What is the evidence that sound travels as a wav0*e;o)rjr4 5t7w2al sj6u wymyh * bwqe?

What is the evidence that sound is a form of()-u-+qgtjc;e rleuod v0+ o y energy?

Children sometimes play with a homemade “telephon4(ey/uc d.bcl e” by attaching a string to the bottoms of two papeclde(c4.uy b/ r 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 air into water, do you expect the frequen,; ) oow0k))c.x vsiytx a8dcgcy or wavelength cg,tsvya;. cxoo 0dk)) ix )8wto change?

What evidence can you give that the speed of sound in air does not depend s0il-fu9w/rw uignificantly on frequen0/u wfwi9-rulcy?

The voice of a person who has inhaled helium sounds very high-pitched. kqi8ap+078*a sfz vr7ko tw/ qWhy?

How will the air tempezcl*m ;rvq4b(bs+ t n/rature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter t mhp2j9a *bdvdr ls44-o reduce the amplitude of sounds in various frequency rp9j-4v ahd42br mdls*anges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3pccz nm1c u*4hz, d83y0) spaced closer together as you move up the fingerboayc 81*u cpn,hz34c zmdrd toward the bridge?

A noisy truck approachesu.z9 ba yk*jrhi98i:v you from behind a building. Initially you hear it but cannot see it. When it emerg hy*9kziu9 bvria.:8jes 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 diffraction.]

Standing waves can be said to be due to “interfe4no1ugivg5: .51 krpc jgqld)rence in space,” whereas beats can be said tog 1oq45incd gg5p lj:v1) ur.k be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the s-s*lg 9)7h nwvwd da*opeakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togethe)v h 9*s-d 7wdgalown*r?

Traditional methods of protecting the heari mn x2vq+e./htng 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 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 no2v+mqhnt./ xe ise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave728ke 3owz393:: hhjf6 wsri bhwnv2uw b fy.n 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 ce:2b39j:2 ynf nw68wh.uwofvhzh33 srbi k7womponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move j el .j0zq r.-3ilm2hmin the same direction, witjl2ri-mq3hl .0j z.m eh the same velocity? Explain.

If a wind is blowing, will this alter the freque vht:6s20o qzkncy of the sound heard by a person at rest with respect to the source? Is the wavelength or velocityo0 2thq kvz6:s changed?

Figure 12–32 shows various positions of a child m4,bsev 0u.iy in motion on a swing. A monitor is blowing a wh4ui0b.y, es mvistle 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 length of a lake by listening fo . m4*a byn.cp 3z96gne1iphqjr the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate theie3hp4q1pc jznnya6.9bm.g* length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship hm81o85lw,olabf4d v just below the waterline. He hears the echo of the so84 ,wb5 ll8o hfoadmv1und 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 tt ,j zgeyt* 0 gh/93eiejj4p820 $^{\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 iftz;z 1ax i 4)jp5c2w gbjg11b )ku3fws drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Figu5 3)pftz4gx;k gbfac1b wz)1wjj1i 2 . 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash ith) 8yo;2xin. siau5 vm makes when striking the water below is heard )yhunm2 5 xs iv;ia8.o3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the6nw :ommb sqilzk6 cqew :+.v4 8i4io) concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1i)qlcm.iwnsikm8 z v:: + 6q 6boew4o4 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)ygcc s7q0ja l/r2upwropa.u /9u v.1 distance by the “5-second rule” for estimating the disjvu1r 0cl.2oa pc. u)y w9p7raq gs//utance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a souw.nw:5r8+ pm )48ho w kirnbmdnd 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 sound whose intensitvqed3,x ug7n +y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaner9er6 jm. (ruaously at a certain plaue9r(r j6ma r.ce, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noi )1idrnu* q3zbsy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experiencezriun *q b)13d if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is 43-t3q swygnp said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 3wpnsq4gy t-395 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 q 3o9lckyj)p 2ojv 2e,of sound from a person speaking in normal conversation. Use Table 12–2. Assume9lck2o,j q)yj2v3 poe the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area imi26h1x p f-xfs $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the moreu(0gvn uc: l9 kvttrntdr65-( 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 connected in turn to each ak : rlun ugvcv(r-t(509tntd6mp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whgv p. lze.(ea+en placed 2.8 m in front of a loudspeakpv . .ezal+ge(er 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 typicallyiz/de mleml3 x-a4 +:qqxm-s9 detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ bxm4-imd9asq z-:qlxe ml3+e/ y this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a souzw8 szz)ai z3.ll0ju/nd wave is tripled, (a) by what factor will the intensity increasew. l lzzj8s0i)z/u3za? 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 the frequ i 7 tt-.2atdupzl n7k1 b.hwbv;p:+quency of the other. Wha1.wvi pa;bl 2+p 7- d.uqzhbtknt:7tut is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that cor,y,qutx 1kagdvpt. la , /w8:oresponds to a displacement amplit,,o t81q.al/ua , dwtp:k gyvxude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem a7dk8kvj1dvm 0/n 3x29mrcc oe s loud as a 100-Hz tone that has a 50-dB sound level? (3rec j 7vkm9nddc/vmx80o 1 k2See Fig. 12–6.)    dB

What are the lowest a 3b,1khjwck,6z ncne)nd highest frequencies that an ear can detect when the sound level is 30 dB? (See Fihcz1 ,6 )nweb j,cnkk3g. 12–6.)

