What is the evidence that sound travels as a wave?:,- zim buq:lj.zpq+ wuwbnxb1p 22o/

What is the evidence thator 5rnuz/qcu9p0 9agx8k yz*2 sound is a form of energy?

Children sometimes play9f) xpv sh;hj1f 3dag0 with 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 be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup hf1hv ;jad9 xgs03f)p to the other.

When a sound wave passes from air into water, do you expect a n kfeq) pw9,qd(::lb.b-v kdz:vvi5 the frequency or wavelength to change?av ie -blv:qk:v9 dfbwn zp()kq5,.d :

What evidence can you alx4n br rx8e;u sp xpt0)rr**o vc,g9wr -77pgive that the speed of sound in air does not depend significantoau n)xpr 840-;x7bwcgrr7re svp* ,*ltx p9r ly on frequency?

The voice of a person who has inhaled h+o (s ;ci y)pr6kyofp+)mv f-melium sounds very high-pitched. Why?

How will the air temperature in a room affect the pifx2dih y3;f627cp n sztch of organ pipes?

Explain how a tube might be used as a filter to reduce the amsd9qn/s /trauw 32y-zplitude of sounds in various frequzsn-/q/adry 9 t32usw ency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together 7jnz z9n:b y;zxc+h0las you move up the fingerboard toward thz :;0chyxnblj7zz+ n 9e bridge?

A noisy truck approaches you from behind a buildih0geue:;wzaj3 r/wh z(v+ z 5vng. 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 eh:z w0vargzw/ 5z;+(j ev hu3on diffraction.]

Standing waves can be saidy9ynijk5oc;3 to be due to “interference in space,” whereas beats can be said to be due to “interference iio5; yc 9y3kjnn time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the zegrpu), d9x nx5o) -fpoints D and C5g z)xxd-r) n9oup f,e (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of ey)uoto:v 1 .mq86h fopeople who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to th1vequ)t:.6ofoy 8home 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. 3 bcvf:pou(6yrat 8 s,g)ep,h Each wave can be thought of as a superposition of two sound waves with slightly different freque3e 8bu,h(yac6r:gtvo, s)ppfncies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move2vswrh l9s.*d sec.q/ in the same direction, with the same veq.h /d.svwcs*9 rsl 2elocity? Explain.

If a wind is blowing, will this alter the freqk3f - zhzkx9t:uency of the sound heard by a person at rest with respect to the source? Is thzxt h:3k9f-z ke wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mytt* c1u b5eg d.8u3qeonitor is blowing a whistle in front of the child on the ground. At which position, A through Eug1uty85be e3 qt.*dc , will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoutvziz,. )ejuk,57lx mba49nv s 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 lakeus9vx, 5n k,i7jamev.)l bzz4 . $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the qyx hefy8ei5kq3c;4((z bde*2ep nl2waterline. He hears the echo of the sound reflected from the ocean floor directlyck ;hexz ql(2enb*pq( d4yef2e 8y35 i 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 m-sgiisb -a/5tijqx )7za18 k$^{\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 )mv 9.-fw si7 cct:ywna school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfs -icwm 9)fy7ntvc w:.ire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash iljvpfyy5y)o 6sx)/p( iu -vz;t makes when striking thzvoji;yxs )f lp v5u(/p6)y-ye water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge /u1 .k1 jt did)v.a6z ku4lgzgstone strike the concrete pavement. A moment later two1u4jkz v.ti16ggd la)k duz/. sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erro c/x2d1) yxdggr made over one mile of distance by the “5-second rule” for estimating the2d)x yxg cg/d1 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 tk)kk3/d707 i( juejug:rp bzvhe 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 lev7cw/m-p . 9po s0aglbg8nrj8 ael of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whp+yt skk..aji3o 24v ben fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: yiob.svk+2ptj.4 k3aAdd intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eqchu7cq; k2na:-ptoz 0)qp4v xually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this personp qh co;tqu7x0 )np -:zk4c2va 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 ratio of 58 dB, w;2xg+b,m 6eftky f9c; qtwiq9 hereas for a CD player it is 95 dB. What is the ratio of in+299c ftfy,q gwk;mtx;bqe 6 itensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sot-u3ip0 m0 wbaund from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centei0ua-bmt0w p3 red on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whos g7)zts0bjhj2 e 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 e2z0zp (g-wngrated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in de gp-enz( 2gwz0cibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dBhj;c /6.nn nhu meter registered 130 dB when placed 2.8 m in front of a nhj6u ;h /nnc.loudspeaker 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 dg;r u n3u5xtpv1w8t m9ifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?t5 vu9;8p wu1r3mn gtx [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatbj8 c8rpesl+ og p4)z4 factor will the intensity increase? Increase bjp) gr+z4 c8pe8l sob4y a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplituyvuz ;9k /6gjkdes, but one has twice the frequency of the oth; /gvj6yku9zk er. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave p6w1c z6:2rvb b,fxxn6gztp+ l7dm9s in air that corresponds to a displacement amplitude of +6f61z :sbt 9pn7,zb6x prcm2vx dgl wvibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what h4xcp9lfvr iv tw3 x5gzs;+1 ;cbgk:o +h q:v.sound level to seem as loud as a 100-Hz tone that has a 50-dB soun+.vwv shcqtk1p +9g:bvx;ci z4or5 xg h :f3;ld level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencica,oh d.,i3bbxtwd 6i8m* s+nes that an ear can detect when the sound level is 30 dB? (See Fig. 12– wact3nihx8m,ds 6bd.b+o *i,6.)

