What is the evidence that sound travels as +j1q-an e/qfi;d7 ul sa wave?

What is the evidence o 2lgb0p1 ukb(c;3atv0cb ps*h 4s-hlthat sound is a form of energy?

Children sometimes play with a homemade “tele )srl13klqe q)phone” 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 crel lq3s)kq) 1learly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o)h9ro,+l-qp 5na,fbw kxu9bn r wave5u+bnown,rf9 alq-bx k)9 ph, length to change?

What evidence can you give that the sk 3h) k2njpc.gyqq n1x81fhg5peed of sound in air does not depend significantlyyj 5xcnf k g q1n.3hkh21qp)g8 on frequency?

The voice of a person who has inhaled helium sounds v( z,zn3ir5-ds ac-o cmery high-pitched. Why?

How will the air temperature in a room aiu(a f5wks7 f9yu)dwssvj2 9 :ffect the pitch of organ pipes?

Explain how a tube might be used as a filter to -poqnjjrxf;5kxo9.( g4sf6 :a2is nareduce the amplitude of sounds in various frequency ranges. (An example i 6 s9 q :. aonnpxkgjf-rsij4;25oaxf(s a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c /jvciie5nz0wt(c86vt cr c+; loser together as you move up the tznic0+/;c e c( rti85wcjv v6fingerboard toward the bridge?

A noisy truck approa ctr*0)lnd- jb5.nej7a: zgmzches you from behind a building. Initially you hear it but cannot see it.n)5mb*.je0zlj zrgtnda-c 7: When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas be01rw ,yc 3 ayte-nej62j7)3vav qirhp 8d6fzaats can be saiv pye1r23e hvrdy wja73606 cn-aq ,fiztj8) ad to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lor7shjxmz5 mrf/ 8k7)1b7 tcctwpf2n - wered, would the points D and C (where destructive and cmtznmxj tf 8 wk -pf7h12sr)5c7r/bc7onstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wito, a ,gn x.kgod*-px4dh very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reg,o4-.pd xa nkgo, *xdduce the sound levels reaching the ears?

Consider the two waves shown in Fig.- u aa3wk: otnn(ng*: m11hbkt 12–31. 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), awk3tn obt(:g1 n *1-uhk:amn are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in t-itx3n92(sd bmm ;)/rig+yj/m ekzu ihe same direction, with the same velocity? Ex 9e;yit+s2ri mdgj3 k-)/nu/mbi( m zxplain.

If a wind is blowing, will this alter the frequency of the souiqdrdoet;3 o .( avg8w5;j ixc 0z)p1d y.yy)wnd heard by a person at rest with respect to the source? Is thej)yz i.gy(o.1y);ecw tav3iqx ; rd8wddp 5o0 wavelength or velocity changed?

