What is the evidence that sound traiku oz.v i* g ;rx4vab3(q7or9vels as a wave?

What is the evidence that sound is a form oe(t tojq(5 n,ff energy?

Children sometimes play with a homemade “telephone” by attaching a stryk,-wef9p.)0y,dz uwv vvcxg0e n*u 7ing 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 thvug 0y kvw0,f7ec9z* xv,u w.n-)dp eye sound wave travels from one cup to the other.

When a sound wave passes from air2myq r.rt kmv5bpjt.wt2bd6 ,,9ek b, into water, do you expect the frequency or wavelength t,2 k mj,5 2yt9.6tbp mreqrdv.,wtkbbo change?

What evidence can you give that the speed of sound in 5)mtfda2 . ycx)idna*air does not depend significatmixana ). ) d2cfy5*dntly on frequency?

The voice of a person who has inhaled helium sounds veryxr66s p/;te c8a iz;oh high-pitched. Why?

How will the air temperature in a room affect the pitch of *e zwnmh, 3 mwm4t3.uworgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sountje h ;w w2dx5zu4.p+.m (huedds in various frequency ranges. (An example is a ;z 25+u he4(j.xw wpdeudmh.t car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you 86a 9 x+e-gtihuifm-+w1pbsvmove up the fingerboard toward the bridge- gtuifaivb69 xsp1ehw+ -+m8?

A noisy truck approaches you from raf6gfu 7iq u98c1 i/ibehind a building. Initially you hear it but cannot sei8fa ci /iu197uf6qr ge it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space1(:qhnkid;e g,” whereas beats can be said to be due to “interference in timi1 d ;ng:e(qhke.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredlhh .)gs* ea5f, would the points D and C (where destructive and constructive interference occur) move farther apart or sflg)e5. ah*h closer together?

Traditional methods of protecting the hearin/idz 0in9*ghbkjfh)*bqug/ 5 + z:kq jg of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, tjq*iz/jqhnk ) *gbb/:5h f0 zd kgui+9hen 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 o5hdj xg/:etqo / oae+5f as a superposition of two sound waves with slightly different frequenceeqd h5:/oxot5 j+ag/ies, 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 shwutdt 9.znis. j--, ixift if the source and observer move in the same direction, wis -,d 9in.xtw.i ut-jzth the same velocity? Explain.

If a wind is blowing, will this altead.46( d-cg8f, sgc bc8lksxjr the frequency of the sound heard by a person at rest with respect to the 86 dxslk.g (csc84afg-,bcd jsource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion uc3p70/ bvx m h:dl4mg/x:ym xon a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? xup0m3 vmby:mx/ g dhl c7x/:4Explain your reasoning.

  A hiker determines the length of a lake by listening fk,7 q3ov(e+ tcqy el0mor the echo of her shout refloeytm+0 k7q ,q3ve( clected 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 justbn 95hlxik x4 fri;how+ h4:9g below the waterline. He hears the echo of the sound reflected from the ocean floor directly below ihx9br +44xnhi 5 :wkghf;lo92.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atsvi)wk uodju/b (rf56 4z4;;msqts x3 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 driftygfg jw;g n/u-f + /ul4bzm;(hing just above a school of tuna on a foggy day. Without warning, an f -+zfub/(mu; yhw4lgj gg/;nengine 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 cliff. The splash it makes wh*ou )eyfi b2hh;1:5x brnk2 ixen striking the water below 1x5yxe fknh oh ubii:r)*;b22 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 the concrete gmuu 4db7-c/j pavement. A moment later two sounds are heard from the impact: one travels in the air and thebmu ucd4-j /g7 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 b j1zoep ui//d dd6z78uy the “5-second rule” for estimating the distance from a lig/e u di6o7p/j1 uzz8ddhtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound a s.+kc rbhoa6bun)m03t the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity i0z9 f 2fxey9mqiw)0 91v ,ghestcwg1 ms $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB-l i.7se6;a8e tomkdl when fired simultaneously at 76ist ;-elekom ad8. la certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wki8dbn5u),l2xky5jb ) e kc5 bith four equally noisy jet engines is experienci k2un5 y,ilkk8)5c)dbbe 5jbxng 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-08 c xf4diy9c puum+f said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiesc4dyum8x-+if puf09 c 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 person speaking in normal coucd0 7z,i9*rnmpg -pphlv6 dh a b1r04nversation. Use Table 12–2. Assume the sound spreads roughly uniformly over7ac,*bgrdphdmvlz p4p 1 ir n-6uh900 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 are p(riu 8wf*x/ea 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 moded 9x21f7h-4cmkqyuk w8vk, rwst 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 c- 9v4yf1kuwk 8 wdh ,kq7mx2rconnected 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 whec. lp4ba2 sp/jfkl8: bn placed 2.8 m in front of a loudspeaker on the lb: 4.b28kf caspjp/lstage.
(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 diff1ayo91gok;f n fe zx9*erence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffeky o;9affen 1*g9 x1ozr by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by :0 gviiv rd;r:what factor will the intensig0i;idrvv::r ty increase? Increase 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 frequeghsjs2 -av (fhq1) i8y,( kut:t n,zblncy of the other. What is the ratio of their intensitisb st tk(n,v, ugq)y28hf1 a h-jiz(:les?   

