What is the evidence that sw6.moyuwdq- bfqwl; 1 01cw p1va 0z5lound travels as a wave?

What is the evidence that sound is a for, h4.gq ftg3vem of energy?

Children sometimes play with a homemade “c :)gz(zga uzih5 (rzwiq96*h ,bsvqemu m2 1/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 (Fi1* 9 ,ai2hig5g6/m :(czmzuzqrwz)s (e h quvbg. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes frbsa- *c) s2v:gfz 2 qh3tjvjv2om air into water, do you expect the frequency or wavelength to change hbj32 f)scj2:svqvz2va*g-t?

What evidence can you give that the speed of sound in air does not dep- rzx l95imq7a.x*2:hzcrd clend significantly on fiqd*95z rc cm2ah zl7xl:r.x-requency?

The voice of a person who has inh23d; mu5wh bxcaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ p-4 dr pu6arf x2n4l.gqd8us6tipes?

Explain how a tube might be used as b- zpuux-8f:ya filter to reduce the amplitude of sounds in :ub ufypz8--xvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move u7) idjvjf +a9yp tafyj)jiv7 + d9he fingerboard toward the bridge?

A noisy truck approaches you frs dx6mbdy471ys8n 7 lyom behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” —4dmydy7 xnb6s 1y8l7s 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 “intx2how f+*xl45o5 hpkl ck7 j.zay8b-eerference in space,” whereas beats can be sao xz25xh4 8fwa* -kch.kple+ly j7o5bid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouldx0nemp vnmg (pl238d, s aq9f) the points D and C (where destructive and constructive interference occq m 3)08p2(gsdlpe,nx9mfvanur) move farther apart or closer together?

Traditional methods of protecting the hearing of people qqg,q+ g* /*tx frdod9who 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 frtog*xq g,qdd*q+/9 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 can be thought of an *fyh,.3bnvsx a/q :xs a superpoqy hxsvnb.n a, f3:/*xsition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and ovl b*8kqww44t*p hw8tbserver move in the same direction, with the same velocity? Explak*p8h4l t vtb qw4w*8win.

If a wind is blowing, will this alter the frequencxl*9pa vq1 ry i.y1b3sy of the sound heard by a person at rest with respect to the so1ysax i 9pql1*.by3rv urce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monis fmrs:8 (rdck 7oj9z-tor is blowing a whistle in front of the co cz7rm9s sdk:f-(rj8hild on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the leng9t/unw ai6(, 9ejpeiwoey 2-uth of a 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 lee- eu9, /wti(owj 69y epui2anngth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. H q(tlr u;p/epe:h2e)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() heuqprp;e 2:/tl he not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng jmv.*e4gs7q g9c houq:. noi0ths 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 just above a school of tuna on a foggy xv2a2 +hshps 9q8fz )gday. Without warning, an engine backfire occurs on a hhzfs9v2x)8 qa2 gsp+nother 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 frof u ;f,msf.3ocm the top of a cliff. The splash it makes when striking the water below is heard 3.sm.f c;ffou 3,5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone ;,qr)r0ezerm strike the concrete pavement. A moment later two soun0 m,qz)err; reds 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 error made over one mile of distance by th,g*1f/ +y r cbgo7lg3hz n1gtye “5-second rule” for est3gz ,hytgbr/+cygn 7go1*lf1 imating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level ofcft)f f9oskcy ,bq7; ; vu+0st 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inwz7.v h s37xpd 25evr q4qseb2tensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simhb9r 7 7kqhj/e g,sjg8ultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’ rb,kqge7hsj7g8 j9/hs.]    dB

  A person standing a certain distance from an airplane with s .7nd4(nmfl8ov+eu0j l n4/ta ovbd*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: Add intensities, not dB’s.] dn . l* tfbe478vjnlm 0/o uvn(s4+aod   dB

  A cassette player is said to have a signal-to-noise lhzfr9,7 t*gch br1j3ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each de1jr lf zht*g37,c9 rbhvice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakixgv(f h tm5(m s5h;g5exdll 26ng in normal conversation. Use Table 12 ;eg6 5lv2xlmtghsm(d(5x5hf–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 an eardrum whose a5nej*f dnwak4j8 m1u 6rea 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 modesae+a4i:h7 uzg t amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected age+:7z4h iauin 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 vbv ti1b6. 5big-2rsxjb 2d.t 2.8 m in front of a loudspeaker on the stage.22 i1 jbvt i-bx d5vb6gst.rb.
(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 detec/f2a bs4alwx2(p+ h;o 7x;px ly vpb9rt a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffe;ybpp2r v7x+lfhspb xlo4 aw 9;2 (x/ar by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave39w rp3tjzk io:b2xw. is tripled, (a) by what factor will the intensity increase? Increase by a factorxpw2tzjb.ri:o k 33w 9 of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but o,ump 7tys0s1vzj n *e*ne has twice the frequency of the other. What is the ratio oj0*7t1ms*u z py ,vnesf their intensities?   

