What is the evidence that sound travak26ke1)pomo3ir z 7uels as a wave?

What is the evidence that sound is a formkv hh- jr+vn/y,fmw xwc6v2n -ab l-u499l5po of energy?

Children sometimes play with1u)0byk yiwu(7 i7au z98,wnrfhjn +t a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can 0wntw78nau i)i,+ yrk9jy bu1(fh uz7be 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 ink9hacj6+ q o(vto water, do you expect the frequency or wavelength to chaq9 c6ov(jahk+nge?

What evidence can you give that the speed of sound,rvfx.ywyrl4+t8 f93qt; ak s in air does not depend significantly on freque xw8+ ,av t3st fy4;ry.rlqfk9ncy?

The voice of a person who has inhaled helium sounds very high-p,/r fq9qu1jhlmrv 2,nitched. Why?

How will the air temperature in a n)sb-x7q5bkns 0j6a/ jd;b6 mvdoy .aroom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sound-tiask:wh 7b t x--mf6;ayf / .o9masns in varifas;7 h. mib/k no6t s:y9mtw axa-f--ous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move upyh cw jfeb-kkv;h2sw*98jmcy9j /vqw. 4u c8 - the fingerboe u8;h yws4k/h f2-jkc*bywcw q9mcv .89v j-jard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hqp+su9t:8ax kear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” 9 psq+tk8 x:ua— 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 “interference in space,” wh kd07l0 qdhoh..j-l n)zn+odtereas beats can be said to be due to “interferehlk+tl zh.d) 0nond do.0 q-j7nce in time.” Explain.

In Fig. 12–16, if the frequency of the sphlk0ekx c /xjawc,nqgp:: 2;9 eakers were lowered, would the points D and C (where destructive and constructive interference occur) 9axce n/ 2kg0lhw ck ,pq;::jxmove farther apart or closer together?

Traditional methods of protecting the hearing of people whg,us-92 :* td9wms tsgcc b2ivo work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphon tucg 9tsm ibs ,v-2s:g*2cd9wes 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 shown in Fig. 12–31. Each wave 6*ef5n0gfx i7was lk/ can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a5gexaf* f6/0wki lsn 7) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the s )s-*tvnk qc+6 ;y +ejx-ychdvource and observer move in the same direction, with the samy;- +6c ky *evvjc)+ stqdxnh-e velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a(nh*um2 fmbb z1e2som6u. ) xo person at rest with respect to the source? x1oso(mm *m zb262ufe nb.u)hIs the wavelength or velocity changed?

Figure 12–32 shows various positions of a chil+ hwdy*j:* uj;c,zns sd in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for th+j,jyz dcsh*w;nus:* e sound of the whistle? Explain your reasoning.

