What is the evidence that sound trav un2d m5caee-3vd0r3 axjsz l2qf*b5 )els as a wave?

What is the evidenceg pbca2aq6l;.gzo62c kk+ 6 xi that sound is a form of energy?

Children sometimes play with a homemade “telepvs;f zw boaz lw8*9znd4mc,7*hone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, thec4 fzdzoa *w9wn7l v, *zb;8ms sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect 8vsq16a)oc3r lmf3 w ethe frequency or waveo31sw a6ev8 )fc3 rqlmlength to change?

What evidence can you give thf )n1v 6;efliunom28 vat the speed of sound in air does not depend significantly on freq1nniemfu6vv)2 8f;lo uency?

The voice of a person who has inha wg-eh*pot xw (k;2ji;led helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ p pwpm e+gfb435ipes?

Explain how a tube might be used as a filter t4apkml0h9y2v1, k xuiiapv4 .o reduce the amplitude of sounds in various frequency ranges. (Aii .a0xv1 4 2,akpyum pvl4h9kn example is a car muffler.)

Why are the frets on a g,pbslh ;29af3d6srwzvp; y b c5+ ,xijuitar (Fig. 12–30) spaced closer together as you move up th3+spwcalb6, dx9pjs fh ,5 rizb;;y2 ve fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initial5t im)3vba* yqjtc-b yi32 e4aly you hear it but cannot see it. When it emerges and you do see it, its sound is suddenlya )qy35ia-v*btc3ijy2 m t4be “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due, d:galxfoc*s crn7u zi y17*( to “interference in space,” whereas beats can be said to be due to “inte*f :*d( zor1,yx sga7cuci n7lrference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the(r:m cyj l5jy1 points D and C (where destructi5l 1jjyr(ycm :ve and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people wh ok/g,5b,+ivwnzy l9dmv3 m6z lt.h3 mo work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it ely,wb.5+,z6/i9mzo3m hnv v3gk dt mllectronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought 31xq*os; xub 6 igqp8oof as a superposition of two sound bxu1;x*p3qqso i86g owaves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer m;)wy:web10s jzfb 0we ove in the same direction, withz: wb ew0eyw);jb1s 0f the same velocity? Explain.

If a wind is blowing, will this alter,ew*13:+ , lg g emtqmbesot7e the frequency of the sound heard by a person at res,7 gslwogbet*3 m:1, + eteeqmt with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moni y (b t:blpot(r,zt8-wtor is blowing a whistle in front of the child on the ground. At which position, A through E, t z o8:l-p(wtr(,btyb will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengo cp a)lw8.v+tth of a lake by listening for the echo of her shout reflected by a cliff at the atw +o8vlp).cfar 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 shitmbro -cv8yc.ti: 33fp just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How- 3tcb3cr:8oiyt.mfv 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 wavelengt xx96ulrdm1atf45z5 6wcqv 3whs 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 dr m ucad3 /;2fr/tnnwq)ifting just above a school of tuna on a foggy day. Witho;u)fm2c/anrw tq /n3d ut warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fro2a.wl0 4vbw w( +uzhupm the top of a cliff. The splash it makes when striking the water below is hearz 2.4uw h0+w vw(lpabud 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grdbiq /w 2m5+t8gq26pybvr-ul ound, sees a huge stone strike the concrete pavement. A momentm5 d8lr2u-pv2 q/byg+bqi w6 t 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 ovk1vxzjk n4,kq (-0xbjer one mile of distance by the “5-second rule” for estima 1-( xjknk0kv4zjxbq,ting the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a souh/:; yo+dpy+gxw-k rm7of-pe nd at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a soundj* weknuat 1-3 whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at gvadc*9r7f- ca certain place, what w 7a-c*f rcdvg9ill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dista0m9o7z v dh:sknce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pers ms079:hkdzo von 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-n..;vzr/ y .bzc3cy +jxnbj 2gdoise ratio of 58 dB, whereas for a CD play2 r+jb3czgj.n/c.y;zx. bdvyer 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 power output of sound from anfab/;f v2/ km(gj:pv person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a s/(n;m2 bf gfv p/avkj:phere 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 nd ;.mvj/x+txind y h-:wc-m.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 ata 0vh) 5trl;.(k mupsr 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker cuakrsrl (; .mv)0ht5ponnected 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 qkyq08 y **eklregistered 130 dB when placed 2.8 m in front of a loudspeakqlk 0*8eyy*k qer 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 typic8/i f-1 z t2hw1fx52srk 1brt*aejlnxally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint/ b-5zf8*tk 121rxswaxl j f 1nerht2i: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will v5 ygb-w dk+fg ni(l,4the intensity increase? Increavlk+(ggn,5y- wf4i bd se by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacem hr(fitc7q6;m65u xm uent amplitudes, but one has twice the frequency of the other. h;r5u6 itqc6 m(f7xumWhat is the ratio of their intensities?   

