What is the evidence that yr m-r4 wum 4si12 rmo*twct i82ica5*sound travels as a wave?

What is the evidence that,tbftmu9)x9 4ijqn g/ sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string ugq+ipfovzh4;6w5pi/k ba-6 e ey6)l to the bottoms of two paper cups. When the string/ qw6gha4;zel6yubpe65v- +i )kop fi 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 fe2 cjjpz- 3 5ujz7)tumrequency or wavelenguz23ujem5-7) czjj p tth to change?

What evidence can you give that the speed of sound in air does not depen 3bebmm-lg/cp kq8 (u1 kb9h9kd significantly o(hmp1-bbgkk /b em9 3lu qk98cn frequency?

The voice of a person who has inha4 )9w8vbo/otq4a ta a,d0qmijled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch ));0luhi7 mv hy) k 0frzokn-3odhm7zof organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundjqcmp ;- (ykb* 7vcw9gs in various freq 7ckcbp*9ygm ;-( wqjvuency ranges. (An example is a car muffler.)

Why are the frets on a8tq af.x -a6 kk(y;qcv guitar (Fig. 12–30) spaced closer together as you move up the fingerb6av.kc;qq8 x kfa -yt(oard toward the bridge?

A noisy truck approaches you from behipcr87 clrf lcn14lr-) nd 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 Secrrn 81pl7- c )rll4fcction 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” 3ixl fcc;3cw4 whereas beats can be said to be due to “interference in time.”;i4 ccwxl 3fc3 Explain.

In Fig. 12–16, if the frequency of the speakers we7zt,6z zlg22sqe fa83 mxa xu.re lowered, would the points D and C (whermg7lx,63azzszf2 2x et.qau8 e destructive and constructive interference occur) move farther apart or closer together?

Traditional methods ,blft.wq 39 awof protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds 3lbqw a wf.,t9it 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 as a xhp250qinpzw7 aa9bidl0* 0qsuperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are thz0i pql*i5bq n0a9h20dxw7 pae two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the ,n xovf62 vejv.bm.bmvm 3.*qsource and observer move in the same direction, with the snvmm v.2fb bv,* qxv.6 3oj.meame velocity? Explain.

If a wind is blowing, will this alter the frequelceby0h mh)1 z 63jfx0ncy of the sound heard by a person at rest with respect to the source? Is the wavele) bl 3he1hyf0x0m6z cjngth or velocity changed?

Figure 12–32 shows various positions of a child in motion oiqa 7xrho.:- a+dt 7csn a swing. A monitor is blowing a whistle i7h t+-o.7csaq rx:aid n 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 thkc(y-b p 9,tdoe length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. Sh,py-ot(c9kd be hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He heavufia l-r5i8u90 zl+b xuy1.s rs the echo of the sound ref0uui-xlabr+s vl1 i9y f5z.8ulected 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 wavelengthsn;hqg-h-bdh4hqc :zap i/-x d+y0c8 l 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 drifting just above a school of tuna on a h.l* .q-t6)fzq 3 .tlgo xdrbefoggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33)l.3t qo-leh. tx qzbdf6g.*r). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking tt -5y4x/g m.ly0n juqohe water below is h/ntxu. 4g- 0qy5ylm ojeard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, r+m h y qu9ttt8:v4:.dlkzbc0sees a huge stone strike the 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 1.1 s apart. How far away did the impact occur? See Table thm z90qrt dylc b+.k:v8ut4:12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance b o 3 sz;m sna18v:njayxhp5v0;y the “5-second rule” for estimating the distance from a lightning stri pvvjza0;sn hms1; yn58xo: a3ke if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t u-drtlrv ,0w(he 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 intensityo dm (bnzup749 is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro/ 1mco6j*1wc/ w( -pu)b b9sbon huhc)a1q hroduce a sound level of 95 dB when fired simultaneously at a certain place, w h(onhbu1 qcc)o/ hj poa16m w-)u/c*w9r1bsbhat 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 equallyi2 qmd-m +r6nb noisy jet engines is experiencing a sound level bod-6nrmq+ im2 brdering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to3qgcmgb64 ;5r x4 g2:gfptccw have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devgg3tb m :xf4c46g5c; qrwg2 cpice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sr5;m2o-ks wos v,hdf -ound from a person speaking in normal conversation. Use Table 12–2. Assume2hwod,mk -5;vs f -ors 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 is4tquydy21e 2 kj;e)dr $5 \times10^{ -5} m^2$ (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, wgvy:at w/f uq8z3nx/(zgz b9ssl*8e 4hile the more modest amplifier B is rated at 40 W. (a) Estimate the sound levqs8z g (g4bafzl/y xst83*wz:9 e uvn/el in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed)mx r),5p9m ;k1dkt kwn5nafk 2.8 m in front of a loudspeaker on the s)k rkx)59a 5ktpmf ,mwdkn;1ntage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a differenc)kt1-g .mpr ine in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: St- n.gkir)1mpee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wve(fa smx,4 ki 6:mu7dill the intensity increase? Inc6mv4 isu(xfam k7: ed,rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one htuvusr, ua r/ 7eo)9 ae47hv,yas twice the frequency of the other. What is the ratio of their intensiti, 97r erauv7 s,v/4h)ao uuyetes?   

