What is the evidence that sound trak 8t l6maul5od b(cg2*vels as a wave?

What is the evidence that sound is a form of energy?08wbuzj zdt(o9wdt-kp65tsw s g,c2-

Children sometimes play with a homemade “telephone” by attaching a string tc0xu 2b-hyt09gv e+ii o the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be he euyi9c t0h v+bx2gi0-ard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into waterb hw.o7drqb6t .e8)ql, do you expect the frequency or wavelen bwd.e7hl6boq )t8q.rgth to change?

What evidence can you give that the speedh/6eq ym 3r*l ac2k7wj of sound in air does not depend significantly on frequen3lw rahk yje672/m c*qcy?

The voice of a person who has inhaled h1gj /5pgaks5- n(7 aco0spt6tw 9cf7(a gdwmyelium sounds very high-pitched. Why?

How will the air tempetip*v opnj o.5np06-n,og fl*rature in a room affect the pitch of organ pipes?

Explain how a tube might be u(zhpz1qofut2yp ; o;0urvv76sed as a filter to reduce the amplitude of sounds in various frequenzq up6p t 0;ofv;(7z2vy1rhou cy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clos (;yxjywlq/*ser together as you move up the fingerbx;ly/(yqsj w* oard toward the bridge?

A noisy truck approaches you from behind a building. Initia*r(o(dn j/edrozx7n;lly 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.jo/nrxzodrn e(d ;7(* [Hint: See Section 11–15 on diffraction.]

Standing waves can be saidsflzl,k0d4i , to be due to “interference in space,” whereas beats can be said ,kzld l04isf,to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of thhog o8 4qx7yjnm *nsu(263csoe speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer 8o4hy627 xn* nqs(sj gu 3oomctogether?

Traditional methods of protecting the hearing of p05(xs ugw4yv j .vht4qdb dp32y ka)t9eople 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 itvb 5dyv 4)d9ktsj wp.0ua txg yh3q(24 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 wave can be thought of as a sanync*qj4o /3 uperposit3j *qncny 4ao/ion 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 apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directiov y0+yw zqku)g(jk7 a:n, witj 7y:yg k(a)zkv+0 uwqh the same velocity? Explain.

If a wind is blowing, will this alter te fub7d*ri 3,khe frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocitr3*dk ,b 7iuefy changed?

Figure 12–32 shows various positions of a child in motion on ir+tf(vi7o/w i.xf w :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 xvitffw: /iri7(w +.osound of the whistle? Explain your reasoning.

  A hiker determines the length of a lae pk)0b7j*z *fk b2*adlkomf. ke by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears kjk)ffkbad7*20o.pm*z e l *bthe echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side ofg pm: del gj(tcc 28mj;*77gns his 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 seawater is 1560 m/s (Table mecgcp2ts ;njlgg*dj :(7m 7 812–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20qvp bc98w 3l;6uiv(xj $^{\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 jzw:jdu k3d4qdkq/p0. ust above a school of tuna on a foggy day. Wi wp.dqk 4d3u z/d:kj0qthout 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 tw snt d-,m*g/lhe top of a cliff. The splash it makes when striking the wateln g, t-w*/mdsr below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huged w2 emcd; i,mxse-k49v4pnq, stone strike the concrete pavement. Am 2ndx,, d-peci4 9m4swqe;vk moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent err:c f;./u n0 rqhg3ryidor made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatu/0curqn:3 g.rfy;dih re is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound aob-jp24xqft4:5svj* sf4bue yk8i8t t 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 intl*54u3rso bb:ik qh :tensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at wy)1aq 3nksc 4o*uq3t a certain place, what will be the sound level if only one is exploded? [Hint: Add intenno4ywtas q *ku qc)313sities, not dB’s.]    dB

  A person standing a certain distance c3c4pmpa k0 8r(d5n ukfrom an airplane with four equally noisy jet engines is exck8c0(5pap rn4md3 ukperiencing a sound level 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 sa;en lakspr5b:9uj( 8kid 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 noise for each device? 5 a;n9rjubekp5k(s 8 l:8 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output oswo: *)8j g4w0r fdeljf sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreado*) wr8:fd0 el 4swgjjs 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 arg;nqfq8o skdli+vm g s8:shz...8tb / ea 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 ranpr: n6st* j)lauec:8ted 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 point 3.5 m frolc rp:a ts)u8 nj:n6*em 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 registpjr1e z8: hi7b)zk1dbde,p ,4t *p jxgered 130 dB when placed 2.8 m in front of a loudspeaker on ,4 g zrz p:j) hki8edpbpd*b,71jext1the 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 detect a difference in souyn4:)w 8kroie nd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levo4 e)y:niw8rk els 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 u 2c3j,a)lgcl3 lbgj+intensity increase? Inc3)jcgclj2 lb gla3u+ ,rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitu9hlfg*7u 0/ (u baffda5 ppqt,des, but one has twice the frequency of the other. What is the ratio of their in9lpdfubg h a0u/7 (fatq*5fp ,tensities?   

