What is the evidence thatfe1 h: 79 zy,;ivtcexl sound travels as a wave?

What is the evidence that sound is4/vjs/74lm: ee fqwu r a form of energy?

Children sometimes play with a homemade “telephone” by a bk;xld, ahm: ))q)jruttaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly howqlxh ;k,j) m) db):aur the sound wave travels from one cup to the other.

When a sound wave passes from air into wr*ys t0a3j( seater, do you expect the frequency or wavelength to change?srt 3s *(aej0y

What evidence can you4d 0:7g4b )b hpxho0+ ihbxg*zz ti3gt give that the speed of sound in air does not depend significantly h0bb0xgp h)t g*+z 4x7z43ithgo di :bon frequency?

The voice of a person who has inhaled helium sounds vn a+ihp85hw( p2rlj6d ery high-pitched. Why?

How will the air temperature in a room affect the pitch of organ b:f(qwgvch r7 t7cv9h d: ))hypipes?

Explain how a tube might be used as a filter to reduce the amplitude8vpajy (qjk94 k1 2glj of sounds in various frequencyva(2yjpjk8 jlk g91q4 ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spsk8 fy; ap,)w a nxpbucw9j,n994p*w eaced closer together as you move up the fingerboard toward the94 jwpp e,c*faw8ysa9 ) kn;nw 9bu,xp bridge?

A noisy truck approaches you fromnc2 se d6m85 d5neu :qid(7 zp;duzk*.bi:ila 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 noisq;u.(i :mdni8cdpiu7zlk s5e5 bd2e d an:z* 6e. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to e0daev2t3-l*ttd ve:be due to “interference in space,” whereas beats can b3 d et*eve20v t:adl-te said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,b n/i w j0/y/5ddrc)ducn+1mv would the points D and C (where destructive and constructive interference occur) move farther apart or clorv /yu/mcn /win+cddd)1 b0j5ser together?

Traditional methods of protecting:sa)a/. oqs;q1zg x cl the hearing of people who work in areas with very high noise levels have consisted mainly of efforz: cg.ql x)ss;aaq/1o ts 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 wavep9vv4c9bkh lp-b cik euo/1- 9 can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the wa9-/9cciklep vvb h-941 kpbuoves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the soujx pzh4f3wu cdaj uk:o -12k4/rce and observer move in the same direction, with the same velocity? Explaihfxc jzup14ao 4d-u:2 / kjwk3n.

If a wind is blowing, will this alter the f52eu z2vb wtp0wd 26jlrequency of the sound heard by a person at rest with respect to tzupbetjv0 w2w 65 22ldhe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing.uza a,/-)wcftq l(lo- 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 the/-(al,u -t qc )lwzfao whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout 6 6q )ghujb6m9qj,mewreflecte bmw69m hj,)ujq6q ge6d by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ecqhz6dja2)v 1mn+ u(xoho of the sound reflected from thehmjd+2 ) uva1z (xqno6 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 aqjq7 v1jb(zq8rwih2 0 t 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a scho1;; nzcn,lxgj zsto/r 64y c.qol of tuna on a foggy day. Without warning, an engine backfire occurs on another;s cnqx,ngzc t 4 yjr61;o/.zl 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 tf7hy*m ux5 gn9m c:pm::uvxi3he top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is thc*fv9u:u73n5h: g ip :ymmx mxe cliff?    m

