What is the evidence that sound traveqh h:u:i*)8wvnlh z,e,;s uyz ls as a wave?

What is the evidence thatuem p6iiy;tq.w 6+o5ptef.j27 r*o ic sound is a form of energy?

Children sometimes play with a homn xie113z i,ymemade “telephone” by attaching a string to the 3y1im,ienxz 1bottoms 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 how the sound wave travels from one cup to the other.

When a sound wave passes from egn s2+fk4b(. )amj;doe..t dw2mnrxair into water, do you expect the frequency or wavelends2 eem)f2a wr n .n..+dkboj4mxt( ;ggth to change?

What evidence can you give that5da+ xz- rbg q5z(3qce the speed of sound in air does not depend significantly on freq5qx5za3drgq bze+ (-cuency?

The voice of a person who has inhaled helium sounds very high-pitche6a+7sm nl)jhl w cva-mt1s 94rd. Why?

How will the air temperature in a room affect the pitch of orguad6h ixd 7r-;r x.bq6an pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sound;3aoe /:jindg fx- w1g rec)a*s in various f /go3a f-r ea*wc;:jgxed1i) nrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer toq)uuln h3l6. vgether as you move up the fingerboard towa)uhq.n6 ull 3vrd the bridge?

A noisy truck approach kg40x8rv 9abtes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffracti g0r 8vk9bt4xaon.]

Standing waves can be said to be due to “interference in space,” wherb1sx *ud6s(nk5f tn,t*1gq 0w4yuf d lafxl **eas beats can be said to be due to “interference in time.” Explainn,s6qnwxbu * u y* tl( xf*lfa5d*tk4g 0s11df.

In Fig. 12–16, if the frequency of the speakers were lowered, would )f-ph t upx;(othe points D and C (where destructive and construc)ohpx(uf; -p ttive interference occur) move farther apart or closer together?

Traditional methods of prote3 :le kt(n* shyjxq y2h7e1in5cting the hearing of people who work in areas with very high noise levels haex:3j 5*ylyiqhn h12eskt(n 7ve consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of p 4p54cwc h5fias a superposition of two sound waves with slightly differe cw ipc4p5hf54nt 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 3/ lbe7zkd,aq and observer move in the same direction, with the same vbl/ a3q,k7edz elocity? Explain.

If a wind is blowing, will this al aat7m k--c+lvter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or -v ca-lt+k am7velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monio c+f/ 6 kv.swkg9 axb55hg(rvb,xb8x tor is blowing a (s xb v f .gxbkx+9b8r/v5,g5ahc6wkowhistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the legf9hd 0npfo+og ,q) w*ngth of a lake by listening for the echo of her shout refoof ,w q *9+ggnf0dh)plected 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 shbwybvk0y gf7ij* w / ) eucf;mx5kt.6.ip just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater gbixk..w7 yjymt60fe5vk/f c) b w* ;uis 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2 bus k6+vfj3p05h 0vcv1: oubr0 $^{\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 ad 6r/up s-/knm school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How-6srm udkp /n/ 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 izxthf /r1civim8:7+e,u y6s,yv z(i vt makes when striking the vcvhii ,rt6y+8xi:/m7uv s(zez f1,y water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stn y+kst0,ls2brike the concrete pavement. A moment later two sounds are heard from ty+s 2t,nks0lb he 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 of distance by the “5-seakyr0) (j5e lqcond rule” for estimating the distance from a lightning strike if the temperat a)ljyk0q 5r(eure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity4rmsft u + vm2qoy)6z+ of a sound 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 w4tcf,-c 1tk2 3heo-osmw6od sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simul 57udmkbt4s1 j+onnh6taneously at a certain place, wh5 bd otsn mnk+46hu1j7at will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancx sctc3g iwg-qal/ df, ui(019e 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 all but o09u ,3dq(t/sig ci1wxal c- gfne engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is saiuw47n,nw:mc( a io0ka d 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 bai(wac:47 nuo n k,am0wckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of soundiqnegx1ze( ;fz5z) : as e;n(q from a person speaking in normal conversation. Use Table 12–2.znfegzsn5 ze (1;eqx()a q:i; Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave str*uqxq5iu 9bb.ikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while tw8dn)h -x 4as+.4x hpdu.wr1;ipys r whe more modest amplifier B is rated at 40 W. (a) Estimate tha;di1w-xw 8h xrsy4n w4s .d.) rphup+e 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 /y k f58zlp65xzd(gyp5box h*dB meter registered 130 dB when placed 2.8 m in front of a p5kzf z85gyhxl/5 dx( 6bo*yploudspeaker 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 typicallyj;1a*fc85u u qshha0kij2 1u n3k1dzq detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of tw 5fisnud;1au01a2 qch 1k*zju83qj kho sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilfl rpf*43i: qcl the intensity43 : cfli*qfrp increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice th7pzreg fx+/k:)axq+r e frequency of the other. What is the ratio of their intenf+g /arr+ 7:px xkq)zesities?   

