What is the evidence ths3gi*m syq/s o;4xej 6at sound travels as a wave?

What is the evidence t2fsbrg2g t3*ihat sound is a form of energy?

Children sometimes play with a homemade “telephone” bypjvvob / dx .03qpm7-00 /o2mbzlipt b 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 to the other.0l0xtb2v/o/0pzoqp7 b. m jib-v mp3d

When a sound wave passes from air into water, do wedv ) nyw3t-0you expect the frequency or wavelength to change? 3v -d0wtenwy)

What evidence can you give that the speed of sac// kxpv sd083bvk3gound in air does not depend significantly on frequ/ kv3xc8g /dab0p v3ksency?

The voice of a person who has inhaled helium sounds ver,d*mi;hja1lkz -y pm7mn.x;abl c 13qy high-pitched. Why?

How will the air temperature in a room affect the pitch of o.n z 9.dtv7smuw+4 xxkrgan pipes?

Explain how a tube might be used as a filtqpa oft;rpnfladp*rf u7s7h,9+5-* qer to reduce the amplitude of sounds in various frequencyaq-5 tn hfp*,; ro7lf dp*+u9qsfr7pa ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. r0k .u pj1e0z;s sz.ag12–30) spaced closer together as you move up the fing0r kagzes;sj0u1..zp erboard toward the bridge?

A noisy truck approaches you6t v4 e:+clakj 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. cvek 4t:a+j l6[Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beath c5i+uzy,ie;s can be said to be due to “interference iuy;e,hi5+ i zcn time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lo5eb 9-:yfs x,lws vd3ywered, would the points D and C (where destrucl 9s, xyd3wsvf 5:e-ybtive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas 2ma)kjx 0;xaw v::rgkwith 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 noisw2 :x;k vj akrg:a0x)me, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each y 2nj.j) 1b+iqvotvy. wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apar .oyv)qi 1jbntjvy.2+t? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in 1 0s ir7uvtq(ei-wmo)the same direction, with the sam-m()iov iuwr1qes70 te velocity? Explain.

If a wind is blowing, will this alter the frequency of tjlr 0,; k3nejlhe sound heard by a person at rest with respect to the source? Is the wavelength or velo l,3;ejl 0nkjrcity changed?

Figure 12–32 shows vario2 cnf7+xgc+3f 6 kj) :ajrouqjus positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain yourc6 kfjn3cj2+rgqf aj7+ )uo:x reasoning.

  A hiker determines the length of a lake by listening for tholkkf p t72v;-1eg2 vje echo of her shout reflected by a cliff at the far end of the lak7k- e2vtv jl2; pfog1ke. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the i*i- mreed ,0secho 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 (Table 12–1) and does not varyres0i *,ie dm- significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavele fvw4,q gf 3irgp h1(mrg-1-jrngths 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 tuni j9 8uy.5 xizejpyl9)a on a foggy day. Wit8e 9ji.5u xpi9y)y ljzhout 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 makeekxn.*8kr uk1 z(r2ves when striking the water below is heard 3.5 s later. How high is the clev.unr(2kr18 zkx*keiff?    m

  A person, with his ear to the ground, sees a huge stoned0b1,qzlsbf , strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air anb,s0ldfb, 1z qd 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 maded8vmj3m jmo ;7 over one mile of distance by the “5-second rule” for estimating the distance from a lightning jm38 mjd;v7mo 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 l5h38x 8qhduzkrjp(v+grb 6y9evel 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 intensid7t2c ;aujguc0uk vf ij;76 t+ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound 5vw kl2 x8ol./rm 7r4i sqm(uglevel of 95 dB when fired simultaneously at a certain plwgsrm8 lkmv5(o.q7 iu/42rlx ace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from kwulc4. 0 gverzc0 +0zan airplane with four equally noisy jet engines is experiencing a sound lev004vc .wgurz ez+c0klel 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 l sfaf (mgyje .4sklul/9dtxe(y38 9 :said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background no: lsll d9/xua.tkeyff(8 jy(g4 9m3esise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power derlzf 27(yx0poxp*5 output of sound from a person speaking in normal conversation. Use Table 12–2. Assume thelyrx ( p70x25d*f poze 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 *jn+ py kbd(dh-x.u5xan 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 atzlh/c d)4o lw1 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level ino4)wzdl/lh c1 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 2sd+ 7jzlz u*+u.8 m in front of a loudspeakl +uszjzd+ 7*uer 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 detec8pw wr 5ss7p:vt a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: wps8wr: 5vp7s See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa*i 4ae9vooc cy)yk b4(ctor will the intensity increase? Increase by a factor o*)ya4i(oc eyckbo49 vf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amcr(8jbx- d4 hyplitudes, but one has twice the frequency of the other. What is the ratio of their(xrd -yc4 j8bh intensities?   

