What is the evidence 6fofc/x: 2dq bthat sound travels as a wave?

What is the evidence that sounde 6i) ofw,pz5z 1k+uwx is a form of energy?

Children sometimes play with a homemade “telf1m g41lj06j h1ptxmoephone” by attaching 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.m11pf jtgjl mh046x1o 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freque)2 m.zcuze2c bncy or wavelengtm2 cc2eu.)zbzh to change?

What evidence can you give that the speed of sound6kqbsxs ;j:: *zgijfca 4)rm gnq5*-n in air does not depend significantly:;)a 6nzgj*kifs s4jgmrnxqc:q- * b5 on frequency?

The voice of a person who has inhaled helium sounds very high-pbvl.1 jo/,mjv itched. Why?

How will the air temperature in a room affect.vd dpq.d3 /2nc8h cry the pitch of organ pipes?

Explain how a tube might g5qx5hfwwf im 5e sjdm1a-8;(be used as a filter to reduce the amplitude of sounds in various freq8 55dmfwx- ha1 jwf5(;emqis guency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethere9l a6lwudox8(gr f4n60j ep, hgu1l) as you move up the fingerboard ted 4xwhl 6g0rlgje 1pu 6l()uf9n,8ao oward the bridge?

A noisy truck approaches you from behinxp)(e/ pl jc0kd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hea l(p0xpek /c)jr more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “int. /l*vld(lrpp erference in space,” whereas beats can be said to bvpp/ .d(ll *rle due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the sn 6ws .-xod1ryr mwg2l05u(impeakers were lowered, would the points D and C (where destrucy.(om6n1rmus ilr 2gd w 5x0-wtive and constructive interference occur) move farther apart or closer together?

Traditional methods of tpx (w n2gj9kvzv/* 7qprotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noi qjg9(xkpnw2t 7zv /v*se. 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. E 3q8mtohk 1- 8pvrl24 ot6qv oqzht)j/ach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies fa6 )v oto /tz1mhpjtql8 4ho38v-2krqq rther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the z rmoy/(;ts taukdh s8.157wj same direction, with the same velocitot;jw(5 s/y umhrs8a dk.tz71y? Explain.

If a wind is blowing, will this alcx s ;ok(d0jdcjwy16 /ter the frequency of the sound heard by a person at rest with respect to the source? Is th01/okscjw d6 ;ydx(jce wavelength or velocity changed?

Figure 12–32 shows various8ozy -0x ql1+2djmwa2 p9myux positions 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 s2qz9xj 2m wu08dyo ply x-1+amound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shou,mn*lq 7-i,egq ia3v /e1gvgqt reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after sho1v,vgea i q,g7nlm- i*g3 /qequting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the water1k4b5p1 t5r4egxar *c 0kvl ubline. He hears the echo of the sb 50r1k4e x1grvcuptbk 5 *la4ound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 o/m/3hd /r ; btygb 9hui9imh6$^{\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 drift)f: s0kpi mqf*ing just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12– *ffqk:)ims 0p33). 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 makesd+py qt- 5fqh, when striking the water below is heard 3.5 s later. How high hft +y5q,-dqp is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete 0nxnt j7dt..wpavement. A 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 Tad0nn.x 7wjt t.ble 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secon7q x*kvg, adc,d rule” for estimating the distance fravg* 7,xq,dkcom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain a.ps58oyr aj ckk-1t2 b- f5hzlevel of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leve-7ov ue* 4v ;uvzbee8fl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB )vr i5 2qpml y:y-xvlj6w)4 oawhen fired simultaneously at a certain place, whaaqj-2l)yyvv64 mlpo : x 5r)wit will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancewwh t08m+t ha2 from an airplane with four equally noisy jet engines is experiencing a a8h mw +t02wthsound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noizyz s3i- rng*o s6t:-ml8hld3k ms.n;se ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgroud zn3m6hs l -li-msz.k *styr o3;gn8:nd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal co;tt(h- -bc z:g rgxg0jnversation. Use Table 12–2. Assume the sound spreads roughly uniformlyg:zg c rx(t;0-tbh-j g over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum w.7rpt4ndtayybk)flh z ;q+s1: grzzuc+ 97 h3hose 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 the7*pj xx4 w mecx m2scip885 v5w7hia3y more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conn3x58a p 7 2mh iim cv5xcspwe8yx*4wj7ected 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 rekrp0 :6mqfcq2.pozrt 7(0ogbs+ir ) kgistered 130 dB when placed 2.8 m in front of a loudsppirfrs+ o 0.)m:bk (oq 7crp0g2tzqk 6eaker 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 typically detect a difference in sound lev5pu ey7v 2le.qch;.b /v:4deyqvk4d aivlz6;el of 2.0 dB. What is the ratio of the amplitudes of two sounds wdv 6a qe/4:z.c 24.pul v e eb5d;yvihyl7qv;khose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by w1px bpzp-i 4f2hat factor will the intensity increase? Increase by a factor oi24xbzppp1- ff    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displcu1mxq 7ff)conh) / ;zacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitim)7q ;xf1 zun/o)c hcfes?   