  What would be the sound * 5b/+/u 8rmrhho,u u1m6nclsir w9s alevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of 5i6lw nhmrusu8r 9*b/uoshr m +1/,c avibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound le )a9zaul4y g:.ho wg:t/obml. vel to seem as loud as a 100-Hz tone that has a 50-dB sound leve4hu9: gobam:.yowt / )zagl .ll? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whenn51qsj 2hndv,h9g82 jz9w zgz rrhhm754hz w3 the sound level is 30 dB? (Seewzvh3nq9zz55hh2n r,jgh 9sd j 41 28rzhw 7gm Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levezhfo) 88:bbmf ls. What is the ratio of higo)f mfh88:bzb hest 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 funda,hif/ ; u.x7:mszfymvmental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g.hf:/yfuim,zx mv7; s . Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firstm bz4;x 83gvajuhn(89y,kby i three audible overtones if the pipe i ,zji xyvbm49k ub3gay(;h8 n8s
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of aigrccm b,mxs ry6-s1 x/7qs8xs g883qn empty soda bottl6qqsm3y /gxxb7imcr1s8 8c8s-grx s , e 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 6x60ve q az:c io9/;u yfvnlv.ezl0d)pipe organ with open-tube pipes spanning the range of human hearing (20 Hey6lc)9v0;i0 :l vqe zd/6xfv uoaz.nz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonwi9c qy+t,p eqb-b17 aic. What will be its fundamental frequency if it is fingered at a y bp 9-i+q7ea 1w,cqbtlength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middu w j6ik.+8ha46m8o2xun b bhrle C (x8 a iw84j 6nbukhm+rou6hb2.330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open orgmq yca34x97ohan pipe that emits middle C (262 Hz) when the temx hqc 94ay37omperature 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 k44 su-c,dp 5.snigzbat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of8mu v;ae1fy40y ey7 c(hu21pb5x qs zo the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at uh;p1 72yy85s omc(eyq01z4vxbfea u294 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 H3ha :besk1/1t( s5tq njdpln 5z, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an opt/ nlp:nh 3eastsbk1(15 dj5 qen 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 end ;0+x-nbwvmwi roe, )as. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wa; ,reo- wi)0bx n+vmwhat 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 t6cchllxkf zu6 /6 90u$^{\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 wi i8pslkrw19c3 4gxm+xta5-q0yze)bcthin the audible range for a 2.14-m-long organ pipe a qbma9c3rtiw-0zyl1c 8e5x4s gx k+)pt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxim6 y*s5y otvsb-vfz: t)ddxo- 4ately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the fre-dy dt6y) vb : t-so5xvo*fz4squencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.b xzzyd5r //z.0 s when trying to adjust two strings, one of .z/ yzd5bxzr/ which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262xv)dlv fhv3p+oju p5,vo 1 d.8 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 atpuco:tg7e(/ vqv(:ec sxzm*6 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand Xs( 7 q/c(u:6*mozg vtcve ex:p.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9p3 lr7pic/k*e t,eyu-/jvw7 p beats/s when sounded with a 355-Hz tuning fork. What is the vi/t3 iw yuplc7 e-pkv ,/ejp7*rbrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are bkyu.ksm 0 ze899dx 9xtuned to the same frequency, 294 Hz. The tension in one string is then decreased b0s m98b ye dxku.xkz99y 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be su4wpje d4hy-:m/o.,t qny)gheard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at thp4/n) y. 4yj: s,mqdgueow-25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, *o -bd5+vwj x-zieja u99au)qB, 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 frequen u+*99j juva d xabize-)-qo5wcy 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 perso0zx5w nyi:h f, qy7k9uiv7tp.n stands 3.00 m from one speaker and 3.50 m froi77i 9 f ,ntyzu.p0wvx5hy q:km 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 vibratingwe; a2a6q4odf*gw1 ms 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 mu;6w *2qa1f m ea4osdwgst 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 2.64n3vt.i6 mx h-6u:65) vhdewr/5r fjst;vvsxi m and 2.76 m in air. How many beats per s )5s-j6un5 vtx i3.6s e :wvrrhdhx6/vv;tmfiecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550ecbuws l2/t/eo- * ny8gu7u7t Hz when at rest. What frequencsw/te/un2cg tu8b-lu *o7 ye7 y 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. W t2o) 7)7cqr+ fxyhd)ye.po-z /t srrthat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s-qx 7)2oyt)fr / t+rhdsyeo)t.cpz7r
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mo0vz jimo92 :3jxadt2 qving toward you at 15 m/s versus you moving tow2oix920 t:vz amjjq 3dard it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same sip wj i+f/ddd-6ngle frequency horn. When one is at rest and the other is moving tow i w/jdp+ddf-6ard 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 ultrasonic sound jybm 7+.fdn *a+ez(gglno q-v cw, (l9waves at 50.0 kHz and receives them returj9bvdl y(-z, ga( lecf ogmn7.++wnq* ned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall 7k f ku(in+e:xat a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bakk+fex iu:n 7(t hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originalzv+ jrx36mz 4l Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the samejrm +zx6lz3v 4 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 usjq4.zqn to ltsw8;: uax co49on.d+x:es ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and then4.t9 ts:qnzd4wcq;u8olxo j+x ao: . speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencijuno k*q.5dw ky z57wgf66:k 4* pyycy $2.25 \times10^{ 6}$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 57lr e.+ seku:o70 Hz. When the wind velocity is 12 m/s from the north, w.rl:eeuo s+k7 hat frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movingnmiqy5i98 hi13o2kmh 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 speed of sound is 33b 0/n p3tkht scxn8x510 m/s (a) What is the angle the shock wave makexbp0 n3 s3tnkch 5/x8ts 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 atmq/ .wot*x -gw3a:soa losphere of a planet where the speed of sound is only abo3 sg*t/al.w- qo a:wxout 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 oceanvn8 dg ia mbr* ifxmah61*po3*+a-xst 9wu25j. Determine the shock wave angle it proiaa* 1-mv* wjfx+o9n6hsd5i r23u8 b mgx*patduces
(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 sxd yor/y9 hr7 1ly9w8 ;:kkbv$/theta$ 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 above the groundg l:3 jzi 4oweipm62h 4.d(jqh 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. (4hm3ipql6dz gj hij o42ew: .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-Hz kks+a q9ulxeth+6 , 92 hwtam.sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh waters9 aqa2l ,9h wkm.k+e+ xutth6)?    s

