What is the evidence that sound travels as a wave?:ku+5vq57zd wcn ud 6e+;rukc

What is the evidence that sound is a form of e(oako:e n uiy;)wl:w/ nergy?

Children sometimes play with a homemade “telephone” by attaching a strwqt1zk.9 foe al 2wu5*j0vs3sing 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). Explawq2 uoje9kal5 3 t.s*0vw1fszin clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do c*j8 riu x6n7 (xqohz.you expect the frequency or wavelength to change?x*67 ioqjhxuc.zn r8 (

What evidence can you give that the speed of sound in air does not depend s:+ /:)ffpqxm90wpkmmq qdw 72pmu.heignificantlyw m0me:2 h m9:f xu/pqqpf)+kpw .dmq7 on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?wi - c5boumq(mxd / a/.ef: /m.pyra7i crje98

How will the air temperature in a room affect th8dms048f ml0, vhyphce pitch of organ pipes?

Explain how a tube might be used as a filter to reduce thretn,;za6sv(jj 0j *g,c qk7s 4xazy 2e amplitude of sounds in various frequency ranges.sz n ,,74 6j yek ja(vcg2qxt0rjzs*;a (An example is a car muffler.)

Why are the frets on kd 9:p,uybsgphvb1 .8 a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge? vd,8bs.h1pgp y:bk u9

A noisy truck approachlx60.6(t jvqu tcwcx f9 o-ryjln2-)ves you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffr.clf) -cwlrytt0jx nvjx-u6v o29(6q action.]

Standing waves can be said to be due to “interference in space,” whe. /gi v: d*p8njl v4ayben9dk*reas beats can be said to be due to “ k/*id lb:4p*9ayjvg endv. n8interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,b 9r wzqnhq l8j9oh4(2 would the points D and C (ww qr q9h(nh9z4j bo2l8here destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of prot7j6qqe 0f b0rteui2d, ecting 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 it to the headphones in addition toqe tr b0i0d,ueqf6 2j7 the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fj 2 kycr15q; jkvoxd.)ig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 1 dxkq;vk)y5r 2j1c oj.2–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if hb9f6glf qd80 the source and observer move in the same direction, with the f9lbfq d8h0g6same velocity? Explain.

If a wind is blowing, uf8 s1nj)p a4dhj-x/uwill this alter the frequency of the sound heard by a person at res 14jps/a hjfx8u-udn)t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a childkoumag8e (f 1e. ;kb(z in motion on a swing. A monitor is blowing a whistle in front of the1 ( e.k8 f(aubgm;ekoz 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 for the echo of 5nc;46qxuy llher shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of th64l q ;nc5ulxye lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hty4abdm- - h8ais ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in- b8-h4dataym seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelenbfrvo xf.9i4;34hbnh (q qzid+ * b,idgths 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 boatk d)vxs8(f wh0 is drifting just above a school of tuna on a foggy day. Withou 8dx(kh0)vsf wt warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes ;2pwy 2a kjdog w47nro9 8fss(when striking the water below is heard 3.5 s later. How (sp g kwyd2so9w7fjr28 4 na;ohigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone yo , l6a+oo7bxstrike the concrete pavement. A moment later two sounds are he bo6xo7+al ,yoard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made overbmpvgli 2jq7u2-2z7( s z ztq* one mile of distance by the “5-second rule” for estimating the distance from a lightning -b*7(ul t q7jzs2g 2pqzvzim 2strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s73wq-lw1mxmh/qyzu2qk x0 vvl 1*,c lound 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 intensin +lorc;w )-yrty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simxhwdm)9 )jvu gvw0;a/ultaneously at a certain place, what will be the sound level if only oneu/wj))h 90gxmv w ;dav is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a 4qdt gs o87c1jcertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the cdo874 j1sqt gcaptain 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 dB, wherealgs0 ;0cb dso-s for a CD playegc;odb s -0l0sr it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking.ddxpf*z,t9,a tj),k9jjglb w(3 t tj in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on th.9t(wkaf x,t)jl9 bg *tp, j,zjjt d3de 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 strikv4 r d,vypm6r;es an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated 19rb0rfg 9cqshh t(0c at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poisrb1qht gf(h90 0cc9rnt 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 met ,ryf )gqmr3z6er registered 130 dB when placed 2.8 m in front of a loudspeaker on the sta) 3 gzyrrqf,6mge.
(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 difference i 2p l+gai6/hcns m-in9n sound level of 2.0 dB. What is the ratio of the amplitudes of/pml9 g2n-ai6csn hi+ two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensiba*9 ;r80sk eaf:/p g kv,yghuty ugk h: k 9a*rge;ap,bvsy0/8fincrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amp5hnn l/t*88(mn-if u hs 0jabulitudes, but one has twice the frequency of the other. What is the ratio of their intensities? 85f a hmbiuj n-(8nu /slnht*0  

  What would be the sound level (in9uax ,ubgm w47zgi*20 yuoz3g dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules u9go307i2ym,z 4*uxzg ubawgof 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levt tu;2q:vo p:vel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) 2p;: t qvv:tuo   dB

