What is the evidence that sound trav 88mjkci+ue*9jo 6qidels as a wave?

What is the evidence that sound is a form -b fp+yz umch)(-xs)5 4z upbnof energy?

Children sometimes play with6na, npu( ak ) 2pfw-ztnw.9es a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child spek2pfa- .ae s6z) wun(w,pnt9naks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do r,tmqnql)5:arwokr*3* ,t mh you expect the frequency or wave m3h: trw, lk arm,tnr*o5)*qqlength to change?

What evidence can you give that the speed of sound in air does not depe2y6lsc h), *ph*vr bb:nxj g4ind significantly oxj h:)h pbinbr2**y4svcg l6,n frequency?

The voice of a person who has inhaled helium sounds very high-pitched4z s ksn9eo (yk*tko-6tmpw1+. Why?

How will the air temperature in a room affect the pitch of r02;x3i yl nfqorgan pipes?

Explain how a tube might be used as a fue2t 9b2;nw i+ 2pzvcatbz 1*dilter to reduce the amplitude of sounds in various frequencnb2w auc*zetzd 2vt;pi+ 19b2y ranges. (An example is a car muffler.)

Why are the frets on a guitar (si0ud4y dj3u.Fig. 12–30) spaced closer together as you move up tyi.d4d0u3 s ujhe fingerboard toward the bridge?

A noisy truck approaches you from behinoac :cdi1n71md 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 diffraction.]o:m7 a1c1ndci

Standing waves can be said ,h+ l .2jzdsfiox;gh3 to be due to “interference in space,” whereas beats can be sd+z;hoshg ,fi23x . ljaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the fre,slc7t)zgig;4z c+x 2ar+ht 2fopuq5 quency of the speakers were lowered, would the points D and C (where destructive and constructive ilt th zf+2x r ,gz+co2s)pa ;754cuiqgnterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in/dsc7u z.qm4 s8acj s; areas with very high noise levels have consisted mainly of efforts to block or umas4czs 7.8q dsc/;jreduce 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 to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shaqxv xfvc./q*)tzi-a+8 ril 0own in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencieqvf)tc-z +i*/0rai 8vxqxl a.s, 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 observazqt8.r7 e gahm-w p7;.klla) er move in the same direction, with the same velma.z)7alr wlge-h87q at; k.pocity? Explain.

If a wind is blowing, will this alteqnip6 )h;j+hyr the frequency of the sound heard by a person at rest with respect to the source? Is thehj +6py;)i hqn wavelength or velocity changed?

Figure 12–32 shows vg+ hh/eg -xj 6i(:yrzxarious positions of a child in motion on a swing. A monitor is blowing a-gxjg/yx h z+:reih (6 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 your reasoning.