  A hiker determines the length of a wk4 1duhpnqv7 w) he;*/ydaz(lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lad)/ y;pewhkd 71z4 un* qvwa(hke. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlidrd i gq7nv/o76 lo/c o(cl;l,ne. 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 12–1) and does not vary signr7 ci/lcn; 6/ov l(dqlgd7,ooificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 f(;l/zrdmci i,3-tm m$^{\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 drifti/ hdpcr ;kq,l/ng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anothe/pdrc;l h qk/,r 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 l m,d4t l1z*c ge5bj:cthe top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How jblld m5ctzge1c,: *4 high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pajm*ppjyj.8 ruu 58sg 7geq uv/,/o34ht g0suhvement. A moment later two sounds are heard from the impact: one travels in the air and the other in the hy.pjm8eug squj/g4vt/p o,83 0sgr7*u 5hj u concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by/bli5-.;rnqnms tdm; the “5-second rule” for estimating the distance from a lightni d5b-n;qm. ts;n/i lrmng strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pqdr)soxhyao06y ilf5+:f o2yt u3; i++b sw;gain 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 whose1 wcs4/ gzrm0a intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslh0boui 0hzw9(:l5w ds y at a certain place, what will be the s5d9 0 obwlwh0u(hzi s:ound 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 noi8s,1 .k 7 db1sjnyb*3rwfljg4c 0z ketsy jet engines is experiencing a sound level bordering on pain, 120 dB. What soun 4rk0j* gdbyse1l7kj1 c 3 8.znb,sfwtd 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 said to halh0q: o:qo tm7ve a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensmqq:ol to 7h0:ities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounds( bn;(tuh f 411fu u3(wkr0cbl+cwcc from a person speaking in normal conversation. Use Table 12tn w1 lu +h30(u; sbrccuf1kbcw4fc((–2. Assume the 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 sn8nf db - 7iy 2,e3bfzkvh-1xan 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 cncb24ing9k tb 7h, b:A is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expeb49 cb2 n:kh g,nci7btct at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2-+(xxc gp fgh).8 m in front of a loudspeaker on the (-cghp x+fgx)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 detec1u q5dris --8n; /un1uktyzva t a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounydn; tu a 1sru1i-u/k-5n8zvqds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound5ny ewnm1hw6adi6 6q/t; t5hj wave is tripled, (a) by what factor will the intensity increase? Increase by a factor of we1/j6a n6ttqw 56yhnid m5; h   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemeuxm- v5h4m(26mf q-defii (xlnt amplitudes, but one has twice the frequency of the other. What is the ratio of their intenx u(ff i hmx4-m-me5 il2dv6q(sities?   

  What would be the sound level (in dB) of a soundge o97l: qzm(hbd,41d:nuuqsbm 0kg- wave in air that corresponds to a displacement amplitude of vibrating air molecules okbe ug 7q(1: z-4d uo0,nl9s hgdm:mqbf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levxhz 6.o zuppf*i68vv,el to seem as loud as a 100-Hz tone that has a 50-dB sound levez6u6*,ihv8x p.f pzo vl? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sou32 2,6sjfimz/.gf*;x* k t rrhku gzihnd ltfzu j,m6*i.k g ;sfir2*krhhg/x23zevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound :hin. ek.usivs n5 ))uwg l4)p.q9 oevlevels. What is the ratio of highesgui5i v sn.nehv). lok)s.w4) 9p:uqe t to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 44leuslr.lk2 vj **a+6 b0 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 u* lr6vs+2j *l.alek bg. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fak,:e+s r 5r dz6:5j yde+5e* pwmktiaundamental and first three audible overtones if the pipeks t*zd:d6m+a p+j,k 5:5irawee ye5r 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 bloib4vh/4keh /z fg(gyw o6(q4bv6b t 21w:wrjjwing across the top of an empty soda bottle that is 18 cm deep, if yr 4/ (tb i/w6ww6 b hy:bvq1v2fj4gk4ejohg( zou 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 owfxzw6 k*t rs6bo1v4u-hxf 4/xgl80toq:yl* rgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the 0 z61 logyftvotx4k4 -f6s*xxuqww: h*b l /r8lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itsi84tc+j 0ddsm third harmonic. What will be its fundamental frequency if it is fingered at a length of oi 0dc+tdjs84m nly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and u 65 gg ./.c*p1lwtcdrnyvy*jis tuned to play E above middle C (3*y1w.nvgg/cp* .dr 6uj5ly tc30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open olhu) w6ytmy hr59e4 6mrgan pipe that emits middle C (262 Hz) when the tempe6 m 9ylmtu4hhwr5)y e6rature 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 *)dyjma -3ianat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fq 1r+eb;cv o.ulute in Example 12–10 should the hole be that must bee o+.vcqb1 ur; 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, 440 Hz, and 616 Hz, but not q; kngyry4b+,pr )bn 9at any other frequencies in between. (a) Show why this is an open or a clo4b,9rngp) y;k+ rnb yqsed 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 r(otx8oyj li9u3ubj-4 fi r(m4esonates at two successive harmonics of frequencio84 (olujfux trim -9 (bjy43ies 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 pem0x41 roglxo-f*/e $^{\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 wi uwo/epbrk1(g7t3,af,q cn5wthin the audible range for a 2.14-m-long organ pipe a/qr3cw5e pngk1of, a (bt,wu 7t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelz .twd w8.d5 1(ez(rud(irvee y 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (ieudrzev(w .5ddzr(1 e.8t(win 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, o ik 8q0zdsqnuq ww.x*-:hdx()ne of which is sounding 440 Hz. How far off in frequency is the other *skq-xzwdw80un) x : iq.(qdhstring? ±    Hz