  Approximately how many octaves are there in the human audible ra* mk8j8 a1ptecd0jbp 7nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sa*a41tj +v+dxd:rt hvw 0nj 3eewer pipe symphony. It consists of many plastic pipes of various lengths, which are openv*0:x dt 13a++wr ehvjdtan4j 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 h r453* sikaoym from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquit*o3k5 h4yir saoes?    dB

  What is the resultant sound level when an 82-dB sou7xogn2ka18 ngnd and an 87-dB sound are heard simultan2on 87ax 1gkgneously?    dB

  The sound level 12.0 m fre:2 )s2ik exwgom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of :gsie)2 2xkew the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The c;*3:4o)g o7dutw: t whzymbypower output drops by 10 dB at 15 kHz. zw)dc:b* gwy :m oo;y47th3tuWhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earswol8 )s:gz :w0oiqc2v . Assume that the sound level of a jet airplane engine, at a do0ww):izqvcg8 so 2:listance 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 systems, the ga5ecpy;f ag vm+po-sa m4+/4apin, $\beta$ 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 tu m ri n;c t-n1(;8pquj4iwss q1if8dg*ned 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 b*0iv4y ss8bw a0yu :*yuvic den)1ro7 etween fixed points with a fundamental freasd 0v*e8 biou s rny04u)w7:*vy c1iyquency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set ins +d +up9h8mwbto vibration 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 heab m+8spw9udh +rd 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 g6ahhdh9e)is8 2 w .flis 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 fundamenthd8la e 6w.2s)f9ihhgal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reitg b73tmu1uo/pq3-+vu6q*sg1h h cgsonate 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 500–1000-Hz ranvd9eb;u(x ppb8g 2l ,xge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency ised2vupx(8b p,b ;glx9, 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 7 2mq5xq u3 g6)ummxbdstationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving q2gmxm u3x m5)du qb76train?   m/s

  The frequency of a steam train whistle as it approaches you isdly vs gx)2s,*7 6zmyo 538 Hz. After it passes you, its frequency iylz*)26 ymsgv7 o, sxds measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of carbu +h.u /29p9yavceqxs just by listening 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)h9 bvyp/xeqa2u 9c.u+ as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding qwy z:zog0hu )zq9(i9together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the oth (g :09izqquy9)zwhzoer?    m

Two loudspeakers are at opposite ends of a railroad car as , f: ur.l-eh4mg(rzb nit 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 speakers, at B, and (c) he hears theerz, 4nmgr-lhbu (:.f speakers after they have passed him, at C?

  If the velocity of blood flowr+pqvw;ks:7a gjzv6liq4 - / b in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves ag/qwvb+ ;qz4r-vls7k 6ijp :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 while the moth is fs1c (;a.akx4)aq/cvhi i prh5lying toward the bat p h.ash4(r)iacak 5cv1 ;iq x/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 reflects off the moth?    kHz

  A bat emits a series of high c3 oeezfaqi+e nv4 bi4007;4dwwys-j frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, anwe-fi ca4eseyz ibqw+v;4007d3o4 jnd each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpinez6sq0h-l 8 *x/9wbjia ap 6hb x-bep5q village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamentalw8/q5 hsb pqb-ia6jxp ze9a-hl6b*x 0 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 compros -w,ln59 f wz(xfmqis;v*6 ihmised 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 long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing w;, li*nfwzxmw5vfsiq9 6(- shaves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rod0e*m f6im t(j16fzq wu+vo0yds,” involves a long, slender aluminum rod held in the hand near the rod’s midpoinmy6qof1z+ev(it 6*0dmf j uw0 t. 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 frequency5rlgs r/ hb+d /)dpmh6gg9f6w of about 1000 Hz is p6 h+6r)m hbs/ /wrgg9d5 dlgf$I_0$ = $1 \times10^{12 } W / m^2$ 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.*/ary,r 6m ioj0. An observer on the ground hears the sonic boom*a,/r6moy ri j 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo) zg o/2e0x4 kfot)qgp*l4 cqwat 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