  Your auditory system can accommodate a huge range of sound leveb pneuc43g+ dg33db; xls. What is the ratio of highest 4gec3up +g bn33bdx ;dto 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 fundamentalt;n6/4igk1qgtlqer75 hn tm 6 *q;eqz frequency of 440 Hz. The length of the vibrating portion is 32ett5*e1 l46z qrm6tq7; k ;hngqiqng/ cm, and it has 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 fundamental and first tht)a 8vuts7u2 p*u ca)5r z9 i0dp4dvstree audible overtones if the pipe27a p vuva9t)d4d0*t8 sr)5ctszp uiu 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 fromzjxq dr)skc. 9 j07xwh) u(tdh 0q5l0i blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it w0 di.7jlhzxh90 qq k(ct dsrjwx5u)) 0as a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a a 57j fe.ze+nn,zy(eis 00+ qy/qijmmpipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the a,y5zjqs7 memi0 fnzni/(ye+ . j0e+qrange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strin u5at3 p jfb/2gs /3-ftxnz91ril 7ifrg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengt-zna9ib/tp517 gs itrulfjf2xfr3 / 3h of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and i dlmzw0 5mi;yu:4jrcj/iqh1 *s tuned to play E above middle C (330 Hz). cu :iq /d;1 yrmj50m jz*iw4lh
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (2*m*:l b-k pbdr62 Hz) when the tempera*m:pkrb-* lbdture 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 hc559dfi9phx am0 le/20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thexu96 j7c*kyvab9z h1d0 ;rvjb flute in Example 12–10 should the hole be that must be uncovered to play Dur61c vvba7j 0k; *9bzh9yjd x 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, bks+r9//lv q;h3zw))sqspa l: 7+lxfzw b 5 bkcut not at any other frequencies in between. (a) Show why t3v/w 7sb f llz9pk; q)bzc+hlxs/ w)kq:s+5 arhis 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 lon/sa/x7)2 s 4pjou.twse;:vl r8 jgxgk g is open at both ends. It resonates at two successive harmonic.get/o)s:l/ u 2;pxgsv4j7awk js8xr s 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 ixhic4zmb l:*y v9i3tk:0( zv$^{\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 range for a 2.14-m-lc:mtto 2pzxhotp)pkt :w001 p3oqp / 7ong organ pipe atom2owp7 01h)c o p3tqt/:0 :ttppzxpk 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open t(a-l a.sr2qgp o the outside and is closed at the other end by the eardrum. q p gs-ra(a2.lEstimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings,(;d 372:eoti dvi0 88b jsvcge4kgsmb one of which is sounding 440 Hz. Hgj s (g34e 0 e;dsoctmiivbvd8b728: kow far off in frequency is the other string? ±    Hz