  What is the beat frequency if7m1h xx4w41jxuzlc r95t wp:kx szuq.xym 4/ 8 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 another (brand X) o4 1.b )b6u dgnab.mspxperates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of6b.a1ud n) bgs.4xpb m brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fory jm id *3;u6 hdi3;pl-rak(cfk and 9 beats/s when sounded di c;jhy(l3kpmr fi6 ;ad -3u*with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz.i5+6y3 )xm n dvvc5bmz The tension in one string is then d6b+3cnzv5 x v)mmdi y5ecreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two i-xpmp*nkosz12 , gj;ddentical flutes each try to play middle C (262 Hz), but one is at 5.0s zonj*1 ,p2 -gxpdm;k°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Cq,fj5o5 8sh.qe kkqg. . Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded toget .qh8s.5efjq,k gokq5 her?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 /a/ltm;sr -g;gc(kb,i*ev zxz ; ono(m apart. A person stands 3.00 m from one speaker and 3.50 m from the othkooitzxz e sma* ;g(;l/,rn(c/gv b-;er.
(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 Hzl)y5d)7i xf ld9z:h jy:ig;r m, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be th5d :yl l ifdr) ;mz:x)y97jhgie 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 i-p*awm j.iwm+n air. How many beats per second will be heard? (Asw m+mpj-.a*iwsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ceqek xay8:ou (3rtain fire engine’s siren is 1550 Hz when at rest. What frequency do you: 38qaoy keux( detect if 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 detect if a fire enginemb8f/e v 5e7vi whose siren 8 v7/5feimev bemits 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 toward you at: p em.q0gpov 4a3s.yvnblwftb *g51 * 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are th a.bovv5wtp4y*:3m*e f0 nsb pgl1.qgey 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 gi4 yb1id 0y9afrequency 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 y91adi 04bgy ithe frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasowdzh 4hzaff)*./ 5xgodz6h4 ynic sound waves at 50.0 kHz and receives them returned 4dz6goxy/zhzaff) 4 *wh d. 5hfrom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an u bf5u .up7 r;fcb6ws,ib( nuz;ltrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear iinbsuc u; w fu(6rbf7p5z. ;b,n the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimba g: sty:hv*0ents, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the statioht0gvs*:y ab:n at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrapl 9ga,szlsm i87 ty )ndteclc,7,n-5 sound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?te8 t cglmpnas7isyd l5,z ),97n-,lc   Hz

  The Doppler effect using ultrasonic waves ofwbiqo/: l v.yx1cxm-0 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 5qoqzmwvs/5b5;7 bd tvelocity is 12 m/s from the north, wh5 ;mb5b/od5w zq7vqts at 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 spyktr6.xiprqb b4( p)2 eed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What is jqk.(8 e-vw mjkjz 6.lthe angle the shock wave makes with the dirl.j. mz e 8kjj-(qkw6vection 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 speefcz( s )2t7bit a*gva/8kgvi 5d of sound is only abotz c(/s2ivkb va)i ta*gf857g ut 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. De0r vq s*.yv9sgtermine the shock wave angle igsr0y.9vv* sqt produces
(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 gb(y eia37s)g fuhb)0; e-p)jr1lsak $/theta$ 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.e.a sz,s a8;lv5 km above the ground flying faster than the speed of sound. By the time you hear the s;,l.ae8svza 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 20,000-Hz sound pulses downwuy0g9m/32 pg n4xyq9 m 7tansnard from the b2n7qny 9/ tpm u3gnx4a 9smy0gottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many ou5ybh59h bo*c.au g-qzu - mt8ctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphp6.6)qxryo nn21 hyr yf3,dja ony. It consists of many plastic pipes of various lengths, which are yn.aod3qhpn r, 21y6 f) x6rjyopen 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 to7;r w odju)iv qkw0v:pyg1:7t the threshold of human7kwyg qtr0:1wv7io ud;v p)j: hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultantv+k7vnp/8+zef ucn;o sound level when an 82-dB sound and an 87-dB sound are heard simultane;cfv v/u+zopn7 kn 8e+ously?    dB

