What is the evidence that soun 16lgdudzbe0 2(eq-dtd travels as a wave?

What is the evidence that sound is a form of energy?.pv5;mf1 ye-uxkseoptw: :.j

Children sometimes play with a homemade “telephone” by attaching a string tp- wmqqzk)m6 (o the bottoms of two paper cups. When the string is stret-6 k zpqq)mm(wched 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 pas svztg4afhrp +c(77b6iw x5pv f-44gfses from air into water, do you expect the frequency or wavelength to chanx6- +fpgsgfwhvr4pb7cva5i ( 7t4 4zfge?

What evidence can you give that the speed of sound in air does no7z8st(8 s fozjt depend significastsj8fo8z z7( ntly on frequency?

The voice of a perso41qy7l*:lz y7 kr naqdn who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room aff ajtihd0*8 hr lz18b+bhs8a 8bect the pitch of organ pipes?

Explain how a tube migtd az m;p*8csf2 omcl 3ep.0 .e*)sdxeht be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.)* elsme0t)3dpa;fpe d.m c.2cs o8 x*z

Why are the frets on a guitar (Fig. 12–30) spac6 yoq lt,j9yvy+duh74ed closer together as you move up the finl q96ydtyv,h7yuo4j+gerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but vq (-6ssym6no cannot see it. When it emerges and you do see it, its sound is suddenly “brighteoym s6qs( -6vnr” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spa/d efgpi6y.vn9 kj( 8rce,” whereas beats can be said to be due to “interference f gk6p(n/dr jyev .89iin time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points tppkd+q35qhf tmunj5b(-i) 6; y-; a kz*g jkyD and C (where destructive and constructive interference occur) move farth ft3*n;y5ktqy;qk pa6 ji-- g(jb + )k5mzhudper apart or closer together?

Traditional methods of protecting the hearing of people who work in arajy *8tc:d- uneas with very huja n*-8dty:cigh 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 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 thoug5+u wgh;2e lu cydp,l;ht 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 far5uclpy,u2;; wle d g+hther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dxfg2qew3 4nw 8irection, with the same velocity? Explaiw 4 fgx32nwq8en.

If a wind is blowing, will this alter the frequency of the sound heard br3fqmilg i7h(xj *,2g.bu-bu y a person at rest with respect to the source? Is the wavelength or velocity chang2iiuq ,3u-gf *bxgl.mhjb r7( ed?

Figure 12–32 shows various pos7m jts r*9xpvp; 5mme9 h+1c-ac4vvoritions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of mrtm- cr7a5e9*x1 ch 4j9ov;mvpvps+the whistle? Explain your reasoning.

  A hiker determines the length ofm v(2h 8w jdx9qgu.h,t a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. jh(8.qhvxd92mtwu g ,$\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ex qi5p0 w6hywrk 07e/pcho 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/s750pwpw/6 qh 0riekyx (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave/m.6/*w3lmzaqze 3yzl a0cxq 8-rbl i lengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is driftuz3bt/ q0kc6a ing just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anoc6q t uba0z/k3ther 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 cl5 :7bac.4zgl(gqe1rw j,x wtbiff. The splash it makes when striking the water below is heard (q7: tj5b alwc4 xgge1,r bwz.3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stv du)u:z.c/ ybone strike the concrete pavement. A moment later two sounds are heard from the iyv .):/zbu ducmpact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secondun*gj+58bdr )mk rt9k rule” for estimating the distance from a lightning strike if the gbrtr8dk5u9 m*n)j +ktemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120m 13y7e ai-wvc 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 sounqy t, /b )+htmc.hq5sgk8 ul(pd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lrh23t.)ocb om-jk )kc evel of 95 dB when fired simultaneously at a certain place, what ) hc)bkmt2j3 .okocr -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 four equally noisy dm,45m/8kgy j3 giyke3t-xom jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experiencee yk 3d8mm3 /og45gm-it yjkx, 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 .km+ d1zf ox ;jhsvo.1qimr0 wnw-37a, whereas for af qzn 1 mks7oim.vw xjhd;r-.0+wo 31a CD player 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 powe ogroau57/d4h r output of sound from a person speaking in normal conversation. Usa75 rg4h od/uoe 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 aytn :u(1,:ylrf(z p uopr.-p;cvm0f ;xmlp 0t n eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more m6ka, bp 03me wei;lx1hodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wou, bemeaih; x p1klw063ld 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/ej3 v)jj4e(6zj,2kzyus:sr qv.p g x3go c5v 130 dB when placed 2.8 m in front of a rx:og3ee cs/(423qvpu6v.) ,gz5 ysvjzjkjjloudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typicall + vgr vmb;t:*zqu4*sgy detect a difference in sound level of 2.0 dB. What is the ratio of thegbt4+r* qg;*u:v svzm amplitudes 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) by what factor will the iapiqtz2k) rec4: 3o 9intensity in e)r3i qpc:2kti 9zoa4crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amp93kcg s kzhx +6vm-7m5mmcd5qlitudes, but one has twice the frequency of the other. What is the ratio of their inte+ckmmm 67 gsk zx53h9vmq5dc -nsities?   