What are the lowest and highest f5iaq vg0 gfthsh u2f7/+ia,k6requencies that an ear can detect when the sound level is 30 dB? (See Fg7ifi5g hqs, haut6va+20/ fk ig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. i4np; td yz(j8ptljme qe u)wk4-1fbv- -m64p What is the ratio of highestqtty84w4;i-z6( -vbu4dj 1 lm- p) nppeejkmf 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 bpwb+,eme7w3 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be p 3pb7+meb, wwelaced?    N

  An organ pipe is 112 cm long. What are the fundamental and first threeg3 /ck mr35hjz audible overton3c z/kg5j hmr3es 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 would you expect from blowing across the top of * weyz( 5inug9an empty soda bottle that is 1egwny5u * 9i(z8 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a-:cc (a5qcar w pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 2c(q5wra:c c a-0 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. Whaadcrbg)*39btun g7:jd,n7gd z j4ym0h3b r2ut will be its fundamental frequency if it is fing) gtu3:dn grbydgj a2j7,r hc3dbub*mz40n97ered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuneuokt)5k8xn k.d to play E above middle C (3ktu nk8ko.x 5)30 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 middli9a k bu 6*5cj;owgl4rf)u3nke C (262 Hz) when the tem i ofn4g)9;cujulr6ak* 35b wkperature 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 ate 2atr3.+xy kzihx3cph;7:vt5xu m6c 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 ;5j+.lia ;fwlfqtt x 5+icv-rExample 12–10 should the hole be that must be uncovitfil+a5-wxclq;tfvr + 5 j;. ered 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:mcsadc5xdgu(i 3 naf1df:2a ,:d-mb at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this 3 5c :u(d:iab1adg fm,n:2add scmx-f 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 resonates a 1-m1 6nt5;z tfpdcscct two successive harmonics of frequencies 275 Hz an dptcsc-5z; ct11 6fmnd 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 unxz)+vyi- p hy*3b;b2b ekc.7 f1lcd $^{\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 audible rzd u8(e4b ,)jctgka dt rd5-r(ange for a 2.14-m-long organ pirzct(u )5rda8g-b,4td kjde( pe at 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 t4a.;ztf b*rsl o the outside and is closed at the other end by the eardrum. Estimate the frequencies (ilzs.a ;4rb*t fn 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 evn6onbt t/ ;7acery 2.0 s when trying to adjust two strings, one of which is soundingbc nt7o; n/t6a 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and)ys7z p 8:)yifsiat4d $C^＃$ (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 g76g.(gm ; rxxnl:ksk v :7urn:w9cmokHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, mk77r.r;swxx c9n( vggkgu6nl ::o m: but a shrill whine of frequency 5000 Hz occurs when 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 tuni sj 6h)7- bsoy, gjsg1q(:ypckng fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vsy(k71csb p, j-yq)j hg:s g6oibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same i7 p9d 1a mb jokt8wac(7t,s;tfrequency, 294 Hz. The tension in one string is then decreased bwt7(t1kjp9 bmsc a oid;78, aty 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard irg a)-,r;:vuw0s dftvf two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at )wd ft; -vr0a ug,sv:r25.0 $^{\circ} $ C?    beats/sec