  What would be the sound level (in dB) of a sound wave in air that ca;mq2 7c;5u2tpzs xymny2 o,vp-4dru orresponds to a displacement am-xsrcvyu5y2m7p 2;ozmtd4 2; ,p qaunplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve-mzlom w-f2 9dl to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See odm -mw-9zfl 2Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the yt(+fmt q (ai.v1um7z sound level is(yif(mt1.az7qm vt+u 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range j 6o;m ym(foz1of sound levels. What is the ratio of highest to lowest intensio ;z(m mj6oyf1ty 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 fre* l jfqzq.2fp8quency of 440 Hz. The length of the vibrating portion jq p*l 8f2q.zfis 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audib wj: t( yj0le tjmjfosg8:s l4x vyj1t2)c+2e1le overtone2c :x ttj12ge(s4l:jw+ jjyy)s vf10l8oejtms if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant freq/ex khb.2+sq7ks hn,zuency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clo+ khz,en.xkshq27b/ ssed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the5xgn-l2:dgaxyo)ao ( ha.e9wa)t lv6 range of human hearing (20do al:atva6-)x)ly92gneawhoxg. (5 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenc6oika 4z0d0 lcy of 540 Hz as its third harmonic. What will be its fundamental frequenc06z4 idko0caly if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tustg 4d io./lg)cu4ybl u)wm),ned to play E above middle C (4 /b.owtul i,c m)uysl4g)dg)330 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 organ pipe that emits middle C (2ukw3 2m/lomo9 97d uii62 Hz) when the temper9oud3okml2 w9m7/iiu ature 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 2cmvr-l 5j(7r qrghb/d:.ne/qt mu/ +d0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampleplb)0 uj:2azn2uo 4mpgqz/r 6 12–10 should the hole be that must be uncovered to play D above middle C at 2ulu:zbrg az4m0 q6pnop22 /) j94 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, b/rd-f2 mup+ w8)xmyey ut not at any other frequencies in between. (a) Sh 8uy yr xw+e-fmpdm2/)ow 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 endkr i/gmns9: o/q5. lmks. It resonates at two succe9/o:k 5ni.s/kg qrlm mssive 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 pvbna cny43,p3rq; +r$^{\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 i1)p nz e95/r 5dh:h7blpavfbwithin the audible range for a 2.14-m-long organ )9p hzl: h1 irbvbn d55pe7a/fpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside andy6:j2op1huk n is closed 26 u1:pkojhnyat the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to p exko2pu ro 4i.g7 o87a4*)hpjbn;zaadjust two strings, one of which is sounding 440 Hz. How far off in frequencypo j2kzopapg*h74.7a)ebor i4u n ; 8x is the other string? ±    Hz

  What is the beat freqd jx:y rxt6p/my. gu8bh+k 2(huency 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, while+9c o 921g ivi)oxeecw2iiq9 x another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played cve+i 9o 1)egxi92qw9iioc x 2separately, 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 whey0 it64n56 wb*;n7g nmbjezwz n sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fo*etwgn5 n;nj67iz6b4 wb mz 0yrk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sam4 murh);e -cga 0t) d:et8jhxdyy0z6ne 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: Recall Eq. 11dz:a)004;)td ygm-uc6he ex ynh 8rtj–13.]    Hz