  What would be the sound level (in dB) of a sound wave ind arv s3tz4;9 h+:;wpsl( bxzv air that corresponds to a displacement amplitude of vibrating air molecs4 r: bhdxvz ;la(vws3tz+;9pules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as louva.0 v(ls+rt89 jwq tcd as a 100-Hz tone that has a 50-dB sound level? (See Fig. r. t(9la8s v wvct0q+j12–6.)    dB

What are the lowest and highest frequenciv0yq,k 2f8 rz1ss)n eies that an ear can detect when the sound level is 30 dB? (i r1q2 y)v,sznk8es0fSee Fig. 12–6.)

  Your auditory system can accommodate a u/aj)2 g eyd)lhuge range of sound levels. What is the ratio of highest to lowestga2juld)e/ y ) 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 funda99e,rotxjljtbc7l+ t rg8q* :mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what 7j8,c :9lj + tr xbglr9tqt*eotension must the string be placed?    N

  An organ pipe is 112 cm long. Whf)-l :04msn 2yweaoq+jlfu)21k p 4x;l e prpcat are the fundamental and first three audible overtones if the pipe ;j1 a :p4 2f0xkr)qlo4mp -fscle+l 2uyne wp)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 expect from blowing across is: hai/da n ntqvwr 7u)dl wx87,r57/the top of an empty soda bottle that is 18 cm deep, if you assu7 / nlrhd7:au5rt8wiq,axv/7)sndiw med it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of humj-f:yk vp+mn1an hearing1p :+jnf- vkmy (20 Hz 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 54)0aa)1 tem 7- (juchrey+t gkf0 Hz as its third harmonic. What will be its fundamental frequentru mtagf+-ha y7ee(k j0c1))cy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lr1zrf((* v,9firee f * nnu.bdong and is tuned to play E above middle C (330 Hz nrr uv((eifz*n d9f*be1r ,f.).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pim92mkn tj yj78j bjw;,d(evu3pe that emits middle C (262 Hz) when the temperature is 21jmje8 vjwyub2 n kdt7(;3m9j, $^{\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 ati98 f1ut eima6 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 f2 ngg36jber-9bzp kb k+gf6/should the hole be that must be uncovered kej9-/gfbgb23 +r6z g6f bpnkto play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, o*qfe;9f tcgif)*ql3ff (p: mn( /ykk440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a c/3 p*:f)f ;eqlfkqyfn(gi( k fcm* o9tlosed 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 ro rif9,rs5jc6x p/d(:apg: uj esonates at two successive harmonics of frequencies 275d s g(r c:xrppo ufj5/i6j,9a: 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 / f.mlq: 5as7mbeb bd1$^{\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 tab+4z d zjy6qc6rxo) -he audible range for a 2.14-m-long organ pipe z 6rcx bzjqo46y+)a-dat 20 $^{\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 outside and ut: gw e5).-:gcxpm jris closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves e5-upw :tg)gjx r m:c.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 eve3iosr7hy +o8j9 gtad-.8v4r st9dyqo ry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is9 ojd3ay88vsg-is.o r47rtt9yo+ dhq the other string? ±    Hz

