What is the evidence that sound travels as a was22 llxwxx 72nwe+kr )l9yxf;-mx yj5ve?

What is the evidence that sound is a form of enjbn8dz9:ia *f n/ yyugvd;n; 3ergy?

Children sometimes play with a homemadeq 5kt5nfx5 (u6vd8dv p “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 o uv(n56qd f5xd8kvp5tne cup to the other.

When a sound wave passes fwnu(b ur+ 2+oc vpw9)trom air into water, do you expect the frequency or wavero ut+v+(ww 9pcbn u2)length to change?

What evidence can you give that the speed of sound in air ;iw8u m0e: p/r,o0sufli(bn q does not depend significantly on frequen w0:sep 0( q;uruobnm8f,ii/lcy?

The voice of a person who has inhaled helium sounds very high-pitched. Whyi8fpdu9y- tq-?

How will the air temperature in a room affy +tk*dsxq 8mzmm (3e1ect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sou76nf:gv v-so7ccjht h4y v:t )nds in various frequency ranges. (An example is a car muffler.)nt4s:h c jv gvh7yc)of6:7 v-t

Why are the frets on a guitar (Ficm,m y75bfn ukg 6fa9,g. 12–30) spaced closer together as you move up 79mm 6a,fknyg5 fcu,b the fingerboard toward the bridge?

A noisy truck approaches ya2 hojg0iz53tj e;y :dzk ifhi-4l e3)ou from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sec:f0y oahj; g5dze 2 3jktlih)3 zie-i4tion 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spe6gk 6yj3q54gzg xm/b ace,” whereas beats can be said to be due to 5z46byegxg/6 km3 jgq“interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakp gtm 38glr2:qers were lowered, would the points D and Cm 2:qrg8p 3gtl (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areaschdi,8ku o ndq0f:y4k:n0 zl :dkl.a5 with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the n0dl u d4cl0k n,ki::5z.kay8do:fh q ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12 u bsk6r+sgqd,im; o/0–31. Each wave 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, (a) or (b), are the two component frequencies farther apartk ubiq;,d6sg/s 0+rom ? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source:pst va*eez (+w3 :ro 1qx;wki and observer move in the same direction, with 1i *wexwpv3etaqk: ;o rs (+z:the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the y 18a09jbjmw fv1k 6d 3msf+vtecc. p1sound heard by a person at rest with respect to the source? Is the wavelength or ve6vm8d1+seyc.0 a wf jbmptvc 1f93kj1locity changed?

Figure 12–32 shows various positions of -vgsx3) c w cphz6/)loa child in motion on a swing. A monitor is blowing a whistle inx/s)c h6vg z-c)opwl3 front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the 5z8 mr/k 6or47 dhmqbalength 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 echozrq 4hao8dr mb765/km 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just beloc dl+i--e0tnhad xa5+w the waterline. 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 ha-d-5aelc+0n t dix+ in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng6h;*bhc 5cdnysr-,w e tlz(l0ths 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 fop1y q;-xbvme0t3 .u .kmchb, oggy day. Without warning, an eyomekbc0;b ,-.1u q3.mpx thvngine backfire occurs on another 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 the top of a cbw :*xqv:hd zw 1jsovad)784 pliff. The splash it makes when striking the wat d*:s4 whpq871)xw jd zvabv:oer below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tue8 :h4fbae*jhe concrete pavement. A moment later two sounds are heard 4: ajebf8*eu hfrom 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 f* 9pmes:zut; error made over one mile of distance by the “5-second rule” for t:;p ez9fu*ms estimating 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 of 12h raarr rf9.f t.8xa8lf(2t8k0 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 whos7ccigae d2o4is2x, my 3ig14xe intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound 0ln dsj,6e-cglevel of 95 dB when fired simultaneously at a certain place, what will be the soundd e06sn j-lg,c level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanhj mne9f/p058ad kn4v e with four equally noisy jet engines is experiencin j84mn9d0kna5 f /vephg 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.]    dB

