What is the evidence that soune1j:qo+;iny 68 dexuzd travels as a wave?

What is the evidence that sound is a form of enerzd4tty3k6 r(r+f l s9rgy?

Children sometimes play with a homemaq4v ot7uwip45f( wx( lde “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched andp4wo75(lt qx4f(i wu v 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.

When a sound wave passes from air into water, do you expec4e31af nz.ax fddu 0+h c00qmot the frequency or wavelength to chanch x03 mazeu dao.1fqd 0f+n40ge?

What evidence can you give that the speed of sound ijdl dutz+2--)zy z* xss y9sl,n air does not depend significantly on fr2z ly s,zx+ j9 d)l-tdzss-uy*equency?

The voice of a person who has inhaled helium o t1ye1br9xs) sounds very high-pitched. Why?

How will the air temperature in a room affect the(7aczj2o odo. pitch of organ pipes?

Explain how a tube might be usesf p.1ou6/ ymn zl 9tsu)ts2;ud as a filter to reduce the amplitude of sounds in variouszl1; 9 uysm nstf2pu/tu 6so). frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) sj v 45;pff :avitrg8 lzz27)gjpaced closer together as you move up the fingerboard towaaljpvzg 4z52jr ff:7 tvg;i8) rd the bridge?

A noisy truck approaches you from behind a building. Initially y4h5snb(id ze h 9+bk0fou hear it but cashzfhn(9ki 54b db0e+ nnot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfereo0 y :po6yp9b7, idcnsnce in space,” whereas beats can be sa,ip7ydb nsc py:oo609id to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouldh922ctycrm8p 5t;l7ar; dus y: g6cofbg4v ; s the points D and C (where destructive and constructive i:t 76u 2; chylmytrf r4o bg5sa8sd29vc;c;gp nterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work if , r4 hdmdy7oec/h38un areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise3dh/c7yf o rh,m8e4du. 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 thougz p fu1z v3(7 o51b9qosa3z+kfwpab2ev79 g uxht 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 freque9p b 3z1ksz vu x5v79f1pb o+7of3wq2zugaa(encies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and o /4q3(sui9 otbq3dne daj*q5fbserver move in the same direction, with the same velocq9aod4sdnft/ 5u3 iq*jq(3 beity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pershx bcixclfv ;6:.0)ua on at rest with respect to the so.xxhu 6c0i ;vflc):baurce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moe/h,))hxnd eo.q ccgaznb ,jrw:3.u0nitor is blowing a whistle in front of the child oab.cx qn e chhj /.e,ud), w3o)0gzrn:n 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 lb9cd7.a ttfcg1 s jr8s 9odq13ake by listening for the echo of her shout reflected9t cd.sds7 o b8t9g1cf1j3qa r 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 waterlsz51b+l8f m kline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s latl z5kbfm+sl 81er. 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengt-*6pzz izqu;q a koh4cf:wrf7** cr;nhs 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 j9lh-bv)vnwjj +r*:v qa9afq1 ust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km aa:v+ 9* vwb-jf)v91aqr njlhqway (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 6r0sd d*2:ngk mu.mwicliff. The splash it makes when striking the water below is heard 3.5.20mdud mn* rws6 igk: s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cof /mfo9(5 rou:uir0h bncrete 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. um :b/ fr50iof9h uo(rHow far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percen);3ao gs v;b zsl/kz.lt error made over one mile of distance by the “5-second rule” for k3;zl./ob sg ;zsa)vlestimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ):ys5/4aulou9stmcead 60u z 5rnt7dof a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levelhsybqx -h/ 9il52a/gk of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level os/p0wi g6wfp .1sx( tuf 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.gu (60w xisf/ppw 1.st]    dB

  A person standing a certaind 5 +vxqmgws9- distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Addmx9d gqws5- +v intensities, not dB’s.]    dB

  A cassette player is said to have a sikvw e1x+ l/ez r58bhq4gnal-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 barz/l81v+hq kb x 4eew5ckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nooyssgp/42qfyr 9 o5;aa)g; b drmal conversation. Use Table 12–2. Assume tyf/ 4 ;o25g b pys9oads)a;grqhe 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 anjvczv2wd oks -0o5o)+ 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 at 250 W, while the more modest amplifier B is a wq46if9*f1b+he zflkkd8d4rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to 8 wlq6 kkh+4zif 4dfafd1 9*ebeach 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 2.8 m in front opc*qnk fa- yy 26d5l530ufmo8oo: hmwf a loudspeaker8p 3afyclodmu y fo:-w06 mo*nk25h 5q 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 detect a difference in sound level of 2.0 dB. w,, p:gb b9;qcuhxwd *What is thw; *x,b g9hbp:wd,quce ratio of the 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 factboc)5i 2du a6tor will the intensity increase? Increase by 25ui)dbo ca6t a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amp ial fhlo+x668litudes, but one has twice the frequency of the other. What is the ratio oi 6lax+6floh 8f their intensities?   