  What would be the sound level (in dB) of a sound wave . jc. eomp/a1fin air that corresponds to a displacement amplitude of v.c1p/ fja. meoibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone zq:d7 nd 38ys: 0g 0xp3qmndoqthat has a 50-dB sound le0p3zs nm3:dg:nyx oqd d708qqvel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that (16km:3hin1 nh u o o5tdxqb-oan ear can detect when the sound level is 30 d1m(nd:5toi hx ob nhouq13k6 -B? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levelp h51f4 nl*i9q,xik4aaik. g ls. What is the ratio of highest to lowest intensini4lkifh ,kpl a* a1 gq.59x4ity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin haswyoxk(s .:v(d9) e zlow78thyz w/e5u a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a massetw wu)eyvx k y 75:w8/(.sohl9zdoz( of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threea+h 1)1 b+sepkbh wf9m audible overtones iff+s1b b 9mwaep)hh 1k+ the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you ex/i 6cwi yftr5bjva1 x9x9nft /u8xy/ -pect from blowing across the top of an empty soda bottle that is 18 cm6t5-xti1v xia/c9fu /nw yx/br j8yf9 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-f 4lk vvz5(;60fqgf qs;m p2agtube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipe4fl s ;q vqfpggazkf2m0(56;vs required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 53ejdpfogh26v,d k 20h40 Hz as its third harmonic. What will be its fundamental frequency igdoph6d2vh 3 k0 ejf,2f it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar)qlmd6.vleq: 1wia p7w (rou znn a3/uy4v7w- string is 0.73 m long and is tuned to play E above middle C wrz vm 4avapl.d/613e )iywl :quu(n -qwo77n(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 o b7is ye( l*6dtg om9ei2jyk/1pen organ pipe that emits middle C (262 Hz) when tgo*i 9bimysjeklyd72 (t1e/6he temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 1u7 4mc dw-p;gc0egjp20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Expl )mz,8pg7 9;u3 oytze8xgbkample 12–10 should the hole be that must be uncovered to play z zg7 yop8kextg,9u8)3l; bp mD above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz,1bl1 x3rjv b*ax5;kl t but not at any other freqx rxk a3jbl ;l*1t1b5vuencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both endlrs 1*prj:n:x q0ge:m s. It resonates at two successive harmonics of frequencies 275 Hz anlpgs q0 :rer*jmxn :1:d 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 xq9w3jo2:4l5l xxgxe$^{\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 w fn1nwui3sj8 3ithin the audible range for a 2.14-m-long organ pipnw n iu3fs3j81e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatebhb/* yyf58pnly 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in/*bn py5h8y fb 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 everya5e umw)ku8- y 2.0 s when trying to adjust two strings, one of which is )ae-y5wm uu k8sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frebs0q j i edg(mwxr2jx,: 03kz9quency 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 23.5 kHz, while any-:edq/ b*vf, fsj2n fother (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 sijf b:,yde*n/qfsf 2v-multaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wh:d:t 4 oa 92v-w jlmo09z+kw:fb,c* kwr pwtpith a 350-Hz tuning fork and 9 beats/s when sounded with o9: -w:w c*r,m w+2hlp f b:kazdwk0vtjtp94oa 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings arehshr f+7,, m vz9hlwaif4s* /k tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are pl s m,+zhwl,vh7 /isahf4k9fr* ayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hemdhbk *+jdik v; q/ew;4n.1wt ard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C aned+i .;k*d1bwq jt/;k4mhwn v d the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4nw p;0a:;l aw s/jh)vy41 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 ;s0pyj: vaw )nwa/l;hare sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from mdf j2m*(d+4ajlb , pd5wnbn 3one speaker and 3.50 m from the ot+ j(,bdwm34d2 pa l jn5dmnb*fher.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner zxi 1ty q4y3*t-o2y xwhears three beats ezxxitytwy *32 -1y4oq very 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How ma2auobx 2/oki3twd tl 1.eey .4ny beats per second will be heard?et bo a/21 l2w3xk4udy .o.eti (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqzhz1wi2ws 9: vi4ssktw/7m y(uency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do youz 9w4vsi1h /ytm (7sz :w2kisw 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 sire6d ok alsrrna91-h(8sp*: c pen emits at 1550 Hz mops h d(-ano18rk:6pcs *al9erves 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 movin fmi.pr wn5n 9kl6w*)0s*dp lag toward you at 15 9pndm*s na0)w5w6ipfl* kr .l m/s versus you moving toward 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 7 a9wn4kq9myqc,ihp(ayd h7xiy k.-0 with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequencyay.kyp( im 97qa9n4 chyw-iqx ,kd70h of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out j*yg8zn4ul3/ak6 3rxz a9lwo ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What /83lg 9zornu4lazy x a*kj3w6 is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at33j l ls i4zb+dgu(ys: a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 3ib yslsz lj4 ug(d:+330.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimenczrl0vc-d q5d,0fqu9 ts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the s5qzulf -9 0dvc0qdc,rame 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-flop9 r3g od pe v7dq;; vinyu0zqaa3.m)8w speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tiss rzv9a pd.d0o;)gqq73u3 ey8nm;vap i ue 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 jr1a+wz *u)a4. zyo jbultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency qkm+pai( ,:fd 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who +(fa,q p:kdimare 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 movi;9 0iopgb4qtxng 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 310 m/sxszc)bo/rfz89) kl 7n (a) What is th)9/)c xfk8 rn7sbozlz e angle 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 pl1.to9ty+ vhjlanet where the speed of sound is only about yjt o+1 h9tl.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 gv. z8 sv*jd;f 4ayhi/the shock wave angle it pr iv d4y 8/.hjsz;f*gavoduces
(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 h3s4cz/i rrb99 x8sgq$/theta$ 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 1z,w.juzwwy5 8 .5 km above the ground flying faster than the speed of sound. wuzy58jw ,zw.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 t( (c ucqwn; 79/31 bvczueqniy.+uyxthat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desincqub yv 1w 9n(z;3y+xci.cu 7eu(/tq gned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many oc ;,tx+ jzsrqk5alx:+ iz4-bzitaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ofqzvh *wb5 xbip,;*ac- many plastic pipes of various lengths, which are open on bothazbc*xq iwb;hp*-,5v 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 pers4 06zvhxtwfa+1ser4h on makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?f6ar4xw v1thhze40+s    dB