  Your auditory system cg 3stryoow9d: z(p,a;an accommodate a huge range of sound levels. What is the ratio o9psyt ow,z:dr( ;o3gaf 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 ywvaai4p;-j 6/rmn -h;b9 sww frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 m/by-vp ;- w9wi4hrna6a;jswg. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental an; gafbergc 46z+pzz g q3-p(x4n(fp7 cd first three audible overtones if thepz4ng bgc zfppzexg6+4far( (cq7-; 3 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( oldlai7 7q6o expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assu6il7do oa(q 7lmed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes))dx+vjjcy63l+pwr z :0uszx spanning the range of human hearing (20 Hyrzcs)x0w )jl:ux+36 j+pzd vz 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 5405mhv* m7y-; q-bl8.lftfjtzy Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 6;f mmb -t.qzjl7-yhy5 tfl8*v0% of its original length?   Hz

  An unfingered guitar string is 0.73 m ,jw 6p-cc (gxg4ofz mri9gnhv(s61*wlong and is tuned to play E above middle C mcxvics ,6 r- wggwpjf9gh(no*(6 41z(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 or-iwfpoy dw j4 j9 -,pfz9dy,5rgan pipe that emits middle C (262 Hz) when the t- r d-p9i,ywodz9fpyj ,4fj5wemperature 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 a)sznyh b,:oz +0( xzheh 5v*itt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutew-l4f ibfh/y tk 56f)ksa1vu / in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 H5f-wtkkbf6u/ vfi /a)sh4 yl 1z?    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 r;/kzmxup; qk 7esonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenc;z 7x;pq/kmuk ies 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 ends. It rest tgt 9:d qe)*s o6nctnn70z90 +mefhdonates at two successive harmonics of freque+)7t tgqeo*d 9nte0hnt mfnc0:d6zs 9ncies 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 oyam ohk-o,,bi*b* t) .2pupc$^{\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 audibl*vgutcfc2t15qkxlq*x 8t ,3xc ; dhs5e range for a 2.14-m-long organ pipe at 2,xk cx;* h tt15qt2cq lvcsud3*5 xg8f0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the ozf4(f4 rgg)t yutside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–g(4ft y rzg4f)6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tw:c 12a 4jtgk fgf9f(rpo strings, one of which is sounding 440 Hz. How far off in frequf9fcf2g j( rkpa14t :gency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andkqcr3 3yf7 j uh c2g9y)5my,zm $C^＃$ (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 anoy.lw4 2 cwpshlrb94 w)ther (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 simulwlwc4hy 2 s)pb 9r4lw.taneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounde.zs8 ua:k;qqn2 xw,yli2q s f+d with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrai.ka,us+wqxf 2s:2 8qn ;lzyqtional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensq tk w by*o4u2p4ps)61zk2c inion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11264wyop)ck1kb sn tu* 2iqzp4–13.]    Hz