  A hiker determines the length of a o cs8fc7n+i rp- h:hx8lake by listening for the echo of her shout re7hnsx-c:ihofr +p 8c8 flected by a cliff at the far end of the lake. 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 )4v m7y1xyx c;zvk;bg the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at t)k;g4x7 b yx;czvy1 mvhis point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airqrmz+g+ j(k0e 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 tunac 4/fao9kdhl554qo c h on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 9/5kh cc 5ho4dqalo4f 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 o)yrqdap-p rowpdnvc )38 k)s5*8xd 1if a cliff. The splash it makes when striking the water below is hedp- 8d 1wryr*x5 )3)a c pnv8)qkdpoisard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike themsju psa m9 +)tw8y3 j1neyo63 concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far6w89j3 pns tmyye +uo1)s3m ja away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over oj,ca )3q6fq:i8isf;ojf1fox+9qkhks 0op 0 kne mile of distance by the “5-second rule” for es6;ii afj)ok fqkjcqsf f:h8x, p10s09o+qk3o timating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the m;7qjg9mrvhb0fz v z.km0 9v0 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 soft6b :f2gm/vrund whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firk a kqv fv*4,2i0dkq.eed simultaneously at a certain placeq qve 0f.d*kva4,k k2i, 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 an airplane with four equally noi:7ra(ddqz1cm sy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level w 7cdz(qa mrd1:ould this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rayh1fal /3l1iqbend : :m 3+slytio of 58 dB, whereas for a CD player i3q:ay+ i1f1 e n:/ bymldsl3hlt 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 ouc/2eoq9w,noig, x b f/tput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on ,/iecg9 woxfo2n,/qb 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 wh.oepbe4o 8 5xya a-u4c7l q6ip,c;ojkose 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 at 250 W, while the more modea9 0 ch pe5;rax9u daq2w5shj0st amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poihaxqa0ua 2w;der90ps h5 95jcnt 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 .ulbs3qbi2-q dB when placed 2.8 m in front of a loudspeaker on the st2 -qb.luiqs3 bage.
(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 rfx6at/ hn7 b2u :.afq66xa.uov6i ygdifference in sound level of 2.0 dB. What is the ratio of t.ga2yqxuhf.fxo :66 6/ 7tiuaa rvbn6he amplitudes of 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 th0ovla24f n/ p3xgb 7.,zwt pure intensity incrrugpp0n v42f at/ blwo,z x73.ease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacei f)b7jc:*rc,q8f*otosa0osgu )y+ +fw s z5bment amplitudes, but one has twice the frequency of the other. What is the8 f*+sogf0wab csorubf) q)c,yosiz+5 t7:j* ratio of their intensities?   

  What would be the sound level (in w lf u*l)w; ywy/487g*mw+ltta5ro eidB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 487r*mywtw wl ioeylwg+ u5at* ;)f/lmm at 300 Hz?    dB

  A 6000-Hz tone must have what so+e ew+z gz)d.g2a egk71km4 dhund level to seem as loud as a 100-Hz tone that has a 2+4g1gw+ ge)kz 7d kae e.dhmz50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequgf9vu3 1o 8jgpzc2ms 8encies that an ear can detect when the sound level is 30 dB? (See Fig. 12–8g83sg1m 92 uofpzjcv 6.)