  What would be the sound level (in dB) of a sound wave in air th n1pt 4:slbp)lbfz-eewl i/91at corresponds to a displacement amplitude of vibrating air molec/ 1zns1-bwllpeb9tif 4:)ple ules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud(grf a)/3;ikqb sh 7ze as a 100-Hz tone that has a 50-dB sound level? (See Fs fqe7z)(a k; h/3rgbiig. 12–6.)    dB

What are the lowest and highest frequenct* f c)8lut.,(7 kh hvnvft ng+gnt5m/ies that an ear can detect when the sound level is /gv7 (h.c v,)+ fnm5tnf*8n gluhtkt t30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soik(ijz n;k37o:1lvnh und levels. What is the ra37ii o :k 1kjlzn;v(nhtio of highest 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 frequency of 440 Hz. The lengqly,.3 r3thbxp *(zdhth of the vibrating portion is 32 ,bl yqrx3z. p3dh*h(tcm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are k2:6 ev )0a tjkxx8z: tk-xivqthe fundamental and first three audible overtones if the pipe tvxxq e0: :a-xzkit) kkj6v82is
(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 :o q-ngtosuz2,tw :y, across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tug usz2n:w t,,t-qoy o:be?    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-fcvuiu.5ws/) n*:j j a5l ququ-zslgh;6ko2 range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requ ki 5usqlfcu uuq.s-6j-w/;nalj2* v5o:g) zhired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has8 g1swat,hq+k8arz 7 e a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingear881ghk zewsq7 ta+,red at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and i cp1 yel emk*;d/fm ;1bda:x62 nt;xarc. m8tfs tuned to play E above middle C (3pl* /1tt1my;ra86m;fe.d mde:2acxfx ; nkb c30 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 emits middle C (262 Hz) wisu lyn h;;1jx838ha f::zgnbhen tjsfn; ux;zha8:81 3bgyh: lni he 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 wq,p/ qzms;k 9at 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 hole be thaa;4 iqw/k alhiq.ei:: t must be uncovered tlw .;a/eii4ika:qq : ho 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 Hq 7fa2rdu:i0 88 5.qtveje i vcglnpvu) 65hq6z, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this 58cq5lu8 6:qdihfn .vv e pqe )7t 62iugj0ravis an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It u2qiwi -g e qp47jw*z;resonates at two successive wqe-quij *4 gw7z2; piharmonics 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 l* xqo xz)bp/ny *(pt9t15er) , eebgf$^{\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 fo +(wrew5 fstjx+.xdj)n rx8 2sr a 2.14-m-long organ pi8 (extsjfrd2+rws5n .j x) +xwpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 ql bs4v e-yc)z.d4dv 4cm 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 syvs) b4c-4d dv4eql. ztanding 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 bea-w/4sgo:/mmiy/cemni+j9aq t every 2.0 s when trying to adjust two strings, one oa/ 9mi-//+icwgn eq: omysj4mf which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C kyay dxvm 8pfj*:pdkoq-909 /(262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (b4ckq 7qbc+,to xcp(jax+5q x 2q8kux/ rand X) operates at bktx q+jcpx,qc( 8u /4oaxq+q 2xck75 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 simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35 ff)d:fcvn95yexr9 ( b0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz try5 f) :fex(dcvb9 nf9uning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Tp9fa 11xha+y che tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togypaaf 1+1c9hx ether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two ident s)pzvo1w.vavc7pc w**j(cg 2 ical flutes each try to play middle C (262ozjgcpw*.c2)apv7 wsv1(cv* Hz), but 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. Fork B hashp t m fg-ydp)-6r 0u4,eo3g,r6egld kw6cel: a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Whepr)0l:rd kpmegg6e6t4 o3 w6 ,-he,-gfcd ylun 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 stands 3.lmam1, c fy2(ai z)ae500 m from one speaker and 3.50 mlce 1a)zmi a,af(y52m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be lqa8c e5ue1r kl8 ):b/msqqw8 vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If /8ecra lm:b8qs5keq w81q)lu 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/-d*z y1ato8qa v6kxi air. How many beats per second will be heayd6okx8v* azt 1qi /-ard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a m. hi;x1s3g9pbpyd xc(h* lm-certain fire engine’s siren is 1550 Hz when at rest. What hg cs; 1h*x9xi pd3.bm-plmy(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 sbv3tict*r ./g+b 6vf7xy9uamiren emits at m 3fy6vb *bai 9cv+/ tgu.x7tr1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward ycthyvi: y)//zsn8h g 3ou at 15 m/s versus you moving toward it at 15 m/s Are t g h8 zvsh:/tynci3y)/he 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 th*/fhhhr b6- qxe same single frequency horn. When one is at rest and the other is moving q-xh6bfr* / hhtoward 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 T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultk,s; wrtpf kdr4 t1jm4,;j4oc, as/bhc6y on1rasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it d;4h,f;mbjo1/nsrt ck4jp 1 oc yr,6at 4ks,wat 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 fliuolw7 -s5j7np v),mm*vb k2zqes, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency doen*w5j km-vobvu7) lm2z, q7p ss the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on6 xbxqtk .2pp8z0x nt jdj9v92 a moving flat train car at a frequency of 75 Hz, and a secondx vq t2xz9x pp 82k6j.0bdn9jt identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spey d5ijfs;osvsq)6-e3 nc jp8/eds. 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 the expected beat frequency if blood is flowing in large leg arts-qdnjsc;) ys6v f8/ 53i ojeperies at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofif6 mw2h/ 9rjj 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 emivtff(2:kx m2bts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who akffv mxb(2 t:2re 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 ydr- /hkbda,;3zyc/3byti /bl ky-p ,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 wlg+;3i y 0gg xj7;3llowq*mbzhere the speed of sound is 310 m/s (a) What is the angle the shock wavez+q7y w 3gg0m*3xglb;ojli ; l 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 planet where the speeddj31f-t+ /cvv asklz , of sound is only about 1l/d,-kf+s3 aj vtcz v35 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 p (5sdrp0lgu)the shock wave angle it producesdpgu ) r5slp0(
(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 21scttwcbhea3m5h ;: $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheayd.4du6kl.c+, bwpthdlv1. z d and see a plane exactly 1.5 km above the ground flying faster than the speed of soulbk.l+ tp1c 4yhdv ,6w.d. zudnd. By the 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-Hubb:ek ;p :3ts0q u3wlz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 20buuw0ls;q:3b 3 :e kpt0 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octa bgm5xcnc(fuc ugni8:r 6sy2 g,)h 1s2q5qr7sves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called ,ps1jay :5nr0o c4g czfk yh/v0b z51xa sewer pipe symphony. It consists of many plastic pipes offo v1rn1ghja5:5s , y x00/pzyb czck4 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 :8vjo xa)hnhm78 yd3/8zfd(bzowz1c the threshold of human hearing (0 dB). What will be td81yc:xz j8nzz(wfo3 7 8/vha)bhomdhe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB . eo6k16rcqxtmfgsou +9)p 3 xsound are heard simultan9trkm61op)c 3eqsuo+f xx6 g.eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is t3 66g -scamao4pr;dv 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direc 4mdaa;to-gp6r c36sv tions?    W