  A cassette player is said to haj1()3yq2ibhin pdi f 3t8ect8ve a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio obinhi38 1y8 qtf32e p) (dtjcif intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a p1z))nidrz( 5f xlpof1 erson speaking in normal conversation. Use Table 12–2. Assume the sound spreads ro o1p)(zr5lif1zd x )fnughly 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 wh ak np2-*s g. p*t+1fkkuc (8v;vzecueose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest ampljy-wv)sel66g7 b roj0 ifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poiyo7 6bsljjgwrv 06e)- nt 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 2.8q6vm jkf/d*;yw o,4d4xej -rg m in front of a loud f6kje d4q/j-r*yv mw,gx4d;ospeaker 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 deh59smpruc-x -pl8 k)io p fn/5tect a difference in sound level of 2.0 dB. What is the ra p snp)c9 kl8-5fo5rmh -/ipxutio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is q9mf8sbnf2kydq9meb x 3ou on9p )c4 p5*jz13tripled, (a) by what factor will the intensity in1sdq)3 3ux 4be*zj5nf 29 y8bo pcknqo9mmf 9pcrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplef8uezf*nu95 8 9giz5o:zg;jh-afekitudes, but one has twice the frequency of the other. What is the ratio of their intensuf5zn f-e95*8e;oj g z eg9izakh u8:fities?   

  What would be the sound level ( w 7,v8s(s)o klyic*glin dB) of a sound wave in air that corresponds to a displaceme ykils l7c wv)o8g,(s*nt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sou ;yaj xmml2 u2two7dd9+uj:,hnd level to seem as loud as a 100-Hz tone that has a 50-dB so +m:yo7,;jatwd u2 m hxd2l9ujund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detet7 dpee1;mwlv k18y1jyf 8mh, ct when the sound ley17jdmkvyhtw1 e; 1mf8 p8l, evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is t b na)m:6,n9stvyok7xhe ratn9:x7yva 6os) tk,nbm io of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengnq(gc 6snc22e e(p ml-a h5ou+th of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mmha ln2 ( +puscq(e25n-6o ecgust the string be placed?    N

  An organ pipe is 112 cm long. 8u)p-na 8: bwtybjdh -,rb *ozWhat are the fundamental and first three audible overtones if theobb-* ) nz8hy:a,p8b w -jrtud 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 frequency would you e ,lixz/ f3lxd v: q9ez1u/em)ie(bx)expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you as f 3x)ii:v 91zq,bduxel/) eme(el/xzsumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of 8glkvh )m(*l-:rqn jxhuman hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requirv ln)qmj-xgh (8l *k:red? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strinouzok m/1*sqzvmqt x 9,zm.:w;81 i9i w *yfgmg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency ifuzswiv.z9, /* k m 8;zmx:y11wim*m9t qofogq it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lonvwm; a xns2 jn15j6lh4g and is tuned to play E above middle C (hv25sj nljan1 6x;wm4330 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 qr( 2,y:ai8a*jkc gw 8zdl)zd(262 Hz) when the temperature i wd2ai)8zc(jg zlyd,*8:k raqs 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 2+(0lgp ,ihf:nd :mduk 0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thaz .wh /i 9jtnm+:e9fue flute in Example 12–10 should the hole be that must be uncoetf/:a z9.whnuj mi9+vered 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 1+ one ,f 2qtttehe/x9616 Hz, but not at any other9t/,2e et1+ xtnoh qfe frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at )2h :pwzud e4p. hg+zcboth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. )pphe2:w u zdzcg+h4. 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 pivikh*,7 wbz u+q a/+$^{\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.tghif 58cq(1 i14-m-long organ pipe at g i5qct1(fih8 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximateltr :jfp2 ajzh21u( b6yy 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate thyb f(j1hua2pj6t:rz2e 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 t 9l pa/4;o y(st3imkybo adjust two strings, one of which is sounding 440 Hz. How far 4ks3ip/m;t ybl o(9yaoff in frequency is the other string? ±    Hz

