What is the evidence that sq 7jaa..g9c ,)demvcsound travels as a wave?

What is the evidence that sound d8-.fd cezoj0is a form of energy?

Children sometimes play with a homemade “telepdi0k1inbhta:(m ad6 uf a3q/9hone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup t d1:i3uibkt( ad6ahnm 90a/qfo the other.

When a sound wave passes from l-7v- s)uz: uyujd/vd nr6on eiv1j:,air into water, do you expect the frequency or wavelength to6v/u7lv :s1 o:d r-vn-e)j,jy iudunz change?

What evidence can you give that the speed ofly,f4tld+ j )5a xab:k sound in air does not depend significajyd5k, )x+fta4 l:ablntly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Wh v2zqovl:-a 4oy?

How will the air temperature in a room affect tgy+x*,i; q8iunf t rb9he pitch of organ pipes?

Explain how a tube might be used as a filter to ree5w8 zsuq mm28duce the amplitude of sounds in various frequency ranges. (An example is8m2 e85s mzwqu a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move vi0ih-jb od;9 ch/xl3 up the fingerboard toward the bridge?b hd0ijch -i3/vo9;x l

A noisy truck approaches you from behind a building. Initially you he;xlnkpx2+ l9 tar it but cannox;lknl9t2x+p t 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 diffraction.]

Standing waves can be said to be due to “interference in spacengc 7a ukqk84-,” whereas beats can be said 4na kqk7ug8c-to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poinc7 l; (f i;lwg,ceww f0ox6ut1ts D and C (where destructive and constructive interference occ(; ,el;01xuig7 fcoc 6tlw fwwur) move farther apart or closer together?

Traditional methods of:l6;b)4yka uq varq:j 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 tu 4k y)qblj:q a;6rva:echnology, 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 yh/2 t5z2s jbrin Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In rz y5tb2/ 2sjhwhich of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shiftp.m28 oye wo2r if the source and observer move in the same direction, wir8mpwyo.2o2e th the same velocity? Explain.

If a wind is blowing, will this alter the frequencyqi 5hh16x9ouwhfp 8p *g q-3yyxr 6t8y of the sound heard by a person at rest with resy 65xph *h1 9r fwu yqpq83hoxti6-y8gpect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows variovlzvs29vwb.t* (j2p vus positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At whichs(lzpjvv2vw9b .t2* v 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 otw1;d7x ah3)u8hin*9*bmx a lg bkd:mf a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She m7;3ba:n1d axx lthdi 9w* *8um)k bhghears 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 hears djt(jgh5wcf aw6y* :2the 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 is 1560 m/s 5*wjyatw6cf hg2:j (d(Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength3/lqxt6 4 whpz-he(j(qc,c nes+r0cis 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 69fz)j ry;za hbye:lk1-ya5ey:jx s,of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time fje9):xy5 1;zlayhzye: -y jbakrs6 ,elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the tbm; k2d 9re 5v-wwuyb z70vld0op of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cl0u rwk2m ye9 dw7d bbv0v-;5zliff?    m

  A person, with his ear to the ground, sees a huge stone strike the co,rb*p9.j5qumcszx a9b)c gp7 ncrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the obp),j9zrsq9 7g.* ccmpu5ab xther 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 onqrk)p; n4*gka e mile of distance by the “5-second rule” for estimating t)4*p;gqnr akkhe distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levelnpaj c0e,d dxi9p4f 2 o4(k+tue; ;bwr 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 soundrss;n ivgx)y s/*p. +lb6tf m8 whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslytg *bakezn ,f9 )lovoi7z+4*m0l6 smk at a certain place, what will be the sound level if only one is exploded? [Hint: Add intkmf*4o z b9 *l,iv6 )o7azkg 0elnm+tsensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four e2 dgrghih 8f)vub:e):qually noisy jet engines is experiencing a sound iebufr vg:d :)) h82hglevel bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 xrwc7j09a6wcm c;:39h e3 b( :eg6h ldpzaufzdB, whereas for a CD player it is 9ewczg 9xm(h 3caar9l73eczw:d:jb0 h u fp66;5 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pek 0a8jk7,a,jt sr id)codl/ *trson speaking in normal conversation. Use Table 12–2. Assumejk* ttoca78l)/dkjs,0a,dir 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 area8jqa5e xz/f n3ydsv73 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 the more modest amplifiethd 72 ykbfv/4r 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 ek vftyb4hd7 2/ach 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 pg 2d5ny0oa 7n 6j2hrdha p3a1alaced 2.8 m in front of a loudsng2h1do7r j3hypn 2aaa0a 65d peaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically de( 1w- z39khemj dglr0m5uqg9q x2(bmu 2e, hfetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levelmr,fxlj q2g5u(2 wquzem0gme99-h(k3h b ed1s differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wi/2 .(zftn+jl8 7a pdnaqr (flave is tripled, (a) by what factor will the intensity incre /rp la7an lf+t(inq82fjd.z(ase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but ozb: 9ush3mim*6 3ecgp*a ro 4ane has twice the frequency of the other. What is the rahgz6s:a4ucpra 3 b* 3 9imem*otio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corrqtc 7mm .t4km6esponds to a displacement amplittmtq4km.6 mc7 ude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hav u0pjm .4(rc/rajz7tce what sound level to seem as loud as a 100-Hz tone that has a 50-dBu4a(cr.j/ z0jmptrc7 sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencieco*/( h dieq1bs that an ear can detect when the sound level is 30 dB? (See F1ioc*(qbd h e/ig. 12–6.)