  A stereo amplifier is rated8e t7knwa :x9j at 150 W output at 1000 Hz. The power output drops by 1k: xj at89enw70 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ove96 , s( zmmuhm,drqy,ur 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 bm, qdmh(u ,6yr9szmu ,y an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications svee13)h7fmcft sv0b* ystems, 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 tun9heeb7cdvb s,(p f3f/s4 q*g fed 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 bei3 c+zqw /,hq)gd: ;rnf/xmuxtween fixed points with a fundamental frequency of 440 Hz +rxn i)qq;xuz /3m/ df :cwg,hand 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/kl9u :up,tklsg44 z3es xle3 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 t u:49p,4ll/33k eezsxgs l ukresonate 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( xj pp il*26l6eluw*j tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) wipi*2u je lp6(6xl*ljwth the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r(q +)ygbzhdf ;4ib o+v2jhw+ xesonate 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 ist aloe2es/j)esq* 4 ;n the 500–1000-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 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 oe2;/ss 4aqteeojs l) *f the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on tw52n pa.g3ch qhe stationary train hears a 3.0-Hzq5gh3a 2. cnpw beat frequency 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 you is 538 x dtr9e5q 206ir4htgldq:ci7 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving g4qrc i29x6he q7 i: ttrd0ld5(assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by li 7 q6/ku;d;kfpl(yigystening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. H;7 /y;ku6plyqf ikgd (ow fast is it going?    m/s

  Two open organ pipes, sounding together, pro p*/zes2l(tv0 r qm4qbduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. H p(q svt0q z/ebr2l4*mow long is the other?    m

Two loudspeakers are at opposite ends of a railroad carge6:34r gc,d)g*j4gho -xg6 lvtol rg as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers havc g3h go6o4djr ,e):lgg6 4gv*xtlgr-e identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally aboutx 8sewejyo1io.p7 74.r nocl/n7obf9 0.32 m/s what beat frequency would.xorpe.8co7yloenf o/in j 174 9w7bs 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 m/s he i8jxm 62fh6while 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 wave6hme6jh 8xfi2 detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it appro fqo:z q ky3sw.6r8fg8aches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away canw osg8z 8y6fqqf: 3.kr the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig4sram. rnn3j y) d 666gjr7klt. 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 as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtone 376mrs 4)yrjn ankrt6 6djlg.s 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 presence of stand lqmu3y :6d8rrv c.1 tsqd:.p 91rhrcqing 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 fundamentcl: stq 8 rrpqqv hudc96.1r1y.:d mr3al 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, s1j w8wtdpk/y*40ihx o1 n4yn rlender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Witn1/4pwok4y0 *yw 1txnjih8d rh 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 thee 3m v6l*f(mpbk(9 skd human ear at a frequency of about 1000 Hz is l3 e6b( pkvd(fms9k* m$I_0$ = $1 \times10^{12 } W / m^2$ 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 observeoo*60xd idy d8r on the ground hears the sonic boom 1.5 min8i 0o doyxd*d6 after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat( 8txzqdsbgk2 ;ok +:j is 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