  How many beats will be heard if two identicalvj/p kuykj d4qbwp. 3 .31fj*a flutes each try to play middle C (262 Hz), but one is at 5.0°C and t 3yj3/j*.1vd.kqwu4pfpa jb k he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forx+rh) le*y 2lsm*r gzy4. rjn*k 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 frequ+xy z**hsrem*2r jg)4. nlylrency 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 3.00 m fr8t)me gi2jozy/ 60yxxk td-k)0 qb( cgom one speaker and 3.50 m from the other. yykt2g0)(t8xcb )dmige /z-xjo q 0k6
(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 vpp2kfszx *r7 *xo; 0nc5l;sf supposed to be vibrating at 132 Hz, but a piano tuner hears zx *ovpls72; r 50kfsxf;*pcn three beats every 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. tw c-(huk;3w8kgbb8 y76 m in air. How many beats per second will be heard?3 uwwt-gc(88bb;kykh (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of vuiwr, /6ph-pa certain fire engine’s siren is 1550 Hz when at rest. What frequency do you/hv,irw6 -ppu 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 da )* (rr2udsdletect if a fire engine whose siren emits at 1550 Hz mdr lrsd*)2(ua oves 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 movp saocclk)p m,ci0.r /)*a 5xcing toward you at 15 m/s ve ac.a*)copx s mkcp5/ci),0lrrsus 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 with the same single fre8+caip: tl+0puxy- jh quency horn. When one is at rest and the other is movingpu0 +taljh:x + cip8-y toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sou/z.k*z: ;awnas*q hjsnd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What ishs;zan*qkj zws: a *./ the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 7d4/ ):-.zb3 x kiwbqwfmvltd5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fr7 w3d z -mf.v4xib/wqkbt)l d:equency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentso38zn5c. hw oc, a tuba was played on a moving flat train car at a frequency o5.c3o nohz8w cf 75 Hz, and a second 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 ttk*ccw+l oj8 kp i3-2x7 xid-ro measure blood-flow speeds. 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 int2o iwlirdxcj8x7- ck+p k-*3 large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrason hi xk2k:x3r14eyhx d.ic 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 570 4mm)z//e)oay x f//vla l)led Hz. When the wind velocity is 12 m/s from the north, what frequency will obmylm/ /o ed4zfa) )/l)/vxle aservers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving o li))kfe3 qkxkqd-(,jj pv6syjyu ( :9n 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 Machj ,jd,1 kmajm/99 +lo6 crrcaa 2.3 where the speed of sound is 310 m/s (a) What is the angle the shocjl,ar6kjm/caro9c,m d1 9 aj+ k 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 planet where the m41smqt -fm:zspeed of sound is only abmf1q:z4 -tm msout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave angteq l j61,06de;udpnomp3 (l gle itpjdu (1 ;3enp0o tqgdm6ll,e6 produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 0 z qdtzleyff(s;uz m sc7v2v:p.0 :i+$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see mmyfbd:7u hy 65ckr6 :a plane exactly 1.5 km above the ground flying fu5y6c7 yhkrb::m mf d6aster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 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 deviczle sgxj8hc(qt 1 6zfz/3qnq:a9099xl6hebxe that 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 designed to work is 200 m, what is the minimum time betwe91l9 e nh6zj69x :aqex8 0zx/hsqzc b q(tgl3fen pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range w) *kt 9h9 jqqiq6udxvop8t35? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display call-6znow7 *kezq ed a sewer pipe symphony. It consists of many plastic pipes of vario6eo w*qk z7nz-us 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 persi3g0dbb yjjr: 6-m(z0z.p o4n quv1sjon makes a sound close to the threshold of human hearing (0 dB). uj6.bzpvm r q0: sy30 o1gb4id(jz-njWhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when anxrm i-2v7 p57:vcxaswynq* . v 82-dB sound and an 87-dB sound are heard s - *x7ivy5.7a qmrp:2c xnvwvsimultaneously?    dB

  The sound level 12.0 m from a loudspea 9l njwudq-yqoti40j4:a6 7i gker, placed in the open, is 105 dB. What is the acoustic power output (W)ljaqytg 6:d9 47uw iiqn0-jo4 of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power05e1or0a,*2nv fepu (lk qbbqz2r wy3 output drops by 10 dB at 15 kHz. What is the power v ,1 b22 zk 0pewrne0y3b*qo(5f lrauqoutput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear p99fk8op vq/j),z0dk o 3 ohrmerotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of me0kzo, vkr39hd/f j)8 9qpoo2.0 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, (v u(k)7al -s:p zlc5tbo) orjthe 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 g fd66n *xam87leh3n i1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamv 7ycl8mi f+9lental frequency of 440 y9 mcvl8l+fi7Hz 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 into vibration above a zw) buhs37g.y 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 iy) bgz3.sw h7us 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 i/w0k-ml- dg.g b6qci5z1ejux s near a 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) with thmc-w-dug1g 6.kqlb xe5/z 0 jie third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f/ xsrnb4mfj1t p,92cy ull 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–i)d:ffp2t c7g1000-Hz range coming from two sources. The sound is loudest at fcgfpit:)72 d 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 of the sound?   Hz

  Two trains emit 424-Hz whis,a-v)-b ulv6enms 1 zltles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is t-vn)abmlu-l1 ve 6z,s he speed of the moving train?   m/s

  The frequency of a steam train8xg (izqty055. wjwl d whistle as it approaches you is 538 Hz. After it passes you, its frequency is measuiz 5d8wy w(05g lt.xjqred as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimat( 5 z(gepjyi bamyt5z 6/w4w:ke the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops5yi6ew bj((y gt5z4 k mpaw/:z 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 togethepv;e9eg8kc 0j (6upmmr, produce a beat frequency of 11 Hz. The shorteru jmmppk;ge0c(e8v 69 one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stazdibqfl;:hki p12:u :tionary 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, bp2q : i lifd1zh:k;:uand (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow *n8bi(y)xk u oor 4w,oin the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MH o)*wkoo u,n y4xi(8brz 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 while the moth is flying towae6j3ao4 n1o zton8*l urd the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after ot 83ao*o lez164jnnu that wave reflects off the moth?    kHz

  A bat emits a series of high frequenc2 4l c2rasm(rsy sound pulses as it approaches a moth. The pulses are approximately4rr2(l ms csa2 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vi( g9n)d5 jyczxllage 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 d(zjn gy5c9)xG 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 s w1dkmgqw607+sd8va6dyh*jotanding 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 frequencddo w6ga7wkmq68d+v*h1y j0 sies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calledp z(2 1paazvf2 “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. fa2vpzpza(2 1With 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 hearing3d, b;sk :lqdr for the human ear at a frequency of about 1000 Hz is b,d3dlr; :s kq$I_0$ = $1 \times10^{12 } W / m^2$ 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 obser / ,k*./rv3wny iqjii rtx.e7fver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Wh/r..vx*qei ir3/, 7nykw tif jat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 pjgr2fzkf 3 fb cx821/$^{\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