  What is the beat frequen7wwbel/j( 2cbiyn33.sdlk : acy 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 23.5 kHz, whilrql2w4k tdol l6pn2d8,8i0g te another (brand X) operates at an unknown frequency. If neither whistle can be heard by hunrtow6 lqp d,li08kd4 t82lg2mans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork il9 y72e/xy :,c o1.a lakbhkqand 9 beats/s when sounded with a 355-Hz tuning 7 h1, y9baaly2kixkce:q. ol/ fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sat :/l)g4.wse*i h tbdweuht 1-me frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint:e b*/ ed-4.gt)s 1:uwh tlwtih Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mi903 abvnmsc0uc8 een+ddle C (262 Hz), but one is at 5.0°C and83en0 b9as+c veuc n0m the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of9m s/2 wof2cok 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Wfwmc 2s/oo92k hen 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 apart. A personxgq - *f1r2i lahrbx1k hjo857 stands 3.00 m from one speaker and 3.50 m from the other. kbh a-27rrx *l18 oxgh5qfj 1i
(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 vibraxti x .m*cnc1.ting at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what n1.xt*mxcci. must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64802ha(e y +x i7 it0uupduf(bam -k8nw m and 2.76 m in air. How many beats per second will be heard+2yfdb wae7ha8pi8 i0uu(x(n 0 m-ktu? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirena - s.ih; l8 xh1-9grsel2vmsb is 1550 Hz when at rest. What frequency do you d;-sll bxsmh9r 1v.-a2h8ie sg etect 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 35yemu teh1-37my57+xzpkrleolczt1 w 2 + yea fire engine whose siren emits at 1550 Hz moves at a swxyyc1lok7-yr zeu+2 +e15 573 lzmp3eht t mepeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sn9 *uyj s/ps6xxo*1a source is moving toward you at 15 m/s versus y px6/n xass*o us19*yjou 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 singl ;5ru xxbi6+jle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequex r5b+ ujl6ix;ncy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recei 1zljn.s0e+l uves them returned from an object moving directly away from it at 25 m/s What is the received sound lujn +1e .0zslfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits anu,,7f;mhl2hp v3e qt8obs3pu6o j- ho ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear t6hl uh2 mvohup;b3- jf ,s87e ,qpo3oin the reflected wave?    $ \times10^{4}$ Hz

  In one of the original -gm3d g0((dokt ph5gtDoppler experiments, 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 pdgk( m3 ( otdg0t-g5hthe station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavob/ z a9 s-:luv+8 acgy6agef(es 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 blovag-fz6e (a9b:suyal /8 +g ocod is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usin7uirp c f/-s;cppbu:ve vur02y0h 4+hg ultrasonic 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 fgrbskb h+ c0k+z5e,c1g ;vb2brequency 570 Hz. When the wind velocity is 12 m/s from the north, what frvc5gbb b +2; +1grz,0kkchsbeequency 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 movihvp1 lg43yfe -;v:t bscm4 e.cng on 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 wherouys,;y, wpwu+u-8m je the speed of sound is 310 m/s (a) What is the anglop ju8m ;w,w+yu-sy,u 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 soundodrh+ e:y :,pz is only about 3 rpyzoh::e,+d 5 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 shock wave angl96.aem9hn c zbe 96b menz.ac 9hit 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 lsch 96/ qa,6zl:tvw ri2b5, -e1 wn3 dhulqtr$/theta$ 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 exactly8i2f +i3b ) ndrq:cyv57*oq gy1ykwxj 1.5 km above the ground flying faster than the speed of sound. 7 qg8cb+wi2*ykydri3: o v1 nq5y)jxfBy 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 20,00dfx;bg lqw* 180-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 m1wq;8dfg* blx , what is the minimum time between pulses (in fresh water)?    s