  What would be the sound level (in dB) of a sound wave in air thatyten4rppb e;l54(n 9v corresponds to a displacement amplitude of vibrating air molecules of 0.13 mmnr(p4e yl;n e9b5t 4vp at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone to lqc wwx.1m1/qyk6fq6d.sv8hat has a 50-dB om8qysv.wldw6 6 1xqq1k.cf/sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequ+ r(jean1v; sjencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–+je ;v asj(rn16.)

  Your auditory system can accommodate a huge range of sound levels. What is the rohlosykz d7; xx21o;3atio of holod12sox3y k ;xh7z; ighest 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 73y lrdppo )pnzb 5/t)fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has 3)t7)/ zbnod5prlypp a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamen3.fqz. xd, eqktal and first three audible overtones if the pipe is3,xkdfz q. eq.
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an4 wi5hj/sg5oh(bij z1h j9bi4 empty soda bottle that is 18 cm deep, if you assumed it was a closed wbjghj bi914hoh5 si 4z5j(/i tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pi6x7iwkpts )a 0pe organ with open-tube pipes spanning the range of human hearing (20 Hz to wip 6axs 0tk)720 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540z2fj;,e: z7cumh s1zk Hz as its third harmonic. What will be its fundamental frequency if it is fingezm71ecj ;h,uz k:s 2zfred 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 middlec/r i1xh5 b0 qdtv2r.s b0y,:hultdoseum78* C (bvqrheml7 s0: d0stic*2 1. 8hdt y ,uxrbo/u5330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an( 9 v8nf)) 7msgmtwkaq open organ pipe that emits middle C (262 Hz) when the nk (vm wf8t)qasm 9g7)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 20 yfm1 lz ih;o7e anv+o:.7io qmg9 0a7z$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouhdh. )z:( brvgthpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middr z:b g.hdhv)(le 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 cajsl2xv;fj8t (t5ynrw65 pb7gn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) t6lv5;g2tnbjxw85fr(p ys j7 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 m long is open at both ends. It resonat)yx0j7 e qzn*xruk z-+es at two succ-ey+xrxu zz7*njq k )0essive harmonics 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 ;l.,pdt r.q)ae:v 1r x lmu3pg$^{\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 audib9pknzriuf+at-. qw9 3le range for a 2.14-m-long organ pipe a-f.z+ w9iqtaup nr3 9kt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxim -w tby ftimxj,bvmkvdqk lt;:*5/-5,ately 2.5 cm long. It is open to the outside and is closed at the other end by thi; t v*vmy- l kbb5-xtmtq,f5d,/k:jwe 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 beahaxs,:l703 fi o3u.3pqu q6ketn 0vyct every 2.0 s when trying to adjust two strings, one of h6vaonpl.03 uui7qxk30 cqf:esyt,3 which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) ande x;xv z*uepu- **z99 jym6mip $C^＃$ (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 X) operated9oeh8 7(nmyfh xf+f,s at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequefhoym7 df+ nfe(h ,8x9ncy 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-H6wfdqsxq-mw ,-zw h2uw1-k5l z tuning fork and 9 beats/s when sounded wuxw f1qk- s, m-q6hwd5zl-2wwith 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 frequency, 294 Hz. The tension in onesjb 0 j qt-(8kpwe/c(e string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are pqe /-b8kpjje sw( 0ct(layed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fqy -z7deykb4har9/) g lutes each try to play middle C (262 Hz), but) -z 9kyg 7rbq4edayh/ one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C3+h o*. rp1 p)qyou )zjq2nofj. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hzqo3ujrz)foh21 q*j .p+ p y)on is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m atixo0h1us2+* ykpdsphp;, f1 n syr57part. A person stands 3.00 m from one speaker and 3.50 0p prnds1 h52 , h oykp;1s7+i*stxyfum 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 pia uhzu9zky77du0e7p s h 69*qnhno tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be thezy 7d7z7hs6huqk9 e9hn u*p0u 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 mcp*t(c (qyv ,q zlq ul*c8-vq9any beats per t- q8zc q,pylv9vcul q*cq((*second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siqou u ;4lv+uag-fow) 5ren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/q v4 agflou-u;ou+) 5ws
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency dov90h/wtl -raa(h0ey, t uzg 0p you detect if a fire engine whose siren emits erz0a,9-hw(y/l aput00gv th at 1550 Hz 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 source is moving to b ;);jarad82vbra5 mtward you at 15 m/s veb )j52m;aa abtrv8; drrsus you 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 single frequency horn. When one isz dhm-hcq 06gbl2p8d- at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of zch8 d2q-db -6mgp0hl 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 1k c ksgh ltby.9x1x-g 44kh1uand receives them returned from an okk-9 tg1h hulk1b14ysxc4xg. bject 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 j0/j5y smals .As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequyj sm5laj.s/ 0ency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a :g ief2::ok v*;2uxdnjxt pria5;r8ltuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba play;;oraviu rg n*5d p :2fkje2l::txix 8ed 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 waves to measur.dc-rb7yj58pp0 i gay3w 6utfi e7mn/e blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteriy8uc03/7weii 6p- bam g5ydp t f.nj7res at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wav6g k(: fq0rqhxe w*wnb,ub( +ees 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. Whe(mddog m:pp*m 9 )qlhf1(y-g vn the wind velocity is 12 m/s from the north, what frequency will obser mq vldfmo1 (pdhg )p*m-gy:9(vers 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 ar *rtv a/q vnaeiq9k 42 ot1nmcx)72yds8 )7ixt 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) i7pq4y+m7 tpa jkm.w9 What is the anglm.4typmpja 9qi+7w k7 e the shock 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 of sound is8f/v.lu( k ndm only abd(mfv/8. nkulout 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. Dea5b o5(eg jl*:wlj j8ptermine the shock wave angle it prodpb55o8j(w ej ljl:a *guces
(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 -9z sv7 edbv5j$/theta$ 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 kui:9um.pz 8e(zek:qsz i9say* d xj* 1m above the ground flying faster than the speed of soundim9eu.p x: jd z*s q(ieza8z1uyk:s9 *. 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 sends 20kos v1* er.c,ugd 5l0o,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for whichrg*oce0u ,d1l5 .sv ko 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 )vz97pgu m 0/og,nbmm in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Irl8lkr: f,o0vt consists of many plastic pipes of various ler:rlk8,f 0olv ngths, 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 m p+ 8t-kij4mdnakes a sound close to the threshold of human hearing (0 dB). What will be the sound+n8 4pitdk jm- level of 1000 such mosquitoes?    dB