  What would be the sound level (in dB) of a sound wave in air tha7r9ksk*xh3r ps tl31ht corresponds to a displacement amplitude of vibrating air mole731 3*trkrxhsp9 hskl cules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soxlf4lt(;m/4p * ,)dpu encyk ta :ibv9und level to seem as loud as a 100-Hz tone that has a 50-dB sound lei*u4p,b/c xl4dmefk9:v nt pal(;yt)vel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when th;s*xpayt::o7m* agwjscq 22 f e sound level is 30 dfxts* *o2wy;s:pmj7a a 2c:gq B? (See Fig. 12–6.)

  Your auditory system can accommodate a h:d4rmk1ywav 1 +p5l9eut x6 9zrl5onsuge range of sound levels. What is the ratio of highest to lowest iek61w +5mrnp4usyo5 1dr 9ll9 vtza: xntensity 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 funda,twk 8)lm,b) futx ac9/gim 0kmental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 gax m8w)u),ft ,lt /m9kkig0c b. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whast v aj iv0g7-f-.j5/h pv,nh:mbs8wtt are the fundamental and first three audible overtones ifstnvhmjf s:-w .vgiht- 780,j/b 5vpa the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top o0dnl 19 okhk:b)t a *cvdr4j7ff an empty soda bottl d hbfta *kdvo741:0k)lnjc9re that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanningx76pl63 x wl+)e(itf hl9 ccmjc*at;j the range of human hearing (20 Hz to 20 kHz), what would be the rangx3mcw696xl tt )* (+lic7 af;ejlphc je of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5fj)2erw0 +eufpcs /r)40 Hz as its third harmonic. What will be its fundamental frequency if it i 2rsefr ju/+wcef 0p))s fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned;q z0ctko5zqkfun+ + 4 to play E above middle C (33qknok0; + z5+4cufztq0 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 organ pipe that emitszs 6*ego/lj qw 0k6gq8pydw78 middle C (262 Hz) when d*6l7p8qow/wjkggz y6eq80s the 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 at 2ciq1(-r rn1clnja9s 2j5;5a2y gvphd0 $^{\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 shexs mkrygcy 6o3y)).u+*v9jy ould the hole be that must be uncovered tooy gm))e vcyyr. *3y9ku6+sxj play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but1rf,jhf t:gp;d r/j .f not at any other frequencies in between. (a) Show why this is an open or a clofd 1 ht/gfj, j;.r:rfpsed 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. Itw5*6bdn.d f -wk /dux j53ized resonates at two successive harmond in d.6fw z-dwb5k/ xuje5d3*ics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 v 0n(w2yz/ )a(wm ad7oa9cvuc$^{\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 rg uc04 6lfud5fp8 :xofange for a 2.14-m-long organ pif8u6plgf4:f d 0cu xo5pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal isxq7lc):u+o d c approximately 2.5 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 +) cqod x7lcu:answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two stri*1u7uy zf nj3engs, one of which is sounding 440 Hz. How far off 1 fuj7zey*3nuin frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) affx(z(( :aaxytk)oe,1tj e ;nnd $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (bi: t3q bk(. ouoo6vpx3rand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simulvit u6 ooxb.o(3k3pq:taneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350xygh)z 8hwze2crp -j* y20qr3u,2dfq-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational y8zwy f)xrp, jzh0re2u*-qqgh 3c 2d2frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tune-yvb/)a5mnh h d 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 ) mh5hn v-bay/played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicbgpfoqy, s9 (*as;biofh .0i2al flutes each try to play middle C (262 Hz), but one is at 5.0°C ayf2,poab o b*ii.9hg sf; q0s(nd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, y5wh:/ rcxxfsvau-z,nojarp i 5+o: . q.;tz,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 A and C? Wha5,:xz sa/-5+orhypxtq;o,v if z.acwn .r uj:t 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 w5r+-tf :p befg.sid +speaker and 3.50 m from tp-f sf.g+wi5+e dbr t:he 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, but a4 niombk04,iq +bm zd3-prk7 q piano tuner hears three beats every 2.0 s when they are played toget k izrbi4p0q,kon3m+dm4 qb -7her. (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 mpa2 7e g8wzy+6hsd3mb any beats per second will b63 d hz+p78bma2ygws ee heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at r7ik)i.q 0yxwx ehb* *iest. What frequency do yo0*7*hixikbiw q.x e)yu 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 3 -3 vki, husacy-/scusiren emits at 1550 Hz moves at a speed of 32 m/s u- a,csck-h iyus33/v
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000+epy: * vkw j9r ez;q.hg:zf096 fvlvj3tznz8 -Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two f;rv 9.zj63 vfwh+:qjz k 09z* v :etgpnfl8yezrequencies 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. 1* ux i m//mm4-v.vjux0cdyqtb6o d6 sWhen one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume Tv xtcob um x.01mmj/vu yiqd646/*-sd = 20 $^{\circ} $C    Hz

  A bat at rest sends out ult *92tf mh3zkqprasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fre z32 *qftp9kmhquency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed og2l 1x z:)jg28kcabdy f 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequenc)yjg1xzgk2 2 ad8b :lcy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, if*r ,q)he: revcbrw/ n *s)2ba tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while aibw,vc2 nf/)q*be*r resh )r:t rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supposev7gv+b u1vj p5 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 the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from tjv bg5u7v1p+ vhe sound source?   Hz

  The Doppler effect using ul3 e vejt ,d cgf)qne-qey 8u;3n)1x2oztrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency,mjy4cl)rl **d6e vw e 570 Hz. When the wind velocity is 12 m/s from the north, what frm6yw jlv*4l)ee *cd, requency 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 molk/iy /a;d.ed 71kbelu58schving on land 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 the sp-bmq p7 cz:h+beed of sound is 310 m/s (a) What is the angle p 7:mb-hbqcz+ the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere o m4dz8ob 6m-ptf a planet where the speed of sound is only about 35 m/6od8-mtm pz4bs
(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 7;sgjzz7 l( ebgg4zi6angle it produce6l7 egj s47g(zgb;izzs
(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 i10rdls kvf(+ $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and slle)uz32at 6+ie*5vvt 8m:z4zft wb f ee a plane exactly 1.5 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. 4elt6z8 lzi aftuv:e wv52)+tzfb*m312–34. 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 dowe n1(/x/gga8us zke -wze*,j tnward from the bottomjwxes /(g,kea -z1zt g*ue/n8 of the boat, and then detects echoes. 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 octaves are there in the human audible r; x pujbem eph-7ab210ange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphone 2 75gh wgeuz9q)+azzy. It consists of many plastic pipes of various lg7+hg e5uz)zzaq2 w9eengths, 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 s uwt 1j5kuu.woro cp4e0s2, :fq6bq k6ound close to the threshold of human hosf6uq6 qwk uc.,tw0b r:j o2 14keup5earing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound pvyc2(y h .xx)la5h .qand an 87-dB sound are heard simultan.vl. ()q yxxcy52haph eously?    dB