  Your auditory system can accommodate a huge rang, 4cjyf ;f8.z vfoo2xde of sound levels. What is the ratio of highe,d4cyzff. o xjo2 8v;fst to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 h3g 2a8q/g*rwro mo9p Hz. The length of the vibrating portion is 32 cm, and it / p3o*9a8mqrw oggh 2rhas a mass 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 three au3uei.t cat(e, 7 )i5j z xp52+qhccpvndible ove )i epz5c,i5ca2ntcx7.j3hpuq ve t +(rtones if 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 wog6mt stm.mu:4 uld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a c.: 4sgmtum6m tlosed 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 ql(o a p4-8ajthuman hearing (20 H4lt- jo8(aq apz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. ( zjgn57qye8mr6s1 oy What will be its fundamental frequency if it is fingered at a length of only 60% of its orig(yjor6 e7nym8 5z 1sqginal length?   Hz

  An unfingered guitar string is 0.73 m long and is q/e)34j i:9ro wdisob tuned to play E above middle C ii q:w edjb3 o4s/)ro9(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 organ pipe that emits middle Cl u1klfph u0nydsm+a n ,1+2;z (262 Hz) when the tedlph yfn1 1, n+zl2ksm;+uu0 amperature 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 20 g1.j7+puv)mhq i ; xwl$^{\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 +i,*b.juv,nlf ,ss 0kalm,f v should the hole be that must ,f*kmls,f0 n,v+, . ajbislvube uncovered to 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, 440 Hz, and 616 Haqc to5.fz0..av,udqz, but not at any other frequencies in between. (a) Show why this is an open odc zut.fa0oaqv. ,q5 .r 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 a9xmq/ .4 tg/j8vafinvt both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What i/8m4n v.it/qfv9jxg as
(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 u,p a 3sw:zi 5o(il9xm$^{\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 audibqvfb kb6o3 ./h4xoov5le range for a 2.14-m-long organ pi4h.oqoxv3/o 6 fvk5bb pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm zza) so) xhlk4 bf. 34t8dh ptynkce,:7/v(t jlong. It is open to the outside and is closed at the other efkbk . th4yn4l ,3ce/)sad8zxthp(o)z:jv t7nd 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strjnu gs* 8vd)5efp(1nn ings, one of which is sounding 440 Hz. How far off in freq n(8n fd)nu*epvj5gs1uency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) s,yv4 uzxf1 r1raf)ukja0ma))7m5u ov s i-a1and $C^＃$ (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, whila-s1t4g/w nls4mbj ;7rgr-sa e 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 wha7gb t-w4mgas rn-;sl 1s4j/ren they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and o9uesg gck1-azm c()59 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string?19gs)zocm geu5k c(a- Explain your reasoning.    Hz