  What is the resultant sound level when an 82-dB sound and an uviqxay:9h6 2 lw*. gp87-dB sound are heard simultanv q6w2 a9ihgu:x py.l*eously?    dB

  The sound level 12.0 m from a loudspeaker, placed inyk32) sh vdsv7 the open, is 105 dB. What is the acoustic power output (W) of the 2s7 y 3hvsd)kvspeaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 H i1tlc-s 9is:qi/3i gez. The power output drops by 10 dB at 15 kHz.g1/ t-sli9eiic s:i q3 What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ov m7ypj6,c z;ku(e/sbyer their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear atyzusmcb7(ykj ;e p/6, a distance of 30 m from a jet airplane engine?    W

  In audio and communications s dj:ji((ct*r eystems, 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 frequency eif. 6/9;,.ckuffgvccx9qhb 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 y9pxq01yzdl) +ysjxh188z w rwith a fundamental frequency of 440 Hz and a mass per unit l+z8w9y8dxlxzyj)sq 1pyh0r1 ength 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 abjbijj69 9qv:; k eno9bove a vertical open tube filled with water (Fb9 ij9ek9jbnjv6q:;o ig. 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 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 :o,unt4s2dkx imi, l5is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it 4t sx,2o:,n ldiu5 mkiis to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ful;cn/6 h5rfebg 7vxl .ql 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 range coming fromaui. v hc*675 nm(bwwh two sources. The sound is loudest at points equidisbawi nwv5.67 u*hhm(c tant 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 of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conducts/ yr3vlhm6 vbxu* thv p)ofe):-6.iqtz4 c6uor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is 6) yp-r/6ux6v t :vhf.q bcomzsh)i34uvlte* the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you isgr 8l1-2zlz,zpa u, hh 538 Hz. After it passes you, its frequency is measured a plhzlz18gah2 ,uz, r-s 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just byn2jyeu k95c*o*zw 5zwext+ f: listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain cj uytneez 9*c*xfk+w5zw5:o2 ar 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 frequencjwaccq2h jt+q2//tic3,8ur ,x f)fm oy of 11 Hz. The shorter one is 2.40 m long. How long is the t+r3x ,h)qic/o 8f,cajj q/c 2f2twmuother?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past am0d8 ca*8oabc 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 oac*ca 8dm b80observer 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 flownn2mhth7: n9*qhrnn0*( tda a in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a nqtdhnhn0(n** h :a a92tnr 7mspeed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the mothu0staipg3w;u f g+ 1fa*n- ix( 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 thn(up i;i-*f g ta+a0xwsu3fg1e bat after that wave reflects off the moth?    kHz

  A bat emits a series of hi;ap wwu n/hgpb.2/s o+gh frequency sound 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 detected by the bat so that the echo from one chirp returns before the nex;/gpw/b s 2 ahnou.+wpt chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sendgm3 f rot;g7./oq7lo 2mc dlk: 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 overtones is re t qo/l ;l3ocgr2:mof7kg.m 7dsonating. 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 compromise)( 3yop4l vn/eni 3/m8ibhqoq0 +lf ybd by the presence of standing waves, which can cause acoustic “dead spots” at the locations of thevlyle noyibb pf3/0q 3o4/8+i( mhnq) 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 waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender j-)slt d0 h e6+rcls)4+kdobd aluminum rod held in the hand near the rod’s midpoint. The rod is strokeh+k0bsd-)ld +ld6 s)jr4coet d 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 foms.r 0ql cy,,zr the human ear at a frequency of abo yscrmlz0., q,ut 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 yom fimz; 3n81at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after 8y1 om3i;z nfmthe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is3nmiq:nmylc 21vf1)o 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