  What would be the sound level (in dB) of a sound wave in air thathezx;nm *c+2r corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 3002 +mr;*hxcnez Hz?    dB

  A 6000-Hz tone must have what sound level to see s7q r*vf( i6ex*nx9loi b8 4cvbq1qy;m as loud as a 100-Hz tone that has1 bx ef;6qq* bi9xvo rslciq*y(78nv4 a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear vcn,4:zd i9ke x(6 og3;v bngpwu-p.l can detect when the sound lvcd;o:pb u.6( 4n zwpig3 e lvn9xk,g-evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wh +ue1 ovfbrc w0ig9x;6at is the ratio of w1u09oei 6 r+gcfbx;vhighest 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 fiqc )w4zhp fn;e:44tg requency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tg;:h)w zfp tn4eq ic44ension must the string be placed?    N

  An organ pipe is 112 cm long. What atj 3nca1:zp1la)ogw qg e87o 9re the fundamental and first three audible overtones if the 9a1)c8g3:wqo 7 1 latgo zjnpepipe 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 e mbm 4g3h:06 as:uxjy0pdqhm+xpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumedm:m+h 4:qjm y0gx0dp63hbusa 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 pipez,7g q p55pd:sl zrifh/,4pdk organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what woulki5 q zlp4 /dgr,:sfppd5z7,hd 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 / jc5 mu0cbe rt;6zvc0harmonic. What will be its fundamental frequencye 50 cmvtr;czbu6/j0c if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p7 1,.l9vc, otepol zoi+bpt/rlay E above middle C (330 Hz).tbril7p 1o o,,c /ptz ve.+9lo
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an o;rutlh 5xt6m 0pen organ pipe that emits middle C (262 Hz) when the temperature is 21 ;x ht0mtu6rl 5$^{\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 q1ja 5fowij54 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 should the hk1d: kh1bdc3:r fqwm8 s u1w2iole be that must be uncovered tqh dc1dsf3wkb1:: uri2m 8w1ko 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,fh+zgw /x/r;jxf0 9xv; ea)vv and 616 Hz, but not at any other frequencies in between. h);/0erav vxf/xg+zj 9w vxf;(a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 3n1i j1q bidu0c1 r(gjm long is open at both ends. It resonates at two successive harmonicsjrcju(g30ib1 11q dni of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 :r ken)os7az1l7: -aw uwgz;h$^{\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 ar6iisv;9i + r*en3k lcle present within the audible range for a 2.14-m-long organ pipe at*r3l e6 ;9sviilkci+n 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is ap luujphd8rwz2 jbhy)0 t (gfm3r8dy)1b 3t3+pproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate tytr)31p0zpbw d(l)hm3jg 8+urh3 2jyb8tdfu he 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 t3u eb8r*r7pzjwo strings, one of which is sounding 440 Hz. How far offe*rjpr783 ubz in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz0.h a8c kc m +j-bpfz,9bjmi2w b*7syn) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand qme2ch rn7q-f 2;f9um X) operates at an unknown frequency.mecqhu7;q 92- f 2mnrf 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 operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and ,*r/ tzd.j-0pu p j/al e fspxg*d/8ho9 beats/s when sounde h*ol as ,ft/xdp rgz08/ju*/-dpp.jed 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 frequ u4j(l-8 up3p5,v mmzbi8drbr ency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when rrlm84,dbupup5 -j8 zbv3m i( the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard ih+)1ak mda bf 7vxz8 ,bol:ph v-.de)hf two identical flutes each try to play middle C (262 Hz), bu, b+1-hx)8hp avdl ):.ahb k7vzfedmot one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and tpp;akz+-,0fgt-8u pf dm/h n 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/- 8ft k-+ppap f0h ;ztd,numg 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;ki 4s+f2 aapo person stands 3.00 m from one speaker and 3.50 m from the other. oiaf kps;a+4 2
(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 t upt:bb40. hf7 m)(e1q av/3 gzxxaicvo be vibrating 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 the0.a/z1)am 7e(v3phbcb fxvtg q :4ixu frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Hoamxqivf0*d+ yva9-y vznkb03 ; zajg;kx5;c 1w many beats per second will be heard? (90 bz1 a-kvyv;5iqv0 mdckan;*ax3x zf yg;j+ Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain kp 6+ aqh,s 8yox+u.jffire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s y u o86+.kx+shjq,apf
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you dqi.n s5*5hbs0 . bv2x 9kenwkeetect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s 2vh x5qbkni new5s9k.*eb0.s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a +o.pu9to ;uvp0l e:t q2000-Hz source is moving toward you at 15 m/s versus yo0upot:;+ vtl9o.u qe pu moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same singleyhopd ))p)t6i3z1q o+ 7rt yhm frequency horn. When one is at rest and the other is moving toward the first at 15 m/s t )z)q +iptpoyhhmo 316 )y7drthe driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anboqy 71 n 9pddxk.ks8w)3h.zom/wpr9 d receives them retu91kpq o73whm py)bxdn r s.dzk98. /worned from an object 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 flies,a:gbplf h 3o8i;1g 2fb the bat emits an ultrasonic sound wavp hl f83o:bf2a1 ;gibge with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopwk2vcsi0j90,ili emjwi c9qp/,; i1 vpler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a sei2li/ 1i,iq9wjmv 0c 90c epk;s,w ivjcond identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound w30di3 y 2( ifzy pmvbi +l4awtj3z:;xwaves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissuftp+ li3bz32:ziiw4wx vy3mdja 0; (ye 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 ultqrabjz1:1 a0brasonic 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 ismf1i m k;whm19,bpali/ z 4 ra::cvq3o 12 m/s from the noz/;b vq1lk9ai3m mcr4fop iaw:1,hm:rth, what frequency will observers 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 (bmw jf ,ywb5p t.