  You have three tuningzj3x bfr2ql:) forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded )lqfz b2xr3:jtogether, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C 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 mijc;* ( 5fyu:rugxlm4b* g.is7bme /3.00 m from one speaker and 3.50 m from the oth5iim/fbm g: uxm (*le b gjr*.su;y4c7er.
(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 vu0ixgu6 kww*8g )9 mjaibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of)ku 6w9*g8 xa0iwmjgu 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.x 9hw4 nkr8:uzbdt75 2 xopab+76 m in air. How many beats per seconbor+7 5d z xhtkpu29a4 xbn:w8d will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eos ylz6j q1zl4m 4;2 jgs.16j mm2ferlngine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 ;s6s.jegmy64 l 2 mz2l 41fjqrzmloj 1m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stillfe2n jd 0/8fh8gr+0 fmgo+hbq11szkk . What frequency do you detect if a fire engine whose siren emits at 1550 Hz movesz+n 0gqkgo/8d1mj1 e+8hf rk2f 0s fbh at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency4rxq ;fg gjxrc, yfjb*d- (75a if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly thyjfcg;7f(x*d j5 -r,b ag4 rxqe 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 t2be nlk)xc /vtcg7 a0,he 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 tcb0/7ecglan2xvt ) k,he horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rsn:b.l .+p ptu+ m)ev6r s/iqweceives them returned from an object ur p)p/q6wl :m+i nbe.+ stvs.moving directly away from it at 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 f4ovt60, wbfq t :xhz4blies, the bat emits an ultrasonic sound wave o0,t4bq bvz: 6htfxw 4with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a trakv 7(:9 qemyxbo-e.uba was played on a moving flat train car at a frequency 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 eqre vm-9 ax7(kbo:y.car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoul;s0orqdv5ww./jw 3e 8e uq/pnd 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 largs w3w/5l0e ./ue odp;r qq8jvwe leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrarm) .:n45e5e x s;xsn tnd;dapdq *-y yy*htd8sonic 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 Hz. When the wind velocity(*q l1yzxaw(j is 12 m/s from the north, what frequency will observers hear who are located, at rest, jy1x(a( z* qwl
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movi q4kpgzf;dc7 /ng on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What isya/ hb8r, 3zvma.y0xq the angle the shock wave makes vxy/aq8 a30rmbz. , yhwith 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 speed of soup5bm/ 2xm nhwy1yh(mkg;d1,l nd is only abpxh1h,2 dwm;(51bky lmm /ygnout 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.q+zir-d+jn9 ql2tac9 g vt+6 x Determine the shock wave angle it 2 zat+jq +cd v9g6n qi9t+rl-xproduces
(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 oa -r ;(:ptj:h7ywge s$/theta$ 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 ne-/d.2f+yoxvpv gq3 epi 5f)the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horix -ed2vn+ )5fo3gf eqivyp /.pzontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device :6s2 ioo 4tanz4cs ix3that sends 20,000-Hz sound pulses downward from the bottom of the boat, and4i:no s624oa xs3tczi then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in n 2n;kex, yu9ithe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a diw wf4b.6jaau80a xy) usplay called a sewer pipe symphony. It consists of many pa)ja y x w6.w8f4ua0bulastic 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 fd1l 1u)pc ikf)rom a person makes a sound close to the threshold of human hearing (0 dB). What wii1ud f1kclp) )ll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB :d811 5xq( tkp2zhm vde,mbvpsound are heard simultaneously? :vbpz(8e hm1 vt,1mdd5qxpk2    dB

  The sound level 12.0 m from a loudspead(:sd2jp/)3s )fa44nunp m5qxnqd xn ker, placed in the open, is 105 dB. What is the acoustic power output sqax(spd 5 /md3p4jq : 4 fnnx2))nnud(W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 Wt;of-4 b/y hm/ l gohgd3i8z(s output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whs3dfb mogz/l;-y io8t h/h4g(at is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear7:z lpr( ly;fe protective 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 2.0 cm. What would be the power intercep(; ry:ezll7 fpted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gtsp lf-kwolvf9x8- ;*ain, $\beta$ 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 .ujfi 4m-/ygta 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 betwej 7 kfx-4(tex(9ufm 3;wktlfken fixed points with a fundamental frequeelf;kx 7 (t(kuw-jmfx 3f9t 4kncy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration abovegz vb-uthoj6 w0nw) l5gi)*/p 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*ot j)ngz5w/hu)p6gb- iw vl0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube 3 cjez(i,l/ou that is open at one end and also 75 cm long. How much tension shouz3/o (ej cu,lild be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was :xm5, 2*r:vmmp ,apba qjqr;q observed 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. Theghfo j/o: 5+it sound itjf +5 ogoh:/is loudest at 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 whisn(sv9be*3 ej a*a8gm unp+v f8i+9buh tles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train*8 9i(+nm9eejv a3bg unha *bfsv+up8 approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whis*s9fn 8qpfho/ tle as it approaches you is 538 Hz. After it passes yonff/s p9q*h 8ou, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can esti+topd bg1xhp: **hcs 7mate the speed of cars just by listening to the difference in pitch o*xpb* s:7ptdhhogc 1+f 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 straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produc.kz7 xnv.j6+ vmtzyv)e a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the otherzt v7j v+n6k vymz..x)?    m

Two loudspeakers are at opposite ends of a railroad car yov8sgumal9* h6 st) ie6dl(9as 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 of9d u)t(9 gi6hl*s8m6eo vya ls 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 lnuk2(e ,c,w dflow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel wen,k c d(wl,2uith 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 flyimvmw 3(f:zjh *jj4z3x*n2mt3quaglra l1.)n ng toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What a:31j2nrumz3g hqf j4 3*xjvnlla t(z mw*m.)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 as it approaches a mothgwpf iw 1h-/c4. 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 thegic1 h/wpfw 4- echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sezq 9.iz8 9;j9a oh/sxhsia.pp nd signals from one Alpine village to another. Since lower frequency sounds./ p9j8;9 h.oaiias hx9pzqzs are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the 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 bek7o sfe+/zy7 r compromised by the presence of standing waves, which can cause acoustic “dead spots” at t7f rzok+ 7s/yehe 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 “singt4n, m7n k60jvysow, 4vrpo i4ing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is str04pyr vjio nmsnv,7w4 tk46 o,oked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearvj4dbf 9k6.ii4 tfc ,ping for the human ear at a frequency of about 1000 Hz pdfi,ivc .b469 f4jtk 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 observ-mjbod 5zs,gum t. 4:ger on the ground hears the sonic boom 1.5 min after tjd 5,bgsm: tmu4og z.-he plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbescqp ;8 mu0)8eo5gif d;gb j7oat 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