  What is the beat frequency if middle C (c4 fb o7kryyx4m0 i6;y262 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, whi(b0 c xarfe2yzj9cdy3c/74 - nmx cem2le 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 operatnbmyxy7/0emz9jcfea4c22rdx -3 cc (ing frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a m* nxzkerf2 f9q 2*ij;350-Hz tuning fork and 9 beats/sxje*2qz rf2m;kn *9if when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenyqc3p w2mh; )ek)j hekskt26 /sion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings)/sje 3k2mp ;cqhty)k 2e6hk w are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutesk:20 fkykmmh9 hr0+sc each try to play middle C (262 Hz), buthks9m0ckhmr kf:2 0y+ one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B,*2b -r6o:qyedsnxe v 2 and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? Wh -ebo2: r*eysq2dn6x vat 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 perr ,nr 2ne.p,k)b7cmlbx 9n4txson stands 3.00 m from one speaker and 3.50 m from th)9,7 n npemb2txln,.4rrxkc b e 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 vibrapi to-2db5f o5ting at 132 Hz, but a piano tuner hears three beats every 2.p5bo2 iof d-t50 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 1;os9je g0s4o:h0;w7ty se fg s+glsnm in air. How many beats per seco0g 19go;yolhts4sf ns 0+7;sgs wje :end 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 1559vagah up465 lw3f(y i0 Hz when at rest. What frequency do you detect if pawy(avh6 l35 i4gf9uyou move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequljuy(27 vu5yr 9v4qseency do you detect if a fire engine whose siren emits at 1550 Hz mvuye jr( 4v9 s5uqly72oves 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 mov ,-nlzpy8iezf*8 xwvur2 3h; jing toward you at 1p vl82ein,zjxzwu ;rf h*83- y5 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 wia sms(2;:jp kwth 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 frequency of 5.5 Hz. What is the frequency the horns emit? Assumj2:sa; (pkmsw e T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wan a*3yx)go1) . yjzcw q7npk:cves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound f:w) gx*) 7poccz.31y yqjan knrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies,i--f.z) cjw7gpvn n;c the bat emits an ultrasonic sound wave with frn vc).z-;j 7 wg-fpcinequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tub+n9u5tn8 uocr, zo g 4p:;jubi ,p.blia was played on a moving flat train car at a frequeiuj o8bpu,+5z g.b;nu,ocrtl np 4i:9ncy of 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 u00*n* )z d nlthxqs+akses ultrasound waves to 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 in large leg arteries at 2 cm/s directly axz s0kl*aqd+)0h nt n*way from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frerh9k .xjv(,zq quency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12 iw031 ivu+v 8h/k k xsro-3j 8wuegvu1m/s from the north, what frequency will observers hear who are u 8uvurx1oh -k8egj1v3swki03wi+v/located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed abj45 t;+ceeqc t 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/s (a) What ih zmz./4 muegvjoz;7 *s the angle thehve4.m7m/ gzuj*o zz; 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 the0 i kmoaxs in4q5i23z8 thin atmosphere of a planet where the speed of sound is only anm2qzx83ii0 ia5k4o sbout 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 ocea-7wwz,vw nvo 9n. Determine the shock wave angle7nvw9zv ,-wwo it 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 8u00h r.bm b(ftuk(+vfcb8ma$/theta$ 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 ground fl8++xoxl)b ep)fvc (k . zzq*xyying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled aq )kcf.xe+z+ xlz*poyxb8(v) 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 devicepcu5k09p 6 )w6x)vuulegg .rn that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which 9pluv)0.ec ugg5xw pn6rk6 u)it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range? cbv7 2ojapx-0:js,1 j-9tiupus ke.l $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonyz6,.vhl9q-r9rkohb zvwg (9h. It consists of many plastic pipes of various lengths, which are open on both endohk9 gqz6l b9,.vr -wzv(hr9hs.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makehllx 260uck bpe( +b4tpxn2v* s a sound close to the threshold of human hearing (0xp0c lpn(x 4bt2ek+2 v6hlbu * dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82 5),x8 o/k p+z+e fgszcpzy2me-dB sound and an 87-dB sound are heard simultaney/eks+z+2 mo czep5zf g) p,8xously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dd * xbflx0m+ rg1+rl.rB. What is the acoustic power orgd *rx+1l+m .bl0xrf utput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Theov(d5njif-fz;/(ecz ;vzlg 8 power output drops by 10 dB at 15 kHz. What is the power output in watts at 15z(;f/jlo- f;v gnzv d e58icz( kHz?    dB

