tqmxh n5i4xn(3la / ,5yyaz $C^＃$ (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 operateb7gdpmx 6c o ;k;lnrxgx. +.x8s 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 frequenc;bgxgrxp.;xn+ox67k8 lm . dc y 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 350-h-zoef5 ( 5ium*a lrjg pg645oHz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency ofoj -iz uh roplgm*5 54eg5(6fa the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension inznk sz(z ehy.kh -uh+fx8u ;360m eac: one string is then decreased by 2.0%. Whe mz6.cn (uays ezhx k ;u38h-f:+z0khat will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try t*h tba,rzh:mab; ak2)o play middle C (262 Hz), butkbrh ,za;) 2habmt*a: one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fo2xt.b0uvpw+-9 bkja g rk B has a frequency of 441 Hz; when A and B are bx0jkuv9g.2 wa t +b-psounded 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 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 stax+b uc;f wzl 3h2;:nvpnds 3.00 m from one speaker and 3.50 m from the oth; l:p;bzwc f2n3+x huver.
(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 vibratingia *rv u sjt2)a5y:aa: at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency)au: t:2yaavi*5r asj 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 2.7satat*n+ l rf;p365b y6 m in air. How many beats per second will be say n*+p5a lrt3;tf6b heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequen-2qskg/z+fm vut gs8p iu/56 lcy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detesi+2 ukzf 58m v-g//sql ug6tpct 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 firee4ev6diqjmm ) 8ph)z; engine whose siren emits at 1550pe qdm46)e)mj8hz vi; Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencyrt00x; z yam.t if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenczy ;rtam.x0t0ies 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 frequency horn. When zg92,gl0 l ,-rg uiqga6wd-7v xj+epione is at rest and the other is moving toward the dgeiv -gijgl,w20,ul prz 7+ 9ax-6g qfirst at 15 m/s the 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 sound waves at 50.0 kHz and receives them re+ax6lw ci)h9lq bk;y;turnex9c b;q+lwl )ahy;6kid from an 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 speed of 5 m/s As it flies, the bat emh*j6mjfog2w2:j0l wn its an ultrasonic sound wave with frequeg*njl 2o2 w6 jhj0wm:fncy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played ooa* +q g-0kxpr(xwf5 )udq+qo.gvk 4xn a moving flat train car at a frequency of 75 Hz, and a second ide fqok+)5gw(r0xp4xaod+u g x-* q.vkqntical 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 ultrimz/z: 9gxmt59ud6fu asound waves to measure blood-flow speeds. Suppose the device emits sounxg/6m5i f z9tu9u:dmzd 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 freque/tvlx; g9sjm.2rph 6k 0.xp qincy $2.25 \times10^{ 6}$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 wind vel (5wuhzu9) hzcai i(;6gesvx2ocity is 12 m/s from thi(h)u ezc29 h 6 g5xzwas;iv(ue 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 its 5mfcu c/x81 ew;3fvjrspeed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/sutf5:fygbqma30hj3 / g)hm j/ (a) What is the angle the shock wave makes with the direction of the airplane’s mot3 g0h/ a/ghm u:f5jj3t mq)ybfion?    $^{\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 pl3//ni*fajku c anet where the speed of sound is only about 35 m/s u ka 3cfij*n//
(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. )c;ile(eto9 p Determine the shock wave angle it produces l 9t (o;e)ecip
(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 ( 796rr2jy*k wlr s vg1idjx+tcw,kl5$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and cs6o7ca3j.7o s s;t+ok 9 qarm48 zuf my4z:cfsee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the timotrs 7ac q4 ocss789ommja4 3;cff u6:z.kz+ye 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 so 7n6 82ochuxy2i/hin tnar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects h8xnyi6/ n7 o2tih 2cuechoes. If the 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 octaves7 l*ds/vhy- fr are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. x-r0md0sw67 v;ng237fnepy oa-vvw rIt consists of many plastic pipea 0wpmvxr ndgn7 y-wvf0 6;ev-732sors of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a soun trdd3/k0 ok3 tu.o:wxd close to the threshold of human hearing (0 dB). What will be the sound level of 10urot x:w0 /kdtk .3d3o00 such mosquitoes?    dB

  What is the resultant soo3 t9emwajs.zy(+ 7m jund level when an 82-dB sound and an 87-dB sound are heard simultaneouslyywm+(z.m9jj7 teo3sa ?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opmeo,y0a5t; qken, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equ ey50am k,;qtoally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The zj1s( vv sx8eo 8bc*r2power output drops by 10 dB at 15 kHz. What is the power output in so 1b*(zxc sjv8rv 2e8watts at 15 kHz?    dB

  Workers around jet aircr oa )9)vzr9pvxaft 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 interceptev)azp 99xr) ovd by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicati..;)o ka7ktn vtunzp7ro7 v/vons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequencynzwy7/a65,a cja cumi-cd iv 69/81mqf ecb0j 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 +zb*7ua5d g ;l8gmvm clong between fixed points with a fundamental freg ul7*zvm ab8 gd;cm5+quency 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 tube filled with wate v/8c)gmvmtug.sop5: e4k7u4gqi df4r (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the 5votvfg) .s mqg:dm/g8u 7i44pkeuc 4water 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 tub 5znm7ue6k yk.akwm3gr8o8 6s5aba2pe that is open at one end and also 75 cm long. How much k3 7ner65 a.a wa2km o8kuzsbm8yg5p6 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 one full loop (/qhyf p;rok ,bl5io+:fs0b- u $\frac{1}{2}\lambda$) 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 tigkfqb8c cz.: e,8+q mhe 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from c:f8 gz m 8e+qc.ki,qbthe 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 whispt sn(h,sh4g rjk7p(8hj ,c3ntles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz7 ( s8npj,kh4s3(t hh,pnjrcg beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a ste km3xfk6umbr; f6;qw;*x7. sj k-i)m anb9lbgam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constaxmf k;liakbg qbm;6 wf 3ur*sb7 ;)9 xj6.nk-mnt velocity)?    m/s

  At a race track, you can estimate the speed of carvpzu a3xm* w13t5o7aqs just by listening to the difference in pitch of the engine noise between approacqmzov715 puataw *3x3 hing and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toh 6u)d1xo +pbp cmlgxhue.9):gether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long.g1h)xu.h dp96e +u:clp)x bom How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movev f1m cwhm9c 8.n(tbr(s 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 c h1 9rbvmc ((tnf8.mwthe 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 normally about 0.32 m/s what be+k wm*n* qbvfyo+ 6uz+at frequeyk bzm+vwuo6f +n*+q*ncy 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 p ,1k- gd7stcko l5/jem/s while 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 frequency of the wave detected by the bat after that wave reflects1c l gpsek, -o75/dkjt off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it apo+ b2x *rkz:gxx+- zczproaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emi:xbzg rkzxzx*c++o- 2tted?    m

The “alpenhorn” (Fig. 12–38) was once usedbau7 v7 o lmu;,jofn65 to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to creat j;6vaul77f o,5obunme deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised gpk wkq goq(1l;1g 3g2by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for31(wk og;gp1qg l g2qk the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, caly+evjqo4. ee1 led “singing rods,” involves a long, slender aluminum royoveq .4+1e jed 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,
(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 .4kt;cje9/ql0 gu w i-u6ozyjhearing for the human ear at a frequency of abo/z .iuoj90 l-ytju kw4e c6;qgut 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 ground hears the sonicel9 so lo(82qu boom 1.5 min after the plane passes directly overhead. What is the plane’s as(u8le2q loo 9ltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 dzb30vh+zu3 kkkd,)wn4vz z 1$^{\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