  What is the resultant sound levelknc,z*rt*gdsffp0kp 6 (y n39 when an 82-dB sound and an 87-dB sound are heard stf93dnp(60kg, s*f cyn* zrpkimultaneously?    dB

  The sound level 12.0 m r hbwh dnc4wk8( ky p4:b03;yifrom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the spe pykd4k:b8rh3(yw40 cbw i;h naker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power pkznu un* ))bl6qbi1 6output drops by 10 dB at 15 kHz. What is the pob puz1l nqk6u))bi* 6nwer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices o,cv1t 6nqwu .hlg/fw7ver 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 ch6ug,/ft l 71qvw .nwcm. 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 communical6dzlwlk- 1 f)nv:gdwq6t) l6tions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequenchzqk, g*;9f( l;7aol ;a/et c dbwqq;vy 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 lonrt ky6-gws ef-2)l0mig between fixed points with a fundamental fr mg-6y2kt0)i els rfw-equency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tux 8a(rt g .fp63ezfwo/t-6vsfbe filled with water (Fig. 12–35). The water level is allowep.-osaxwf zt6/r f fe638vtg(d to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g iszc 5mo6 3b si/ez)hp0r near a tube that is open at one end and also 75 hs z)3p6reb0zciom/ 5cm 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 tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as on zj(8 erevyz72e 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(jo lwa*rq*n3–1000-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 leqna *rl* w3(jovel 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 m .rr es7kb3h,is stationary. The conductor on the stationary train hears a 3.0-Hz beat fre 7hb.krm,r3e squency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appoq4/d +8 zbqugroaches you is 538 Hz. After it passes yo+8dbqo4/z q guu, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just sb 0b0x)6m4 lingek-rby listening to the difference in pitch of the engine noise 0ri6 lsm bk-enxbg)4 0between 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, pk-v n2e nvpnc;yx,4 :jroduce a beat frequency of 11 Hz. The shorter one is 2.40 m;2-yp,xjn:n vc evn4k long. How long is the other?    m

Two loudspeakers are at opposite ends of a j,ro-mj/.dj c railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front j jd-com .,rj/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 whkbwdkpp)156 . xmqyf9 at beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speb) 5xm9q6pk.y dk wp1fed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whi l0x63sw+ fjf8-0r-snauqgizd t6z7p le the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 q0r -x0z- faw3 +86j zdus6tsngfip7lkHz. 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 approachep1*1 b ikuk;xis a moth. The pulses are approximately 70.0 ms apart, and each is aboup kuk1i; b1i*xt 3.0 ms 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 Alg :.oalv 82ecvpine village to another. Since lower frequency sounds are lessc.o :2v 8lgvea 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 compromised by tp,fo;3hj) l aollb dc 04)jpw5he presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calcw 054bl jjo)3cpl,) lda;hpo fulate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvesgr- rk5a-o :8pa/az ld a long, slender aluminum rod held in the hand near the rod’s midpoint. The 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 ro8rra5:ld p-/g oz-k aad,
(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 t d;fb1f:rua h6hreshold of hearing for the human ear at a frequency of aboutbaf f6hd;r 1u: 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 t+vqpr4 dk39;2ux72wv grm j)q;b rqqehe ground hears the sonic boom 1.5 min after the plane passrv7u2q4 v;mqrekq )29g3+dj ; rwxbpqes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbvm+ f3mkw:i.r o/ria 4oat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h