  Your auditory system can accommodate a huge range of (y ir0 iw p4xdy:(zin.sound levels. What is the ratiyyiwdp(: ri xi0z(4 n.o of highest 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 hasgke sbaz 5/w,/(hj0i c +z4ssl a fundamental frequency of 440 Hz. The length of the vi 5//, swzkhi0sagj(z 4sb+lec brating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cmecaxhcym5 g- :7 (icr( long. What are the fundamental and first three audible overt ic(g: c5ma-r(hyecx7 ones 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 fre cm+b l )9w;/u+9ecocuy)comr k h1vh,quency would you expect from blowing across the top of an empty soda bottle that is 18 cm y9clh;cu)v+k/r)uh, ow b+ 1c9c mm eodeep, 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 pipe organ wvg2z7-psb 1/q)xds rcb;m*uo8 :czzp ith open-tube pipes spanning the range of human hearing (20 Hz tozcg1x:prou 8bp* v7z) mq-;bsd /zc2s 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strinzu4:-cgn vm;38r nc xng has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% on4mc n-xugzc8v 3;nr: f its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above midl 86u5 qgomt4.ymvy6d8+ peridle C (330 Hu 4 +6yqrei mdy86tp58l.o gvmz).
(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 ek9 :b cf,yfv-organ pipe that emits middle C (262 Hz) when the te9:vkyf c b,f-emperature 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 2090kaut5csto7 k 1pg+g $^{\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 be tww5dqk iu- 0 xah7lbj07sy92 ijb3(gzg.6thhhat must bt703q yl s w x52auk9 idb(h 7h.zj0gibgh6w-je uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 4 y (6bqgylu87v40 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this isgu(y6q y7v8lb 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 at two suc oq,ds6fy :rhwn*nir 7c4 8.plcessive harmonics of wi,ocq n8sf :h*pdrrnl y764. 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 e gnnhg *w0hy 9(, ausa)j+z4x$^{\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 ranjjtbu 6dx 6 s,njm3):lk x*)ixge for a 2.14-m-long organ pipeblk 6 ij),dx3xxtjs)n6 ju*m: 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-y8.a67jwl.a )nchg mn+ x cyy is open to the outside and is closeyycngyj.+ awal n-.8mc)x 7h 6d 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 adjrm/tr9n 4(f0rjv. :eeuvx,km ust two strings, one of which is soundi4vvnerxe0j rfmrm/ :9. t,u(kng 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequmlwxu s/yw/;+x68 cr ax 8set:ency if 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 2oz3drxi (z 4t)93,2pszfff dt 3.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a4)op3 fxtrzs9f,2i tfd3dz z ( 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,vvyk 2 w/el*zl ,id5d sounded 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 reasoning. v2,ie*/d5kzywvld l,    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in on8ao)w-sp y1 qhdk7c0 gfz+a0ne string is then decreased by 2.0c0wzgh+q k0a-y an o )87sdfp1%. 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 if two identical flutes each try to play middl3gpxni+g 5+k kb2tohf6xnbs45o 6-ud o j)hg-e C (262 Hz), but onh kju g635 +bpbxingtgof- 2)h o4 ok+sndx-65e is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B6ap::nvqg uj70d5:bvcg ;.k ;goon bv 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 sounbg0qncj5oapg 7 6;koub gd: .:;v:vvnded 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 3.00 m from one speakercs4zj 2frp64siawj2g ) 6c9rv and 3.5c2 svs pj46)2 r6c rziwjfa49g0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pi-ogrvtiz 4 4d2ano tuner hears three beats every 2.0 s when thevi4-tr g42zd oy are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound o7 3 h(po; jy;en7omxgcf wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard?pxjm( oegc;yoh7n;73 (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at qn + za.*,pxjxrest. What frequency do you detect if p.+a,*njxqz x 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 frequenc;a wnuyc 4dk0*zu6ji/y do you detect if a fire engine whose siren emits at 1550 Hz movesj uaykwn z*c ;d4u/i06 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-Hwo5 xk2tyg*i ed)x8,pz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two fre5tpwx d,)2koy8 *i gxequencies 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 equ6wel5oq) py :bipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of o5lwb6 pe qy:)5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounbv/l tz 5osm, +6mafc+d waves at 50.0 kHz and receives them returned from an object moving directly away from lvsa/b,cfz 5tm+ o+6m 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/8esh: 5qw6cc v 9twnj(5.bvpc s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What:9cvvn 55 bchw(qstc6.w8j ep frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fla, ph6bga36zxbck )6o nt train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway bhp6gzk cox),a3bn66 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 waves tw; n f gbamvxw35u-7q*o 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 bw -*7;wq 3un5mav xgfbeat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ult /ik76;s pjpzsr6n+abd *4cktrasonic 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 veloca 3ymthr,+8lnk 7 pu1kity is 12 m/s from+ kh7y1r plmtu,kna83 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 oi*+1 ff4ov. 3twjinuk n 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 /u o6q-8 -mqqspo,lmnwpi 2.yis 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motio,puisy62-m.oq8 wqpm ql- on/n?    $^{\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 soucnn2xh+c5rr1 nd is only ab+5crxn 21nrchout 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. Determine the shochpx* 6gwonwmp4:(+ (ok:mqp l k wave angle it produces*wwl 4:hg(pn p(k: oxmq6o+ mp
(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 w, z+tdh/b2mm$/theta$ 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 1:8e/b uy:hvuhq y6fb ).5 km above the ground flying faster than the speed bu :yy) he /:v86hfbuqof sound. 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 device that s(xc92 vxcu5sh ends 20,000-Hz sound pulses downward from the 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 betweenhvccu x5s9 (x2 pulses (in fresh water)?    s