  How many beats will be heard if two identical ;i eb ru)/1.cmc4h(hp 3u 3wcyfol z,wa+ a1qrflutes each try to play middle C (262hfru.ypz ac(hcq1w)i 3 l,w c/;b1 +uaoe34mr Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bq)+lt0 ve ywtst4-ry : has a frequency of 441 Hz; when A and B are sounded together, a beat frqt4wt)y 0 -ry:tvsl e+equency 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1. ldeb+onc :9i+dqoon /-bg-3 t80 m apart. A person stands 3.00 m from one speaker and 3.50 m fromqbc bn-dtio lgo+9 +e3d :/n-o 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 t8aia isj k0a: z9we3:yo be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the oth: skaw30zy 98i: aiaejer ?   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 many beatf-yjn)k b-e fc56/*z p-dzm scs per second will be heard? (Assume Tjf sdc)-z -mp5zk/- nyef b6*c = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15eh)1+zp0(jcpj ec f 3d50 Hz when at rest. What frequency do you detect if you move with a speed of 30 mj+(dz 1p 3e p0cc)ejfh/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency dfeoke hus ,jlk8e+ax6x;f5/09r e a v+o you detect if a fire engine whose siren emits at 1550 H+e8hjvsr+fxeo xk 0 ; aek, fe5/au69lz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frgbmkx+ x 9j 6ihhlg5x*lcyn:j(/.w4sequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two fr.4ij +g/ x9:n5 xscjhwlhml6* (gkxbyequencies 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. noyf kip mpbaf7 ii)0yj02 91:When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the yiip0 kn9:2i7f0 m)yajo f1 bphorns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound opwd 7.zy.:ahgrwihgs1qm c 7a*f(20waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receio.*.aqri: cdpmwz yw(21ags fg770 h hved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, t;4 bttl ww-5ayhe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected4y twba;-ltw5 wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a ywnv-,t6;+9ec6q 9suq wne bn 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 freque9be-+qn uqyvenn, 6sw;6t9wc ncy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoundyc26(f-iyb-eydf8lx4l pj ad(j7g d / 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 bea yj7 (dj i/gf fc8yyeb-4 l(dd2pxl6- 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraogt6l+vi4 t5r sonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz.og-qmf )7z* )rfpn2u k When the wind velocity is 12 m/s from the north, what pqu7m)*k)zfgn- 2fro 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 its4*vjj: h4 k;t:so5uwahxux1l 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 Macgbp, (sd9tfga8)- y qoh 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directi8p( aydts q9bo ),-ggfon 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 l29* b(o/qxc0,y xjaq lq7ohkatmosphere of a planet where the speed of sound iscoj 7 9( ahk0l2q*bq/qx,o lyx only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave anu)rq xi*k5 dvxu .y(uo+ *d1jngle it x kr()*n1ijouu.dy 5 qudvx+ *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 c, ixp5cuj1 c/07 i.m)v 07g *lbmlbee.bgjeg$/theta$ 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 km above the groundr qe0k 2/v4k*wl*c9vcuh-kveimo*s , flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.k/e9*4*mu r-,w olk0cvqhc2*vsvi e k 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 devic1lsb wxyw.t- 5a2ul1 ye that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maxituw lwx51y. y1-2 lasbmum 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 .che mt )1b/-gt3urep octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Itwlqqiowc2 .1gcx . m,6 consists of many plastic pipes of various lengths, which are open on both endq1,xm6cgl.ioq2. wcws.
(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 to the threshold abj6z wvk1f:1* 1gqlyof human hearing (0 dB). What will be the s1gfvqb6a :*lywzk1 1jound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB so(y7scjlq ;r:f )dg6i) vgur 7xund are heard simultaneo v:dl x7fu6yr();sgg)c 7r qijusly?    dB

  The sound level 12.0 m from a loudspeaker, placed inevs 2q7 xlr*r wwfm-,f1j;wr6 the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all;1-*2q wwer w,rlx msrjff7 v6 directions?    W

  A stereo amplifier is . ez0: 0qxadrnrated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output ir:xz0qan de0. n watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicegt u3 dt1;e.g2h cv/fqs over their ears. Assume that the sound level ofggc qu.tdf1 t/e32 ;vh a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicat3t uv2u1je t 7s7+y:mo1l .ot j)wtqgwions 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 iu+uy *cdpeb*44nr 2g3tynjp ( s 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 fixed poinx8 +ts0*uze-fhsab3n ts with a fundamental frequency of 440 Hsfhet*xa 8 -b+ uzs0n3z 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 vibrati9d- laxp-pr)/mt wc( bon above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As imx-pcpr/wa ltb9d -)(t 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 is near a tube tha9syi /1t1f. vw:jrgojt 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 mode1oi g.:/ 1w9fv rjstyj) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to6q8,g 5g0vzsz y33smd,wjle k resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-H )jye( e0d+mlgz 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 level is m+(dlj0gmy) ee inimal 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. c ).1 k4skce 3a9gymfqOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed ok g fy34me)a1s ccqk9.f the moving train?   m/s

  The frequency of a stk-+fq( gwvkh2 eam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movik2v -(fwqg h+kng (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of caql -7lcjfxcc1b:nxgf ,xhp2* d6*y c4rs just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a cer27g ldc*yx,:1jp *cclxhbxf4 nc -fq 6tain 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 bevgp k 97)yi9ku q5xr2qq*qs0fat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other? s2g5f*kqyq90)i x r u9 q7kvqp   m

Two loudspeakers are at3j*dikt2kp47 ml md1k opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in F k*dkm34tk pm 71jil2dig. 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 3jz4 rr6 d wt,y:tr3nein the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along we tdjy3 6rt3z:,r4rn 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 whiyuyzs*t22l t ;m3pa4jle the moth is flying toward the bat at speed 5 m/s Ty;j2my*l2tu za3s4t phe 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 frequencyx6aiakov+1 ii6rx- hyv m+p6 nu 4k97n sound pulses as it approaches a moth. The pulses are appro64mavnrn u +kxp6i7ix+ i-o1yva6 hk9ximately 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 the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once ute h z03p 4llv3qc3rk2sed 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 G02pc3r3l4vqlz htk 3e 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 ste)q et 4cjap3k;w /+wncreo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of+p;w k4nq 3/caec)t jw 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, called “singing rods,” involves a l1m8abrlisl;p en4 4k-ong, 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 ro1 lkrisne-84mp a4lb ;d 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 uakofcu8 -e e y3 zt2,p5u-ch-threshold of hearing for the human ear at a frequency of about 1000 Hz is -ek35c yz-t uuu h,2a8-opf ce$I_0$ = $1 \times10^{12 } W / m^2$ 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 observert(7c1yb* qzzk on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altituq yk7t czbz1*(de?    $ \times10^{4 }$ m

  The wake of a speedboat is 15qi8q-m lh bjyv -1w;i8 $^{\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