-uo9at 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 d bu9kzfs), 4-;m/dkjr/;h+ xs mwcnf2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directionz j,bs9;+f/ rwdd)m nhsk4-xkf/u mc; 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 3g phd1 kgl9m.speed of sound is 1 3pk.9hgd lgmonly about 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. De/ e(.:xsl1alhmet g 4: akwi 6rqzq0f8termine the shock wave angle it produ(l1a hm:t.zwg4:qfexqrl60as e 8ik/ces
(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 i 9hx/ws 0ghg:.epod/ teu:) f$/theta$ 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 bw-s*:6 zr lxpground flying faster than the speed of sound.*-wp zsr:x bl6 By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar descna/m 4*s2ac(vpokiva0n,6vice that sends 20,000-Hz sound pulses downward from the/a0mcann 42k vp,6o(iss acv* bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible 2+ps li)dguy( range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disxcc0k/ n ,;c,p .svlvps(zwm ,play called a sewer pipe symphony. It consists of many plastic pipes of va,.k n pczv/s;xcmv(s p,,0w lcrious 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 close to the thrend.wrmp7 ta0 fhz(zll v36/y3shold of human hearing (0 dB). What wi ld.zr3 /(mf3n7lytph0 6wvzall be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when7-fd6xvjdw w04.cah-bm 4-vya fw o: c an 82-dB sound and an 87-dB sound are heard simultaneousl mww0.j7-f- 6vb acoyav- c4xdhwf 4d:y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 d;vbv;pxh f+v) B. What is the acof+pvv)h;b vx ;ustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drorp4/l n 19pqa9znkzv;ps by 10 dB atr/z;pa 4q9npvl9 1kzn 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typi/36eefw o5k dfcally wear 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 wou6f5oe 3wkdef/ ld 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,7xu0ehubq99f*3h vw cj r-100 gpyfl k 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./qmp u +cq (x((mr iun-7ne-mwimv(o 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 cm long betwee1bfb q 4w2+n ,8zmnzz+xyus(h n fixed points with a fundamental frequency of 440 Hz and a maqfuzbm + 8s,yz+x w1nh2bz4(nss per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filld9xa6lfcym5s sz -i)5(5m10gqdz xw ued 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 fo0xg5wmqi 6z 9lcymz dx5 (u-51f)assdrk when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 6o-* ltaot6fv s(h5n( mou ga *i/kfd,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 fo l-6*gv nt 5 d/om6s(ta(*k,aihfouthird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full looq:3 las;wjulx 91my1 ;apdi-xp ($\frac{1}{2}\lambda$) 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 50irk kwb5b(o:noc*.;nj2yy24nj; ze h0–1000-Hz range 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 finds that the sound level is minimal at a point 0.34 m farther from one source than the othry5ojnb;*cj b2kn;z4( k.n 2e:y hiwoer. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on tuof1- oes 9q5the stationary train hears a 3.0-Hz beat frequency when the other train approach5 fos1 qeto-u9es. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After ie:r4 q; yjchh2h9)reot passes you, its frequency is measured as :hjhey 9cho24r);erq486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, youg uc++pchps x- p6wg,lcc;5y(qh. v a6 can estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching a +y5qxs c-.6uc(wach hplp;g +6v pgc,nd 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, u)2tf5ak )xhzsounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. )ah5 x)z 2ufktHow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a st f;yxv;v.d8luklw68z ationary observer at 10 m/s as shown in Fig. 12–37. If the speakers8zl;;k ylw6fu8x vv.d 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 (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorts-36o)e2n wssbhla m 7mqj7 v/a 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 mj27 6 w37eslh v-ssna b/o)qmtravel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towd a2qdt8ymnkr j/60(kard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave tdq amk(k2nd j/8yr60detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses pf qrz )7*lg(:c)5mo9uq g *bi+9 xhzubu t(btas it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 u(r9oh x )9zlq:g5)b+gcpzui qbu*7b (*fmttms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villad1owx t)ed u*9ge 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 sh1 )x *9owudedtarp (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 3k1t 5 y d,zxkd1inyv7vpj(;rcan be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodesy5vznpyjxv1kt d,;7k(r 31 id . 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, callynb-pm71z wj 27ws asv ,r6bs/ed “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the o vsp6 j w/21zsaywm -bbn,s77rther hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear nrqu(v)(b9 ff at a frequency of abou)ff rb 9q((vnut 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 son9ew*9s xy z75hnml b5tic boom 1.5 min after the plane 5mz5s he9nl9xb7 yt w*passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat jb3y 5na)s)eqis 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