  A person, with his ear to the ground, sees a huge stonq3 foyhz,-pyf.5 -hi be strike the concrete pavement. Az h-fib 5 yhf,q-p.yo3 moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile o5+s v4v:k2cmd b; lknaf distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (aln ckb v2:5; ka+vmd4s) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level oao kt-iwa6)qsuf7 + ;nf 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 whoa.7esa 9 cxacr;3p a,x3bvhz (se intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 e tjd* m)u z )-cv.u6csya0zqx99r - 1:bmjuqodB when fired simultaneously at a certain place, what will be the sound level if )- 60 -ut.u bcs:oqm99yxczr)*1vj daquemz jonly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certai+*ofov7sd bow u /s6-xn distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down afsx6 w/os7 -v+oobdu*ll but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is sgcpnx4mz ; kzr 0i:-kz-r76ld aid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for ea 0z p- kr4 lir;xm:d6nzg7zc-kch device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powmm2,webfi7f j+ 2pda 8er output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mbi2 +ma f8fd7pj2, wemouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whmlrl1 )ke1zc/ys4f,7 kth9jzx ht6 (kose 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 amplil.e(m* ze 8l6 hgey7mq35mxqo fier B is rated at 4zlm6ml eeqm75(3y x q e.gh8*o0 W. (a) Estimate 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 2p( ,1vhl+itwv .8 m in front of a loudspeaker on tw1 vhlpv,i+ t(he stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 /p+c8n u-ac+ zu r9zykdB. What is the ratio of the amplitudes of two sounds whose levels dif+ zc /krczup9yn+a u-8fer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the i(fbp pir;iee he,y -1+ntensity increase? I p;y+e-e(iib,fe1hr p ncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement +qte 9 dc ,cy:whb)3wuex/)mk amplitudes, but one has twice the frequency of the other. What is thek+xe)yqwh3 )bc/uw dt9cm: e, ratio of their intensities?   

  What would be the sound level (in dB) g p,g2fod:.c2zep8 lgof a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm,ggl2fzde:p.pc 2g 8o at 300 Hz?    dB

  A 6000-Hz tone must have w64aq , fxzj7zghat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See F, 6fz74xjaqg zig. 12–6.)    dB

What are the lowest and highest frequencies that an ear czur g4:rm4n) 91 kf ,j-c 8cj4ixasqvk3p,bbwan detect when the sound level is 30 dB? (See )9 38icjpxk :zav,n 4k,cfbsr-w4gjb 41m qurFig. 12–6.)

  Your auditory system can accommodate a huge range of ghl 1v+c+x85dtrt yr/ sound levels. What is the ratio of higrg c8+ty5r/ + vdhx1tlhest 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 a fundamental frequwfq* b)vq -.awency 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 placqwva-* f.wbq)ed?    N

  An organ pipe is 112 cm long. What are the fundammzcgzul,j.- ):hqrq (ental and first three audible overto(q,qzhl ruj.cm z): g-nes if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would zpf3e2 lymc; 36og/pxyou expect from blowing across the top of an empty s3pfy6 ;cp e mzol2g/x3oda bottle 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 spanning the range of r;)+r mojlrj1 human hearing (20 Hz to 20 kHz), what would be the range of the lengths of jo+ rr;ljr 1)mpipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has2-*9in5 z cij+orwykb a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a leng- nr*z592cbo+k i ywjith of only 60% of its original length?   Hz

  An unfingered guitar stri4* ku+bi ;k7rtrf k(jxly 6;yhng is 0.73 m long and is tuned to play E above middle C (330 hikr7( r;6 l4* b+yxyku;jkftHz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hp ye -qajg. 1pf4ol:;nz) when pa4g yepn.1o :fq -;ljthe 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 abz;t1 muw.u 8/tr5fz oxcex 88t 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 holez t mt+-f 7y/4jf.ftmz be that must be uncovered ftzmm7 z/t .ff4y+t j-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, 4tbgx dt)/ 5:ef1aqp+g40 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a q/ pgagbd 1x)5t:tef+ 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 tw6p qscn,p 5tn2o successive harmonics of frequencies 275 Hz and 330 Hz. W ,2npp5stcq6nhat 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 +-zcb gd/6ijylyt+d9 :f1ocvm y 3t w:$^{\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 2.14-m-ptshqwv ) hpf-yk8gvcj1 08.:long organ pipe at 20 .hs0yt8) q8h: 1k p vvgp-fcwj$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It oo*ro 6c ;mc/eis open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waveom6/*;croe o cs in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryincdex)-y ow 6gn8f (2phg to adjust two strings, one of which is sounding 440 Hz. How far off in freq)x68e2 hfop dwny(gc-uency is the other string? ±    Hz