  The sound level 12.0 m from a lswj 0 awoi kz2p7 .54yg)5rghj j+8jqtoudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming +ikj. gwjhyqs r2 8a7t jgw545) p0jozit radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output d ikhynmguctd4llm3 0 4d3 ) 8-tows+n/rops b t)lydisd4ckt4m 3 n0 nwg/l83-omhu+y 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protec)xdaafh j7 b;(nhl 9+u v,nzaw;kvp)5tive 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 a pun)v97n;5;, wdzxvab+hh)l af(k j at a distance of 30 m from a jet airplane engine?    W

  In audio and communications k3( b1ngdre u/.4sd ousystems, 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 is1ym2zd ,g eccguz6d97 tuned 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 g2c:gguijv4//9nzi h points with a fundamental frequency of 440 Hz and a mass per unit length ogj4 9ni2ch /v/ gugiz:f $6.1 \times10^{-4 }$ 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 vibratio,cdcu* q8il w.n above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As 8wdluc q.ci,*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 is near a tube that is open at ong(85 s 0oubpjqo1wv i4szzd18e end and also 75 cm long. How much tension should be in the string if it v0qu 1(w diz8 szgb1o j58ops4is 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 lc ,olevd6e 71 6dkvrnd)(e0gfull 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 to mmg/h61z meq0ne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly mm1mg/h6z0e qwhat 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 train is stationary. The conductorrxz 89fs dqsj3eif/ )f(+ 0bfk on the stationary train hears a 3.0-Hz beat fr (qsdx) fi8jkff+z /rbe93fs0 equency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches y o,1hm6ej) yp ;o3mtldou is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velmho3pe1 6 ;ojty,dl)mocity)?    m/s

  At a race track, you caop cz;)(ym 9h1wfmrf)q tqt1 -n estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and recedm(1w-c; tprq)o 9ty1mhqf )z fing 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, produc +ud 6j 7vph8vls,(0uli.nuq je a beat frequency of 11 Hz. The shorter one is 2.40 m hu76 sv+l.uvqlpdn(j ju8,0ilong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a l wiauh/r /zq o969jf2stationary observer at 10 m/s as shown in oj69/alhw 9q2 fz/ruiFig. 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) 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 3r*l w2nh7ltk.k h2ntflow in the aorta is normally about 0.32 m/s what beat frequency 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 spel3 72kt.n *k2 wthnhrled 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 flying4ln x +czdl7d2 zu9:q,4 rmb ;jx4dsvv 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 jzcvn4;l zv24ux, 9d sldbxdr 7qm: +4the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approachesh(n 5pyq qq0z, a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the mq5z yq(qp0h n,oth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig6tiwkzou 1u/cn85q 6q. 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played asqc6q 8uou z1n5k6/wit 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 by the pgvi9lq4z:fdjzq z04 (resence 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 frequegz z:v4 9f40z(d jqlqincies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves my1q/* dm0ckgyev nx+ht3,i * ;qvng1a long, slender aluminum rod held in the hand near the rod’s midpox*;1ncgm0vk y d,h yveiq+ /31g*tnqmint. 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 hearing for the human ear at a frequency ofo pvea2f1m8xodn7:8f about 1000xa1ffv 8n7oempd:8 o 2 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 o)vae3 ,/atqgxptz z./b7 7fum)11z4 lridyo fn the ground hears the sonic boom 1.5 min after the plane passes dirmzdgbz )t71uar f p. 7yezil4,1)3of/vt/xqa ectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1(h,:h1 hd7mby7h8jwjx,ssv5 ovrxt :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