  What would be the sound level (in dB) of a sound wave d9 zcuw( hx53ke y0o,oyo,4(r6gbmw ain air that corresponds to a displacement amplitude of vibzuo4g(b6(k ,a9wo ey ,yo0wdh c5mr3xrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to5xi(cdq0 wm /b seem as loud as a 100-Hz tone that has ( qcdm/wb ix05a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detittu70ej)-z fc* u 6iuect when the sound level is 30 dB? (See Fig7z0et fjt 6i)uc- i*uu. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. W*m 6xpmx ;ma/rs.wfo; :4wv /p9 azctohat is the ratio of highest to lowest intensity at pc*9o6sw v zw xx: m /m;.rafp4ato;m/
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamb2(9im+m j xg+mkov7b :kpwk *ental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must+:b9wo2k(j+mg i* pb vxmmk 7k the string be placed?    N

  An organ pipe is 112 cm long. What are the funda*q; q) w*zkp;vxpte :umental and first three audible overtones if thx:uzwkt) v;e*q*;qpp e 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 ffiwc7p0x /e ),vx z3nthe top of an empty soda bottle that is 18 cm deep, if you assumed it was a cl0xp/cf3x,)ei7 w fnv zosed 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 9 ind*hdhk:u1b(d z2p of human hearing (20 Hz to 20 kHz), what would be the range of the n:z *db ( 1kpd29iuhdhlengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a feho17 f zu9kei*arm,-ur(5pe requency of 540 Hz as its third harmonic. What will be its fundamental frequency if it auf5 i1keh ezru,7*om-e p9r(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 play E above middle b5u4hj,5::gn aza,ypgyc(, khr -hmg C (330 H,ykcnr4h ,mzp (ugyjh5 haabg5: g,:-z).
(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 d*ef*yb .gw9+c8 f2z jrhhqc9pipe that emits middle C (262 Hz) whenqgf8c*y h z*bfjwher 2+.9 9dc the temperature 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 1y8 tfb2/atx8rkcnmi8 wn15u20 $^{\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 hole b hmvrn6uqu6 20e that must be unv6uq2ur60 nhmcovered 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 Hzj17ly2w*q6he fa qm /i, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pie*/liq q72 wmhj1a y6fpe. ----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 reso, zg9, wkq29ypyi3xqx ec:nq8 nates at two successive harmonics of frequencies 275 Hz and 9g3p:cqy yqnew zxq82i 9,k,x330 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 mu9a( /uf) otc$^{\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 +0:mbwwhrm v)v.yb h*present within the audible range for a 2.14-m-long organ pipebh)w0+v: wh v.rb*mmy 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 h 4qj e .tlxkp/9 2,ef0vexw6mopen to the outside and is closew.e40xexf l/hjtp m9k q,v26 ed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, onex alowlex9xl 5,8)yx :ecfn1xg1:3w j of which is sounding 440 Hz. How far off in frelajwn 9lo c1g ,e :x83x)ex:x15yx fwlquency is the other string? ±    Hz