  What is the beat fre.+dp;6l6m og5c 1 .ghjioylzl quency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at :w2whxa0ey-k92exjc ,pl9l y23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be 90a:w,je9h yw c-l2lpkxe x y2heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s wn/e(8hdridr 1 hen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibratio1i rhd(e8dnr /nal frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the27x6xedkk ;3o3uwl*/eaufm w same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. Whalx3x2au wfue3m6 *;7 ko ed/wkt will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hhyn(,n *-gt g( b-gtnjyi*8fdeard if two identical flutes each try to play middle C (262 Hz), but ot(*ggdj f-n in -y t,gy(*hbn8ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,e7emm em3xn o+d* .is, 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 A and C? What beat frequencies are possible when A and C are soun m. ,m3eme+nosd *i7exded 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 speake4k/6 pia/c9l:zzej+5jl rh aq r and 3.50 m from the otherj9erha ja6qkpl cz5z+il/ :4/ .
(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 ar4 j1juh. 4uf4i enuyn:e supposed to be vibrating 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 nu1.4 jyi:u 4fu nej4hfrequency 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 bel) usrq7p u4jv:5cq ;74nhn yge)n x drqe;;d6ats per second will be he xu;dqh ycsq46u ;7nr)pl7r4v5 q;: jgenden)ard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550+m9nk w/ dp-p(agl m*m Hz when at res-l+mpw p*m(/n d9ka mgt. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose xy9rq;ob p.i ej1t/7 aa8idxz+ga+65cn.fnrsiren emitsn iztnax +87a1i.r j dqfy5cx /6gp;.ao9be+ r at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fre;xss zq-9 ja1vquency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 ms-1 9 q;vzxasj/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 0-i +5ajqc9lq as0eyffrequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a 0qaqae- jfcl+sy09 5 ibeat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends ounn73 ,yt am (g(msz6dq 7betu,t ultrasonic 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 r qtu6g ad(s n3nz,m,my(tb77 eeceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits 8l47 rw1 1up f5mnreuwan ultrasonic sound wave 11mp e7nur l4wrf5u8wwith frequency 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 on a mow-bzzzot: 8*+ edql* nving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railwayelt-qzz w* zod8:*n+b 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 sp)hyedoy, .;oqhym7h4( q b*jheeds. 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 thye. hdhmqj qy*h 7b4 (;h,oy)oe 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 wavese:mt *d2qc ,fq 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 wind velocity is cef m mb8k zokh4x/++s1-tq; g12 m/s from the north, what frequen18 z4b+;kom gexkc/s qh+tfm- cy 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 speed at du 1d48xo8pdhsc:2l xw8(nf2c imh,e y9-ye g20 $^{\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 wb( spmin. g9 7g19pgzxhere the speed of sound is 310 m/s (a) What is the anglmi x1 sgp .97b9zgp(gne 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 of a /a o5uhh:x5urplanet where the speed of sound is only abouta uo hr5/:xu5h 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 angiz 5h:pt+ k5cele ietz+ :pkc 5h5it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle zwiajs3)0 0xtuc jz4:$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km ac 4xn0ln;u4 wxkf a93p r77golbove the ground flying faster than the speed of sound. By ;09ax 3xkpl4wgn 7 c7or4 lunfthe time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hzzv4 0558gg+9qacptfa r mv;z a sound pulses downward from the bottom of the boat, and tqc4m 9pf+v8 azga5z ;grv0a5t hen 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 ynn/yxt0pmil fu y/33 79(jx orange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consc+9 )oa 4 i ./,bisvo9bajxuovists of many plai94aoovvb.c iax s9) j+o,/bustic pipes 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 sound close to the threshold of hu hmt)jx13hvqqym78tt k2rtxt9b4a 7m+p/ ( a zman hearing (0 dB). What will be the souny78t+t2zb (4xhj3 7p/mqqr1t)avamh 9mkx tt d level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundwf ; afapd:o15 and an 87-dB sound are heard simultaneously?1w ;:a a5fopdf    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wh:+wbi xhx2mm1 at is the acoustic w hxmx:ib2+m 1power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops i zxykk,;pg4d5f3)la by 10 dB at 15 kHz. What is the power output in watts at 15 kH3i zf4;ykl, kp ad5xg)z?    dB