  Workers around jet aircraft typically wear protective devicis em,wnbt vtk6262cp 0wo3c2 es over their ears. Assume that the sound level of a jet airplane engine, attbc2i2k6,36pev t mn0sco2w w a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gai94;qrq9 l; bz95welf ay2d wern, $\beta$ 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+aksa798p v ch/l lklo r0s.9f tuned 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 q,f i+der av31z/xk 698/ feetcvt2licm long between fixed points with a fundamental frequency of 440 Hz andtq8tkv,zf9xv6 +r3 a/e2ic 1dlee /fi 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 abootids y03 .pev; 6finl27k 4at8huh7tve a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What i7kdel 6hui4ft to sh2pn t.a8y7;3v0is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 1,*+b, atanmb tqfte72.10 g is 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 the third harmo7 tf+etqatb,m1 *a n,bnic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obs dm 2hgipx.t::3yt(si ilg*h9e5c/sh erved to resonate 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 range coming from two sources. T( mn4we9ygdfuaofe s* l.7e 8inm:: m4he sound is loudest at points equidistant from the two sources. To determine exactl f*mwna8ef9o: .:7m4s4meg lnidy( euy 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 whistkureq.hc2;a.ak 6f u.les. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequencae k;kq hfuu.c.2a.6r y when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz ma8-k0snteu) . After it passes you, its frequency is measured as 486 Hz.u tmkens-a8)0 How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to then 3 oo6gr(h+q:m c,uen6n26 kfy;ph be difference in pitch of the engine noise between ohour6(+mchnp6 gefnb;nk:6,ey3q 2 approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togegd, 7*+b wv;ht9dvynjther, produce a beat frequency of 11 Hz. The shorter o *dgvbt,nj 7;h+vdwy 9ne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of atd )- vsx(dg 83mawvec 205ezi railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers hazs23)m vx-dtec a( v 5egdw0i8ve identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow inz) m7weo4 n-+h-fiifm 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? Afm+-4ofw h i- imze)n7ssume 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 flyingej,busgupp +y 7wh .y;n-;fsd(e7oc , toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after jec s,u+p7 o gd e;7b,pyfyhusn.-(w;that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches 0:e9 hwvz:o6d n7wwila 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 t09iwo7ww6l ::e zndhvhat 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 je lj ;,os4r, d*ryezdsif-1 w8g 4wa(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 resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp ( er flwjdz* rj,g,s 1448-aw oeydsi(;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 b-je yxc nb5rn09x oa**e compromised by the presence of standing wax*aj 9y 0-rx*onnec 5bves, 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 waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves aeivcp-k p-y* ix,87i y long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, l-eyik cpiyxp* ,7-8i voud, 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 frequency of ,hlf81chg )ukmd9gh* 1jpx/ j about 1000 gh/ c)8xhj,uf j1d9gh p1l*kmHz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2d9i rxux5e-m tx)44 uo.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s al4 iom5ux9x)ud t4e-rxtitude?    $ \times10^{4 }$ m

  The wake of a speedboat-m3 r np-o1ursqf-h 3a 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