  The sound level 12.0 m from a loudspeaker, place s35pnsw agrvxs: b 8,:cu6u2zd in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radw: 3bsz u2spnsc: 5,u8 rga6xviates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pj 7ds.6pir+ 3 1bnj7r+ffijyv ower output drops by 10iv 7irj.j+ fdb367fr +s1jp ny dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectio tx uzm849qzxs( d23ove devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distancoqoxz s32u84mz 9xd(te of 30 m from a jet airplane engine?    W

  In audio and communica1d;mhq4m* dvn tions 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 tune,twd9y* +hak od 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 points with a fundamentalimx :g*dod+, 58io i )h1ln6zcv3xgr*synh 5h frequency of 440 Hsxyo5id6 n8g +: *zi, rgho5)ln*3hd x1vcmhiz 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 imp,hvr(a* ( cir/ 8sva 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 openingh8c ,(ispm(/rr*aiv v 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 jaa 6y566n wzvg 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 pazy av6n 6wj65roduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loophnb ,7rfg i+k* ($\frac{1}{2}\lambda$) 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 rd b; -l+jjyd3qvmw l39xf45vrange coming from two sources. The sjb3 r34fw5yv -jlqvxl;d dm9+ound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Ontz*b 5tge nwh7m,x su25,7rtce train is stationary. The conductor on the stationary train he5x,g7 emhr , t2tb *u5t7wczsnars a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you (boky( up1 px+/g ;uj awoh:ctdsb-67 is 538 Hz. After it passes you, its frequencj p ;/(o-hub1wg+uc p6b:y at7 sdok(xy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can e- k+eyt**w5hj g 5rlnha2+ zjestimate the speed of cars just by listening to the difference in pitch of the enginejh2*- h5wn yrzel+ +tajk*g e5 noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat qz)u 63,- ek9nyuim hsfrequency of 11 Hz. The shorter one is 2.40 m long. How l9k su 6-iyznq)h m3,ueong is the other?    m

Two loudspeakers are a8kiniyj m- 15cssxw(a le28w6t opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical swcx-sn8m8a56j iwi2kl ye 1( 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 is normally about 0.32 m/s what bex5p, lj kn,j(io 48g- s9zxam2aize.lat z94eln -x pm8soail ,,.5ik xjz(j g2afrequency 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 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 j47qzg3c)wb8 -hemb obat at speed 5 mm87 3h4bg qbz oje)w-c/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 s a.itp;zmf: rw;r/ efjqn-;e,b/j-heound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that tht ra;-ewjpn/ qe-:mf, ;zbi/hr; fje.e echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used t03 ap5yfceh5c g xk/:do 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 a3d:5 /0gxchcf5kep ay s 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 c/ ),4ada/ahw9*1 qx cgloz ugzan be compromised 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 long, 4.0 m wide, and 2.8 m high. Calculate the fun4g a9x)q1/ ozld c*/ahag,uwzdamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, c4+nzminog2l ve i;zg0 tqnn/5ci 6 6p/alled “singing rods,” involves a long, slender aluminum rod held in t ;zl6 cignm4pz2io/g0 /+vnnt q n5ei6he 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 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 hearingfsin2y ss0m sqlg36k1o(s 7)d for the human ear at a frequency of about 100iysqs m 3)lkdn og2s6s1f70s( 0 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 grou :.ochb r,6vxy7 )bvzend hears the sonic boom 1.5 min after the plane passes directly overhead. Wh vre 7x) vyb,zoc:bh.6at is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat35-4br+ ax 8rdr fobh.jja5lc 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