  Workers around jet aircraft typically wear;4+rcqjmcw66dzg 4 c d protective devices over their ears. Assume that the sound level of a jet airplane engine, atcd6czcdj mg r4+6w4 q; a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy0 swkbe6o g7wxii154i stems, 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 frj ek( 3 *56hsjda0hnizequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundr :wi jl8gr06samental frequency of 440 Hz and a sl0g:r8rj i6 wmass 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 vibratioao6bf4w1j rg b(jt21c n above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 cj(41ro gj61abbfwt 2m 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 onec8ch5 u/yug3 m k11r3zlll*mf end and also 75 cm long. How much tension should be in the string if it is m58*gruz1fcy lu3k/3l lmch 1to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reskvh no/6w/xo 6i 3:sqrtn8ypw)m ir,:onate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500exbo *8 v8k 6n98zhcqh5djhs) –1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the p8ebh nk9chx 6vh58*zj8os )d qerson 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 conductor on the;z*o29n.u.som fcy yi stationary train hears a 3.0-Hz i. s; y.ozcu92of *nmybeat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a s y.iajv. -y2ma3 udhp2team 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 (assi-.a2 . jyp 3ya2mvuhdume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenimv9jj8 evvr 7*k wj)o0ng to the difference in pitch of the engine noise between approaching and receding cars. Suppovjro m9 *w ek7j8vjv)0se 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 freqbjz2l-3 ;3i5 vv rmgpruency of 11 Hz. The shorter one is 2.40 m long. How long is the otherj;-g5 r3vrl 3pviz2mb?    m

Two loudspeakers are at opposite ends of a railroad car a a;sv0awj+km0oc t p+7s 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) he is between the speakepav0st0moc+ + ;7j awkrs, 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 a :8*yfs iyb:jws. sszdfuxur*z16,q; bout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrabyuis:uw r yfqd. s8j;xz,*s sf*z :61sound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whil:u(s4. i.rs oiijplz .qq(vsm ugz(1+e 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 reflecz .g. ri s:(uzuii v4q+lmps(1.o jqs(ts off the moth?    kHz

  A bat emits a series of high frequency sounm 1n azehkcsm2z m5cb5 0ork3 y)vy449d pulses as it approaches 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 detom )0eysamzkzm 54c5b3ycn 4r hk1v 92ected 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 from one Alpineuxt+ sce t7 b,00m(rte 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 resonatitubse(r m ec0xt0+7,tng. 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 lista+cs1 qkt:e 3gening can be compromised by 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 lontag1:+ seq3c kg, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender a/bis+xe:- h35uo7,h kypbzjpluminum rod held in the hand near the rod’s midpoint. The rod is stroked with ezp 7j,syki:hh /-b +uo3xpb5 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 thr3 xhorcwz6 y8n/l-k5leshold of hearing for the human ear at a frequency of about5/r3n hzll8ky w6 cx-o 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 sonic e7sf m,xunx*n 6;p9put04hxq m ;dbmpl- 4b*hboom 1.5 min after the plane passes directly overhead. What is* ,;4ex;-nhmh6*xqm4 bmnu9 lp u07fsxdpp bt the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ix:(1fv9kk,repa-l zsbg0s i3 s 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h