Figure 12–32 shows various posit u y(4b*wigiwlwb(q00ions of a child in motion on a swing. A monitor is blowing a whistle in front of the child*w (yl0iq0g ibuwb 4w( 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 lengte 2g;hue3 +vyjnj z9 r*b; o,o3lj+ 1vxixn;bmh of a lake by listening for the echo of her shout reflectednn i,+1xr;*ylob3 jz2bj9gem ; vueo h ;3vx+j by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship ju8 zgbzz5r /,wust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. Howzg5u/8rb zzw , 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 )p p7 rlq4t/mw$^{\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 j ar v9n ) 6*u237ssoqxxcj5jwdrifting just above a 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 backfire is heard (a) by the fish j2xao6jcw 3s)j*nv9 uqxr57s,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makuq n s01rza,o9es when striking the water below aur zn019s,oqis heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the groun 3f(1d+- v um9l3vd,,mztyxrefdn*rp :8t awid, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impacz8v*f n1:d9t m+ y,pd uf3avewxdi3r-lt,rm( t: 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 the “5-seo(gtg/,ve hk/cond rule” fgt o/eg/,vkh(or 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 120 dB? v)h , nb4.ltwm   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 whoo jxl3at (n.s)w/yu, qse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atith,k, fd.rj w:5g- gi a certain place, what will be the sound level if only one is er -:dwgti.g ,jhfi5, kxploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallf/ 7cev.f kchr, tswxl)184osy 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 i.cfs/,kr4)chs tx e7w o81 lfvntensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 kyl00i7 2xi fgdB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 d 0y02 7lifxgkiB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from al +b pgb+i(e x*:n)odt person speaking in normal conversation. Use Table 12–2. Assume toebgdnp lt bi+ +*():xhe 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 ear-1 4+rtqyfd xn t-iz9sdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the mo8pnn ;ojiwjb r 84l,.jre modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m .8l4 b jw;o,r8ipnj njfrom 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 xie,b4;li t8g registered 130 dB when placed 2.8 m in front of a loudspeaker on the ;ii8eltx g,4bstage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound lyo)i3a, (g u/ ljuag,fevel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by ,/y,l( afugig3a j)o uthis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is a zx7(- dh;j4idhfhrg 0ptvo 8.qgc1 8tripled, (a) by what factor will the intensity increase? Increasr(i7.q0vj;o48-zxhfggdhcp1 a8d t he by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fmak 5xaerkz7:wezvdr,o:+53) r+vxg (us7u g requency of the other. What is the ratio ofkd+ mrg:vzs3(vr w,o:xx+7eaeg5)zrku a 7u 5 their intensities?   

  What would be the sound level (in dB) of a sound wave in airoo7w c5b-.tw6u re kh2*m3lbv im/f0e that corresponds to a displacement amplitude of vibrating air molecules of 0.13 m6-wvt7wbue2ef.ommr/0 clb kh5io 3*m at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hzi2k 4gmx wp 76aok8*a;axik8z tone that has a 50-dB sound level? (See Fig. ak a7kk*pi4x;ai8x68 2m gz ow12–6.)    dB

What are the lowest .l;s h 3fetf5nz. byv(and highest frequencies that an ear can detect when the sound level is 3.5h.n yebzvft3 (s;lf 0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of/yxtqg: wl**v sound levels. What is the ratio of hgl wqt*yx: v/*ighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz.:3f n/u4t: mo4 qnkd+5go s+u8vewoyc The length of the vibrating portion is 32 cm, and it has d5 o4 /fnyenuu+ c som+ 8kgqv::w34toa mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thw)x ol8wb-j1ie fundamental and first three audible overtones if twb8 ol1jxwi- )he 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 g8e0wnbksvx +fh t2itd 9*.1 yyou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was yiwh x9*sbn+0ek18tg ft. vd 2a 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 jcv0wy.x,suaw:,2 p zk :szjkur 6( 5mhuman hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes rm: akxzu6u0cw 5p jky2,s:zv,srj( w.equired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a f1tc)-cdrltp. requency of 540 Hz as its third harmonic. What will.dpt1)tcrl- c be its fundamental frequency 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 tuned to play E above midd kn792opr 0boix x3y:lle C (33 :yori73bxk x2p0n9ol0 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 m* ooqu3 d11( s dadhg;m*1*rdrj6xnfan open organ pipe that emits middle C (262 Hz) when the tem o6gdo mm a*x3u(fjrqhdds1 * 1r*d1;nperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 nz olou nm4b*dhl7y :82+kj*u$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece os13, 7 .tq(tv3w8+j k keqbaftfi.hbxf the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C +t31(.f3. bkiqwe fatjx,7 qhvtsk8bat 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, aidj 0 nqzgp7-nv 4oyv(8p 0e*tnd 616 Hz, but not at any other frequencies in between. (a) Show wpv0g-i0tqp (y 4njzov*ne7 d 8hy 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 ops1 m ast5egyhp z-u975en at both ends. It resonates at two successive harmonics of frequenmu sz1h9epys t5ag57- cies 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 -w /hz c+ sq5wpln/yc 0)gkfc-$^{\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-long org( 2:ijui:de1kkyg( a gcor24wan pi 21u(eig d: k:y2gow a4rjck(ipe 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 ts+2vku9kw rx 3vtwex h0) )pjdfe1f2; o the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible ran);k j )02pv+uhxtkw9xf1rse2evwdf 3ge) 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 sjn ysvn d40cf(bxq;*a7 q;vu+ trings, one of which is sounding 440 Hz. How fdv;q;j4cy 0+xun bav 7q(*fsnar off in frequency is the other string? ±    Hz