  What is the beat frequency i5rzh*a4usw7jux h/ * cf middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anothezu0 (n-av i)ufr (brand X) operates at an unknown frequency. If neither whistle can zaufu ni v-)(0be 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:t do4 p(pop8dlg,vk5k99d pq with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoni9vkd9pdd5 (,gq:k8tlop p4pong.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in oneh-7l0,jwhsg+ot0av xkn6. cpx79xs u string is then decreased by 2.0%. What will be the beat frequency heard when th,wg sl n0c79so+x 6 p-h7xkujxa t.v0he two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be .da xrji5l(, gheard if two identical flutes each try to play middle C (262 Hz), but d5 (rlxai,.gj 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. For wayxk+ )6q2lsk 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 togethe2 wyx6sqk)al+r, 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 pers/ 73gwi a.drm jt0+7fo0yyakp on stands 3.00 m from one speaker and 3.50 m from 7f0y0 a mkigrdwpoj3+ y.a/7 tthe 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 su;g)yr) bo*rb lpposed to 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*gr; r)ol )ybb at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How mank/u2.w qcdld1 m s io:0seu;-uy beats per second will be heard? (Assume T = 20;1su d.2:udu-o wsk /iclqem 0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency +5hjm r ac+.x9ilp9qoof a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect iqr hcp +.o9a9lmxij 5+f you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you dee3;h/bc dok 9c+(rgb,e+szul tect if a fire engine whose siren emits at 1550 Hz h+g+uz;beb/c3rcs9od ,ke (l 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 sb7 9+zzgu mto:ource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are9bz+omuz:tg7 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 singl7mfg36s xudo s+ojejpo1 0;r: e frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T =r1xoej7m+dgo :u3s sp;o60fj 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 knch/i;buk0jaxd 2 8g3Hz and receives them returned from an object moving directly away from it a/ i28gck3;j u adx0hnbt 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/sy0xd/k*(b3 iqvjp-p d As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected ( vi/*bxd 3jk-0ypp dqwave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wo iyxa ;05+m zzqkom1zi3su/;as 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 frequenzm1;/5+i aqzxso o30z;myki u cy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suvw)d 6z/kkr yu5o/6 y +h-yw6)vrfeaippose the device emiu yzyh6k5fived- )+wkw)6y/r/ v6roats 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 frequ7cu*r ;w+jc ,hoxeox+ency $2.25 \times10^{ 6}$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 frr+) i a+yn(.lj;bdcc iequency 570 Hz. When the wind velocity is 12 m/s frir+n(c cj b;al+ dy).iom the north, 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 /0edkg (1wkuk41xfen b qo;+cspeed 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;/z zh vym1n rv)3jyt; is 310 m/s (a) What is the angle the shoc)nz jt3 rmz v;1yyv/h;k wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed w fe6ct,b pp3u(cm i) so.oga8(ak(5 kof sound is only abou e op5ut()cmk6c(f g.3 b8saikpaow, (t 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 thr ,..wvy)oz2cabnd(o*+ gwn re ocean. Determine the shock wave angle it produc+y.d nnowcoza( b2)w rg,rv.*es
(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 o8 j3;w;gai ogz 0rsjzki.j4ya(k * :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 hlt9.zl4i nmvmd4z 0 6f6 w+rokm above the ground flying faster than the speed of sound. By the time you hear the sonic boom, thetni wdlmzf zr6hmv46o0 + l49. 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 device that sends 20,000-Hz sound pulses downwapu b(t(ggxuh6u z0:fv ue 17k,rd from the bottom of the boat, and then detects echo0ukv(u zt, f6ug:(1gpeuxb7hes. 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 man wxutrkqkl0 vb55)7q+y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consi, rvu)/(udyof sts of many plastic pipes of various lengths, which are openofvyr u,u(d)/ 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 t16/m8lb x9ryv od nvn;o the threshold of human hearing (0 dB). Whatdr 96xmv8o;lbn 1yn/v will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are /gt ghhr2vvq y* 5zs9sx(q,k134 zjn;cbp b1sheard simultaqb;zx 9b2s rh 1sspg q/cvn 534jkv gz,1h*(ytneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 6 8 ex(ip4 g6qj-f udjh7b-kprdB. What is bje 8-pqpi 6r7fxk6(hdg-4ju the acoustic 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 outpu0gxpdj2*7q ujpm/-r pt drops by 10 dB at 15 kHz. What is tj0/2rx q- gdm7pu pj*phe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective de,fmn. ;oty7* bk yj9wgr:l8yevices 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 intercepted by an unprotected ear at a distance of 30 m from a jet airplan*8w ; .9kj7m b:o gftynler,yye engine?    W

  In audio and communications systemsf odpx6y87sly0 v9 kco*a nal(j4 ;i2c, 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 tunea57 joybgp *j7 biz2n8d 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 between fixed pp 4 5/9nlecwfzoints with a fundamental frequency of 440 Hz and afw/4c9p le n5z mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a/vx3fke uz r22v 8n8mx vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of thze/rv8n8 xf2xu3kv m 2e tuning fork?   Hz

  A 75-cm-long guitar string of massh rjv.(le7eq+ 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third hahqel( rj.e7v +rmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as om 6 zrqw me/8.ul2ikd;) mt/fwdane09ne 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 auz ai.q h9/2asources. The sound is loudest at points equidistant from the two sourz9/aa qh2aiu .ces. 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 whistles. One train is stationary. The conductor on thw,t ,p:a:d o-dpa*jp me stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of th*:ajmpa,w-p:tdop d ,e moving train?   m/s

  The frequency of a steam train whistle as it approachem 3xzp1aq*.ad5 ,:sja kh-m gefuwq;: s you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity.g: j15 :s3qxue;,f phaz-a*qw ad kmm)?    m/s

  At a race track, you can estimate the speed of cars just by listxcw68awh o 9, )cod,yeening 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 hal, wccx ,ea6ohow9 d8)yved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency .4o+fw zybro* 8x ah2)o* yfmiof 11 Hz. The shorter one iso8b f+wr24* *f mo.)o yxyzahi 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad j ty25enmn+, k ugadhavbre 0- y1 22y,r14hntcar 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 +,au e r n5 yy 0vtj,2kg1-2hr2aet1ndhm4nby 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 aorta is normally about 0.32 m/s what beatp( dlfi,v2d4w frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bloodd,d vpw42(ifl cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the li2f r*1l f) qnrg9 qz.oujj)(bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detectef fqrl)i*29og1)n zj ulj.q (rd by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency souncx/mhl u)6od* d pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far awa)l6d*hmu/ c xoy 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) waszmak*g+)hf a7 once used to send signals from one Alpine village to another. Since lower frequenka7 )hmfag+ *zcy sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or 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 be compromh:v4 3a bcruw*g uh-g+ised 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 longgh ahu:bw4c ur-v*3+g, 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 “singino); cdiz:ov) r0d* gczg rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked wr 0d;g)z: vczo)o* cidith 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 thresh3m ) oi b n/)v)mb96mwa;kueueold of hearing for the human ear at a frequency of aboutbunoe wbak/e; m69)m3)i m)uv 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 hef 1rnbo :6h5 2*qlfrgipamq33 ars the sonic boom 1.5 min after the pl3q6ahl qo32 r*g:i np51fbrm fane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ti * b5ug); wu/hf.ausis 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