  What would be the sound level (in dB) of a sound wave in air that correspo)r; 0*opt jabi g-hjg*nds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300*gbj t0rgp*-)oi;jh a Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hzvn 8 58yrxiq,twz*j fmab28 q( oqhw3*b-rxc: tone that has a 50-dB sound level? (See Fit3(:*hcy a8 zb fiwv-w52jb,*qrqmn8rxxq o8 g. 12–6.)    dB

What are the lowest and highest freq b v.bhg33z*utuencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6 u3tv3.ghbz b*.)

  Your auditory system can accommodate a huge range of sound level 1w rkk/xm/+jfjn8)my s. What is the ratio of highest tok kr/yj nxw m18)j/+mf 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 length g(:sa2l;1qj(ovw tad6fz/l u x ,m3 ioof the vibrating portion is 32 cm, and it has a mass of 0.35 g3vtlu:z wi,s mf a 1;ag /62j((lxoodq. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental andk mio ,/v*ev3d first three audible overtonek/o 3*vvd e,ims 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 frequency would you7hjby5uu um y7)3b3u2 mltd (y expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wasb2 bmt(uu37ly) dhjy7u5 ym3u 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 s,v:g.urr:3fx bdm 4hi+/o syxpanning the range of human hearing (20h.rx m4v3d/x,: +y:i ubfsgro 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 frequency of 540 Hz as iexl,0+ hgutg9ts third harmonic. What will be its fundamental frequency if it is fingered at a u9x0+ t,g hgellength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunegi(qc9z;oz1yf gx cng,q8 4(hp;sd4cd to play E above middle C (33;sgqzdx ( (1cf cg9ci4ph,g yn z;q48o0 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 (262 Hz) wo2(3 kb8m ims3hcmi/xhen tmb2s kxc i8m3hm( 3/oihe temperature 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 w 59yu( tueh /+lq3dlx$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examplea n; /jnzqhbu3km4 s01 12–10 should the hole be that munjz/m3a0u nb4 ;q1shkst be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hdhaa h6h(;z4p- s d 3b*hp.8aezbvdke;6iaq- z, but not at any other frequencies in between. (a) Sa;dv phd-.ph*6b8q4 h3hiak( b ze z;a6-d esahow 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 fu 8/3qhcso), zwbb;efr5 4alopen at both ends. It resonates at two successive harmonic 3fq;f ,hoebb8c)rl4 za/wu5 ss 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 h u4d0:k +wnbz$^{\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 fovicg5 ss5l99 m,c 7tdsr a 2.14-m-long organ pipelv md5cs9,s cg97t5si at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longwl+a(hxiz ,lbt /h-.f. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audibl,lh/xfz.bl t(-ai +hwe 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 sias0u75*1e:wf*r exd+ p m1usvwd j;x when trying to adjust two strings, one of w 0p;:u*1fr5 u vx+xadsj esw17wdem* ihich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency iow hxt j tqxjrf04o3q0b416v2f 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 Xlsp/.b - o;u mhx: n-acrm1u(u) operates at an un-ah:(cbo /-mn r.musplxu 1u ;known 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 sounded with a 350-Hz tuning fork and t2j b k)e;f9(pcsry5 h9 beats/s when sounded with a 355-Hz tu; p2se)b 5y hrfjt(9kcning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequ)8vmmydz sd*: lap56lency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be 5 zpv*8sda ydl):ml6mthe 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 flutes hlq:+1r ef uc4i08maheach try to play middle C (260+uq18ehhcm l4r:ai f2 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,-s2o- mjd c2zs09o maeef,he B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of mfoahz- c-sm e 0s2o,2jed,9e A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker nnr cz +2librj:wp0t)0*1afwand 3.50 m frw)znnrf0i* + 2p:w0jat1 cblrom 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 e v+)bgq)1ug g979s7mktlq nch-j8lx to 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 t-q)l svxh+g79nlkc u978j eqtmg)b 1g he 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 p2v5jklhz+ funad3212.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 12a3 pfk+lz5hjdn 2uv$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s si0ztfr48gm5kb 2 jo: wjren is 1550 Hz when at rest. What frequency do you detect if4jm :b rf08wgozj2t 5k you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eny a.*ai z.t.nh)llf3qdzckz axn, 1 )3gine whose siren emits at 1 k azfq ax )t),.cz3 .1y.za3indl*nhl550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift ir31lsy2vxf k1ty 3o-sn frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at rv s233yyfo-xtk ls11 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 single freqn*wt8c( s-zo xuency horn. When one is at rest and the other is moving toward the first aon-( st x*zwc8t 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 soenacv ;8v2h0eund waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivh e0v ean;v8c2ed 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 ultr c b *gat-pkx 8zab3;;gisdy.tcc0/q* asonic sound wave with frequencx. s -g8kzctc/ ca*;aqgt*i;0b d3ybpy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tub47hf ra 1xc1klnh0guh5p( ui7a was played on a moving flat tr0 7 (4hnfrp h k5ch17u1lgauxiain 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 usese.spzfm3n x*0 ultrasound waves to measure blood-flow speeds. Suppose the device emits sound azen *3.x mfps0t 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 ultwg h8nr792329znuhet-p1 qg yxk lkw2rasonic 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 4wptm.*5 eoib570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at r.ebp 4w*o 5mitest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed cza1*lk fxgt3)tk+i: q- + nciat 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (bz m,*mc1zx0:qh2 qaw a) What is the angle the shock wave makes 21azm0h wz:c, q*qxm bwith the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where t*sef );:sw fothe speed of sound is onl:* ofss )ftwe;y 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 angsq o pc)zzx t893t2jo3le it p2 93)zo8c qt p3zxtjosroduces
(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 pazbn,fx ge y;4:u/,j: hmww/$/theta$ 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 ex:v8.9nfrf kcxb.sl 3x actly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic bolbk 8sfxnf3r c9 vx.:.om, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward beooq2mijg ,u/syc/ bu18rf0 p /;,oyfrom the bottom of the boat, 8j;,// 2qpg1riocuyob sbu yeo,0/ fmand then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves ar va*z p fz(,4v *7auibs;:gb7dwksmhw* go(s 8e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Iwke.cj)dx, gib3p z 5:t consists of many plastic pipes of variou ).,3dx5w k:egi jbpczs 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 makez8v07hq (n;ir5xa; qhib*wnh s a sound close to the threshold of human7h8;5vb ah0 irnw;z*qhinqx ( hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB q nbg1( (o -:komkxou.i0t9gusound and an 87-dB sound are hea.g9to k 1 go (xqio-ukbm:u(n0rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker g 0joxb7mcyi8k2iu nc (ok7 x;d2)-kr, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equ mkk -8xx2;c ybo (kiu)cjd7g0nro72 ially in all directions?    W