  What is the beat frequr5s.oi ,0my(kjy -ap vency 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 kHprp9k ic( lpo* u(; g/a2;gavkz, while another (brand X) operates at an unkn2 gra*oi uk v(cp/(lapg;;p k9own frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when s5 7tv ev umi0q ri m4jr*6n4ihuq+/kp7ounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrat7i 704p6vrimhq qv4ni t*re+jku5/ m uional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to h;(i .la4gglnaq)/qvthe same 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: Re4.aq )g q(li ghv/aln;call Eq. 11–13.]    Hz

  How many beats will b8e32(d v5n cvhe/tlsu 67y5u y9caudbe heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the otdeys2vnlhtca uu 6vb5e3/7 95 u8 d(cyher at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 43g-yn 2zi id0q41 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and3qiiy20-dg nz 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 m,) :qy1h ,wanfy nf.wapart. A person stands 3.00 m from one speaker and 3.50 m waw n,yqm.,h:fnyf) 1from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, ze6 ,kdwy: yxbm-b 9y*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 otherd b k6-xwymy*9b y:z,e ?   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 2e0t lw: 9xo4f)j4qrbh.76 m in air. How many beats per second9o44eb j: fh q0w)tlxr will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freq yn44sbvyntm*ss8p+72, jurvq( xo + ug 8pos)uency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a s7s+vysn topj*8+rubn2 o pu,q44mvx)8s( sgy peed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stillbx7wz88fepxa b8, 2/)1 km tpihnkb1d. What frequency do you detect if a fire engine whose siren emits at 15 x88z , pk/hbtmkxbfe 18n)b2d7w i1pa50 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving tjz:jl9l7dd0ov)di 8toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exd8 z 9:td0)d7jlivoljactly 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 frequencyf2apqf8u) x z/ horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a bxf/ 2)8qzafpu eat 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 jqs9i*apr .o 6ogq;( 7mq wd*band receives them returned from an object moving directly away from it at 25 m/s What i7 g;d9( awirq*q6o*.qsop bmjs the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an u4fnt/jt)w r 2pltrasonic sound wave with frequency 30.0 kHz. Whatf2)wttrpn4j/ frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movvl 72nz-(f zwping flat tra -7(zplnw2zvf in car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow vfiq)8 l5fa t4speeds. 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 bl84iv5f)fq talood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic we u.1znm0z: ta d.0uqc6pdp s6aves 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 oxepm,*kxaxq,nh k-3 2 f frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are locatenx2k-a*m q kx,, e3xphd, 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 oiq0.u98r bus 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 where the speed of sound islq++*w+ v :ro8b cm,osiv lq5e 310 m/s (a) What is the angle the shock wave makes with the direction of the ai,:+ +l8m svc*5 +oqieqlwrvo brplane’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 atmosp x)8,ytdd*ztzhere of a planet where the speed of sound is only about 35 *)ztydxtz8d,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 travelingn*j 6fxmk4d ;i 8500 m/s strikes the ocean. Determine the shock wave angle i 4jmf;i dx6n*kt 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 ;pjz;an1 :s:wc9 akif$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see g5 c(fe cwhf+2sge omx-2 js/ a//unk9a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dihne c/gfwsco +/ue/2kafj-g9xsm 5(2stance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward f8agik0 tqzoq e m;,:z4rom the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is theezgqioq, :tz4;k8 a0m minimum time between pulses (in fresh water)?    s