  Approximately how many oct6jd8h2*wlqal 9n hegmk2-o x3 aves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistwlnufh9vo 1 k8jo781ljj9r; ds of manylj;vho1fw 9kr j718 ldj8 un9o plastic pipes 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 froav9+sg jmy1(/ xwzd5n m a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound le a9(sg/jz1d+mxwn yv5vel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB qk5jjhk, jaroyp0.x.k oa 8,; sound and an 87-dB sound are heard simultane;j khq.o xjyj8k0a o k5,ra,p.ously?    dB

  The sound level 12.0 m from a loudspeaker,o 3qyo)nb: p6ol: z:zt placed in the open, is 105 dB. What is thz :nbp:o )y:qtlo36zoe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier i, 4d*fu,ns4epfu )t acs rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts atead f4,sp*nfut),4 uc 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicp6)s hmj-bao-es over their ears. Assume that the sound level of a jet airplane engine, at a distance of-aojp6m s)-hb 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, 6bscb* l yb1b ymi,g-2ot8qy:t.di ;p$\beta$ 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 isx6im cf+(stj : 1iaz4kg:wpw- tuned 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 fiq*e8fzr m z- *dvxgo)zmij j-:lv .d)7xed points with a fundamental frequd 7 )-q )jme.f:8v-*z l gxj*zozdvmirency 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 tube filled with wat98o.n r da-qpler (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 dist rp9a.lo -8qdnance 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 o h.6iq l,x.yp)zuhnv m+u.4muf mass 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 tubev.ulmhzi my u)xp .n6u,q.+h4?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fu*ae*ahx3. m xwll 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 cominz8bo8mx+hf:0va -ufk g from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farthax0 8:f zfv-bm uh8ok+er from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train 6e6u 6wgj8wh6g3dugk kl0v . 6eni/mqis stationary. The conductor on the stationary train hears a i66e mg68kjgw eu/udv6k w 3qg.h6n0l3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistl r2h 1xpkl1:jgce.; pjbr+ 9fje as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 pjbc h1;p grl1 9jr+fkxej :.2Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spx; 6j*gkxy7uvf 8cdx. -g0yr zeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaz dvuyg-;y8 grc7fk0*jx.xx 6 way. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 113 ltndx ,2*k6alymc7l Hz. The shorter one i2xla,l k ytln 3mc6d7*s 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad nc vkqte p*2,h o)a3 1coyho7-car as it moves past a stationary observer acn1)2ohctkvp,3 ya *-e q7hoot 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 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.e:edmcdn/iuaa25w4 5 32 m/s what beat frequency would you exedeaim:a/5 n5w4c 2 dupect 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 (6-7.kp4io fuai, 0z9sqyk8 bzdpm zfthe bat at speed 5 m/s The bat emits a sookp 8d7i6af4.p-0q uz mi9kz b(y,fzsund 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 approachz evinudfh-pb 0b(.4*es 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 bu bid0ph- vef(*4n. zso that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usemq8/ eyeyp y2;d 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, and2yep /eyqy m;8 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 the presence of standnjs 2+pryc: +eing waves, which can cause acous ypsnr2j:++e ctic “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 fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, callo5p+w49clc 96)fm5 pe(go de tt1lbyxed “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Withed+ yp cl5)wo1gp 9le5b 69tcmx 4fo(t a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequenc78hchu3 rqq +oy of abou8uhr+q cq3 h7ot 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 theu . rei+opqn48 ground hears the sonic boom 1.5 min after the plane passes directly overhead.8rnou.p ie 4+q What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i;m)imgz .g 7x9z .g1)ua g*ec qpelk+ls 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