  Two violin strings are tuned to the same s- 4i(x ugotjgcu:0;b 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;s0j o 4utg:ucbi(gx- are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eesga4b9o-1wv: sxk khg1h , )qq.o0 hsach try to play middle C (262 Hz), q)904xe wkkb 1h1 qs.sgoohsg vha:, -but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. c lku2p.6jr1oFork 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? What b2rj1 . k6lcuopeat 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 aparn+qu/)x-aq i8f6f avat. A person stands 3.00 m from one speaker and 3.50 m fromnaqxi /f 6uq-aa+8vf) the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to betrq/y*w kz16n vibrating at 132 Hz, but a piano tuner hears three beats everykryt/ z* w16nq 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 vyzpwtx i.3+ 9 t-.wfxwavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assumetx9xyw-iv+ .zf3 w. pt T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15bexi3nh.y5+cjq0 nf0j 1u vm6 50 Hz when at rest. What frequency do you detect if you move with a speed of 30 qxjfbucy6.5 m nv+030n1e jh im/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you der4;s2:s4rpcqc2r u kpjb;t0 xtect if a fire engine whose siren emits at 1550 H2 c0rutpprb 4csrjsq2;:x;4 kz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz soarg13c-c;wr.e2m xn(x, zb lh.skd+aurce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are thee hamk+ca wx3s lbr c, 1g.z;x(d2-rn.y 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 equippelh41pr d-qd.m fp 5ws1d 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 frequency of 5.5 H lqpdfswmdr51h . 4-1pz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives 2sgy-aju7 cz7them returned from an object moving directly away from it azja7c s7u2g-yt 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies cd))a8q e(szu, the bat emits an ultrasonic sound wave with frequency 30.u8qs())d ae zc0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppleaztm5 ip2/gm(mg j4j4 cc .1qd 2ky7ber experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second i qyi 2jg5/aj4zmm .dm1cb4pgec7( kt2dentical 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 usesxt6z frmk 16x+ ultrasound waves to measure blood-flow speeds. Suppose the device6f x+mz 61rxtk 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 away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of wh 01c q65pq./z6q hznlgf*nd 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 souect/,l-s dz h*we2e .dnd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observ d2sw-chel*tedz ., /eers 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 on land if its speed at 20 5 k5 ba30ssuvjs:(naa$^{\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) Who4q *m5cogad /)x ;ephat is the angle the shock wave makes with the direction of the airplane’s motiomhp) /4qgox 5dc;ea*on?    $^{\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 planetly:,pn*tm mj7 9hp ln* where the speed of sound is only about 35 m/s ,jy ln*h *lppm7:m t9n
(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 st9vf 8*q/ c cuu)fno7ezbc h;l)rikes the ocean. Determine the shock wave angle it prod fbve)h8ucn/;lqoc7 zcu)* 9fuces
(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 e(ql6s( xl:rp z1(tkx$/theta$ 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 exacrez88 h8xe nh w33d/ggb;;hq ltly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. Seeh/zl;d;gwr bh q8 833x8 hgnee Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound puls9l ; igfuwy-)h8/e(i8qdb if kes downward from the bottom of the boat, and then detects echoes. If the ma-iq8i bwiluk( ehd/yf8; f)9g ximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves agir2b8n 81 wzvre there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe swdk:( :9ty.q fhp;obxn 3lao4ymphony. It consists of many pla;d9k3hayqofn: ox:.w 4 (ptlb stic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound closea6 a+fzzuf:*(py- jzy to the threshold of human hearing (0 dB). What will be *f6fy-uyzz zaa(p: + jthe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hla(z u6uwd, w1eard siawl,wdu1 (uz6multaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10 npt3hw.1 ay/b5 dB. What is the acoustic power output (W) ofy/ 3.nawbph 1t the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W hy6,lp6 .vixux4,p 4mhq84 frv)ghyvoutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts6yx 486 4.,qvv4xh pg ru) ,fhmpyihlv at 15 kHz?    dB

  Workers around jet aircraft typi/n25+ml xsxo 8:phkg lcally wear protective devices over their ears. Assume tk ohs nm/+x5:llgpx82hat 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 at a distance of 30 m from a jet airplane engine?    W

  In audio and communications h) +g(gx qjj+ih,d/zx systems, 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 r-j 5xyj3vh9z7o ef8s frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wit(gjaxm .ts ;g9h a fundamental frequency o. agx9tmg (sj;f 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into ve6midz/tw) d,c n0. *x/ wahfkh y5u7ribration above a vertical open tube filled with water (Fig. 12–35). The wzke5d) *dm7.i ,0 fxnru/h /cy6hwtawater 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 7nupr n qg-wx2o mu3cn20q(n):ap- gn.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 0x qpw-a(r-7 m 2qn3:u pu)n gn2cnnogmode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ful 5vjvyfb)d+ul2 6fl) il 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 rak9 mvg,s :m49p,9gv tl qhjwj1nge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and fin4m,:m ,qk9 t v9 1lpsjwgv9gjhds 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 traikm. 7wf3 ja4+hog7rmbn is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other trai+.rgf7 hb3a ko 7m4jmwn approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 H/*3wra+dq c,sae*s ycr,y5n8ku f,q dz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constantkrqdqsnr5a a,,+8w3*s/y c ef*, ydcu velocity)?    m/s

  At a race track, you can estimate the-xl)urf1 (9hdcxi vp1 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 drops by a full octave (frequency halved) as it goes by on the d-rh u) v1xfp(cil 9x1straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a b2 m 0ps*u*h b bapvg:s+sq/.ujeat frequency of 11 Hz. The shortejm/gph :q+2pvs * sa*usbu.0 br one is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppoovv 2+7kai-i 6/dj rc h2uit.msite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and .2jkrvca2ih6 -oi t+7v md ui/(c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally arr *-y8 +hgpdobout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directrp yr+g -hd8*oed 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 morhi7b4 aclv10mg nqbiw( x)37 th at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.3vaw) bi( mihx7b1g07 ql4crn35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses qdre y)*;w)f cas 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 d *c)yrf;q)we the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpingzq z5 m,f6y4rsw a)h6e 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 thhz ,m46g)y 65wz qrafsat only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the 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 vdc6g )xs-2oep/hj,e l w(a.z listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roz,.v)h 6la- w2e cgoej/s(xdpom.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singingllsv 4j-bg g0c lu.. nd :3gi)ews2xv7 rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a . sc-4w:0ve usil3gv 7jlb 2xg.)lgdnlittle practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for tm5bja; f/)qa/fkwj)z a1 i;v phe human ear at a frequency of abav)q ;z5jib f/ aw)ja1m;/pfkout 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 at Mach 2.0. An observer on the ground hears the sonesr,j;. 6iz4g+fk iuf ic boom 1.5 min after the plane passes sr4i,zfu .g j;e6+fki directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1mylo+4 5(l3v hotf1 dv5 $^{\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