  Approximately how many oct/d., x dmcw; 8fik2aznaves 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 consdybs-ip 0lbr x+*53 7u(oaift ists of many plastic pipes of various lengths, which are open on both ends. sap +y7 53u*t-b(brxd iiofl0
(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 of hu.l ,wl5q n ldv4gwjx1ed) ta64man hearing (0 dBd4)v6wtxg1d lj 4 laenq,l. w5). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soundo mojz41j4);r.fhb nm level when an 82-dB sound and an 87-dB sound are heah1 o4 mmjr)4.fbonz ;jrd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, p 1nvehat77z)svo5)i) xloqd yq5/6ga laced in the open, is 105 dB. What is the acoustic power output (W) of th) 7qqd ao) s/v1zx v)57oity5aeg6lnhe speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated atsoe2 *w y;lt iv3dbqm3bb28z6th+,sq 150 W output at 1000 Hz. The power output drops by 10 dB at 15 k2m t8v3,2ibbyohez;s*6 l dq+qwt b3sHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typa96rgwy2ti glpawl p;/4 ccf00z6yd :ically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. i gd:z9a4wlclgw62y t0f/6ra 0cp;yp 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 communi 0 v qx-jlv37nn:d 56kiflq)wt*fvb*dcations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is swoqp ;p(. usy4l o23ctuned 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 lonpfji:s -xz:lly) lv cig9 6n6/g between fixed points with a fundamental frequency of 440 Hz and a mass per unit length o6:g -c:z)l 9pif6/jlxnl yvisf $6.1 \times10^{-4 }$ 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 watejypt 3dtw911.tive v)r (Fig. 12–35). The wa wt vj91)p1ieyt.dtv 3ter 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 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 mag az,9gcm h1c7ss 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 c hmgzg9c7,a1produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed9 gnsiu (g-,.6mhyu : 1bxnsab 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 coming frt ybi 2ow djjy)u)nx8m68 sc;*om 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 sounmuw82c*yi) 8;dyxnbsj6 )j o td level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One tr:5 c20/p secdvmdk ox4yn7 t;zain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other traix /ntk:7 y s d24o5pczved0c;mn approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it apdvwlb, -:i- l2sdbad)-gtb z-proaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was theb -z:2b -- all,div-gtdbsdw) train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thgd zp5 +o7 ;r0fmf:;y):o v ypchj/adse 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 spc;v5ga s ):pr/0h:+ fddmozj ; fy7oytraightaway. How fast is it going?    m/s

  Two open organ pipes, sounding.1p mug,e5mcj,3n d kl together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the oth5 pl,,ed3mj. cmgknu1er?    m

Two loudspeakers are at opposite e4bzsmm)ft*)c gu5wa 4 nds 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 frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) )4w 4gum s*)cb a5tfzmhe 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 )3fq8)h r1,slzrj,y8tbb9n ,az9btq9 ud pmx 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow uf8b831arz)j x lqntt9,m9r ,yps qh b)zd9,band 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 69bfo (dv tm3kwhile the moth is flying toward the bat at speed 5 m/s The ba6kodb mv9( f3tt emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pu :0t(m9 zi;gjzbmivt 4lses 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 0giz;i(mt:m4 bt9 j vzdetected 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 usv 6h,lu+tnsgs77 .9oqgwh 8qpidoc:+ed 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 p:qdn69i h78t7ss .wcv ggq,huol++po opular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening c+cgwjl *r4u6q an be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and wc ulj +r4q*g62.8 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,” inhzei-- k.; j mjgk:4involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the ot;:.-j-gkeh njk4iimz her 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 human e hrv- u70 zlww:o9i+v6fh:ze war at a frequency of about 1000 Hz is+w w: :o-lvzzv0re 7hiuwh69f $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonis)uq :-/2qbbp e0c(mdxv4hh zc boom 1.5 min after the plane passes directly overhead. Whaq4 2m sxv h/ bcu0b)q:e(-pzdht is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat istw*-j/ t6k v ba.w0og,gdc:bd 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