  What is the beat frequjuax :f 7w5q/fency 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 another (brand X) operates k5 fakh6wnhha*f49 6-k ilgy 3at an unknown frequency. Iffay -n9k6 i*wkhh6a3gh4klf5 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 of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz t2jo w5zzh)4crfpb) -tuning fork and 9 beaprobc2z4wh 5tz )-fj)ts/s when sounded 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 fr2fol-zia9/a ; ,vagxp equency, 294 Hz. The tension in one string is then decreased by 2.0%. a/a,voxa9 lp;fzg -2iWhat will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flu6xe:fi9f0og ,1xhhm xtes each try to play middle C (262 Hz), but one is at 5.0°g6xm iff0hx1 ,x9 h:eoC and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, anwfbx 5-l z c87qpl,iq2d C. 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 4xbc7zw p llf,52-iq 8q 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 are65o 7eq iubdek qw3k0(9grj 3n16j alk 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the otherj 9kr g3olke6ukw6dn7e0b j1 iq3( 5qa.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hearmbn7 l6x4 u*jfb,aih0g bnc0g b),l0 ss three beats e l,xnm74 hfbni0g s060juc ,bg)a bl*bvery 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m awwo5u 4w lvg6 72rhk6g)953 moefgkmwnd 2.76 m in air. How many beats per second will be heard736gh4 ewmog26)v5rk59w kgmlwo wfu ? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when i .xob+wd6q ;mnpil annfyd 2vpj1xt4, 46:3iat rest. What frequency do you detect if you move with a speed of 30 m/s pndxly6 n4fni3o;dv4i6 t2ijma ,xpb w: q1+.
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequencyd1 k pz4y bi-fq5jq1-dd-a lp) do you detect if a fire engine whose siren emits aak bijf1d4z-)q-l5 p -1pqyddt 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f 1sndv ovtw2g/skod,9p6tu )/requency if a 2000-Hz source is moving toward you at 1t2sot/ 1d)vs9/,o nd vwpkgu6 5 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same si7cu+ ur9awjzlo)8o-u ngle frequency horn. When one is at rest and the other is moving toward the uo 8jwzlaor+97cu-)ufirst at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and reco/jl,oogv 79 jeives them returned from an object moving directly away from it at 2597l jv g/ojoo, m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall a e (os3f4r rq*hr7w cc,s)ck(at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the re 74*osas,ccq()rh r krfwe3(c flected wave?    $ \times10^{4}$ Hz

  In one of the original Doppag:br8 w6y-v gler experiments, a tuba was played on a moving flat train car at a frequency of w8grgbvy :a-675 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 station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-frhmx vhmi*e+ 70:uo(ntf* -xplow speeds. Suppose the device emits sou itrxh:*(mhe+ounv7 *f0- pxm nd 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?   Hz