  Approximately how many octaves are there in thn sjjg2fe .ee ;ck;n u( d048fxdyh*j)e human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of *hdy d eid17 a:o.dci,many plastic pipes i :hdoc. d71edd iay,*of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sounds (0 2i-xvk qsmrcs.sfnt za m394v)1t close to the threshold of human hearing (0 dB). What wkm4zt-ai3t .)q1mcv( xs09f 2nvs s srill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soundok v3woxmr 7eq127c 9m are heard mw o2k7m 31cv7req xo9simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plamidwk8s3thjc-(pu /ks8 69 hoced in the open, is 105 dB. What is the acoustic power ok pc8h - j iou3t96dmhw(s8k/sutput (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 powec,(e:j r7a00f52fxdieernctsy m 5. lr output drops by 10 dB at 15 kHz. What is t ri(n lcf275e ,s5r0te:cx.dy0ejafmhe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectiv3 ,vgi 0oxp0.mnbb2drge 1em2c 8xe 0fe 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 thevp egf8. 2o xr32d 0 eecmi0m10bngb,x average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, j j fflnb s*d(c/./son- m1mq6$\beta$ 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 h)7 a)i m*oz1ab)xjpkto 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 points a54g h 3s1ryh*exnu4hwith a fundamental frequency oenya3 hh4 h*5rgx4 1usf 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 above a vertical open tube g(2dfvc li 696g pyd7vfilled 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 the9gddg276 if6vlyp cv( frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of ma.y+s1 m .a f7vo s:htfjjmjz6-ss 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 harmonic in the .+jz:s oh ym6vfm 1 s.ft-j7jatube?    $ \times10^{ 2}$ N

A highway overpass was observ.vfhiz0p h5 e6ed 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 com.eng 9nb3rxq x/5h8o v2 vd)esffay 91ing from two sources. The sound is loudest at points equidistant from the two sourcs fohfeba59 n.dveg)xnx13 vy9q 8 2/res. 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 o1i)mzf7 c ; 1es7cx4plsdbo.yn the stationary train hears a 3.0-Hz beat frequency when the other train approacd)411xblc;m 7 s .pof 7yszecihes. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afterw tro*b.b* it yqwyri090dy/ (us)10o (dqan v it passes you, its frequency is measured as 486 Hz. Howa 0dotb.v/)or(0 n r*swyiqw(*1dy 9b0qiytu fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the di j3+xukxq un;)pdft*/fference in pitch of the engine noise betu*k j3p+f dn qx)tx;u/ween 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, produce a beat frequency of 11 s 9 oyb;ox4.0godtw; pHz. The shorter one is 2.40 m long. How long is the othexo4 ;.9pygdwt b0so ;or?    m

Two loudspeakers are at opposite ends of a railroad car as io 5kl1h// qra1 p7qzuxt moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the spe xuh/5kor1q /plq71zaakers 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 aorta.3o spmje24tx 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 celp.mos2 txj 4e3ls? 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 isr /2fkm 8lkuf( flying toward the bat at speuf (2k mlkf8r/ed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approacjtsfz5jtb8)ug mm7 to/ :.snze09 m. ohes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can tho 70)btj:/gfn. z9eumo tj s 8m5szmt.e 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–su k*t ,tu;mz)s -(nvm38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 1u)s(ku nt;mz*s vt-,m2–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence zj2a+5 phiu.f of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamenta+ pu.j25ihzfa l frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called o3w.)1f (7lciiy(u tv5kcit l“singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. Tto cw7)il5k(.t 1ic3 ui(vfylhe rod is stroked 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 hearing for the humany9zuo*r*ywj + b(5ljt ear at a frequency of about 1000 Hz iu yjl+(jwr*byz*5ot9s $I_0$ = $1 \times10^{12 } W / m^2$ 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. yluha3p : dt;w4oau74An observer on the ground hears the sonic boom 1.5 min after the plane passes dir ;:4l7 tdwa4yuoh a3upectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1i9i 85xfz(zvi5 $^{\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