  The Doppler effect using ultrasonic waves of ro1p; 2m (fj;lo hizd/k3 15po* ufcjfd2)joafrequency $2.25 \times10^{ 6}$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 Hzwe x+c:.*s adh. When the wind velocity is 12 m/s from the nor:.c* dxshe +awth, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving o/jc s)n .ks1g( -wdotsn 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 wh4zsy2d m0qziji dd(;hj;d r0 t-wy68jere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airytsj 2 iid8zdd6;0d 4m;jyh-j z0wqr(plane’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 atmosphe sv scetd q(18em;.gxs/a2j3o re of a planet where the speed of sound is only about 35 m/s /a seq1xsvd oj c2t;g8 (3m.es
(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 th7,c (cphjft)te shock wave angle it productcht ,)7 cfj(pes
(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 faf4g9c/j1czqs ad/+ o rwp 1:$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andpqxi4 dq*;wk7 see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear thew4 q pi;k7dxq* 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 pulseslq;4nn t 9ens0 downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is;nnqelst9 04n designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are ir zr9-.wdi /n )r(fysthere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of m yhuss 8qhfe rj2em,8fx9k m(*.92kv pany plastic (8khmv2 98,q.m xshe*rfe9upjs ky2f 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 from a person makes a sound close t2pcw2d h:a m0wo the threshold of human hearing (0 dB). What will be the0:cha2d2 pwmw sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound aryxv km zmxis.)f gpv+w o ,0m0*fd4i *0edu8h6e heard e+mi vim u)yd8 x*pgdox* 0kf04f,sv0whz6m. simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, pbr9 m+ vj+cmbnxk a+0*laced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuar+bx m jc m+n+9k*vb0ming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output df37x/lbif, uurkh1s4j ga:f 5;mmkx3rops by 10 dB at 15 kHz. What ia m 3fxm gf 3 4urkkil;b/u,75s:f1jhxs the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thei22:febyu 5bzf2j/ gva+ d5bnmr ears. Assume that the soun/ bdnv2 5 u5+g2e2b:bjaffym zd 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 distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the ga9 ri(z3n ari w*4q;qbzin, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a freqwbupr -16dvh8 uency 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 bet*v icqz l8jsnng478sbi0t 7 g-ween fixed points with a fundamental frequency of 440 Hz and a mass per uni4 b tciggs8zsn7- i*0 lq78vjnt 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 tube0q 0.,uvdcb uw4gp vi( 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 opening to the water levgud .p c4q0uvib vw(,0el is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar str2 vk-z8+:t/s flo;y ww mtvqau( )ow(aing of 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 reso;tw8 +kwmv)o(yo2a(:q vtlu sz a-fw/ nance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was ob t uu4b)kun36(y ,pixjserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range comi9 aqg+h(eh ex4; oz,dkng 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 farther from one source than the other. What is th qek4x; (z,gaho+ de9he frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statio0k3nzr 1 n0jkpj *spo-nary. The conductor on the st13krs nzpk *np-0oj0jationary train hears 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 is 53i1pw2hve)7u12h er6*ifuic h 8 Hz. After it passes you, its frv h 2i uh27ir)uce*hwfi61 ep1equency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lik.rc e* i9wk0(ijnw2z stening to the differeww z .92ji0kr(i kn*ecnce 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 straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz.iw w pll3*utor3o58 br9r1q ;i The shorter one i9iwtuorl wib 83qo5 l3rp1r*;s 2.40 m long. How long is the other?    m

Two loudspeakers arem;fphv86y2 ve at,mw p7i wig nf12kui1dk+83 at 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 sound frequencies of 212 Hz, what is the beat v7 +8gwiwm2y1 nauf2 evf3pd;p 8itmk,k1h6ifrequency 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 5byb 9ubq/aquzx+f( 5g( 8b( xuq7ou cin the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bubq7 b9(x q5yg5u/qc a(b bfo(8xu+zulood 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 s9hstxsh(se8zd4 2t7 b peed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.348zbx shs7 2tt(d9hes5 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 pulses0(gu-,l5i b qscared+ 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 lrqs-da0 5cgb +(iu,e that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals frov6tx j5f+u -apm one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns wt-u a6fjx+ v5pere used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromist :(:s7hhvgtr )gyo1h ed by the presence of standing waves, which car)toh ys1vht g gh:7(:n 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 fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstraaj7+r/t:gqucgj t 2 b8tion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint.c t2tq a uggj/j+:8r7b 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 hearing for the b2(pjxc zn j3wj9)) rlhuman ear at a frequency of abo wx ()j2zjb)jcplrn 93ut 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 axle* *ko 6tk9 gyu )3.rhgoo g4c5 /jb4odhj:st Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alo :xy4l hu6*e kg4oj jgb*/rshog35)9do. c kttitude?    $ \times10^{4 }$ m

  The wake of a speedby* (ra3x )s47( d*kzttrgmmvzoat 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