  A stereo amplifier is rated at 150 W ouyz0te.s+kyt+2 q whdgj8 8w-rtput at 1000 Hz. The power output drops by 10 dB at 15 kHz. k 2+8zs hty+ t80 w.rq-wegjdyWhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices -,e-mslg *emz lt0r 5oover their ears. Assume that the sound level of a jet ais0gel * -t ro-ml5,mzerplane 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 communicati 7r,,sbg;2 g: vlwkl ,ibdh3xnons 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 violin1 w:kv8ln4 p m/lk8bqe j6k:qh gv-kh0nj/a3h is 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 violi9dj td**1m bpb*8j nq qa;cs(xn is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit lnbs 9dmqdj1*pxb8t a*; c*qj (ength 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 vibfna1kjg;1r: )yp6efk(, ng cbration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork wh: jbpf6n,rfn)(kke1gca ;y 1gen 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 stringw;eehy7h -oi 4s *+sis of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should b ;e7-sow+iheh s4 syi*e in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as e a4 dxwb.4vi d8xf+8rone 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 from two sobt3udgz ;ve/,d/k9hq 23bhu vurces. The sound is loudest at points equidistant from the two sources. To determine exactly what the freq233e/ kdhh;uud tbqvgb/, zv9 uency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statiocw2vd 1bilb qa99gwt 9l: h3n8nary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed acwqi98dwvl 1th3b 2:n g 9b9lof the moving train?   m/s

  The frequency of a steam train whistle as it apph oc5yi s/; x7h )-vi15ptghi,xp6 pwhroaches you is 538 Hz. After it passes you, itsipx-yis 1xp/7h, t vh5 )hc5hp6gw;io frequency 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 ofw 2*qt 22jjrnd cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightr2qtn 2jdj2 w*away. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat i: a2n8k9ivegcwzcpka) m33 )frequency of 11 Hz. The shorter one is 2.40 m long. How long is i8 :m ng zi3p)e2kvaca)kcw93 the other?    m

Two loudspeakers are at opposite ewe(b /ku4oe+e 2o5lc wd- (ppynds of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the sy( o+ke e5dpu(we2wpl4ocb/-peakers 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 q; 8xn e7*jqqfflow in the aorta is normally about 0.32 m/s what beat frjqfx;qq8 7en* equency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speedchu((kz7 ad--m6k zue 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by tc 7-uzea(-zukkdmh( 6he bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency31v;h lwhqw 4c9 :ekhmjor/1y sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is ab3hh: lmo14ver j qcww/;1k9yhout 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 used to send sig lh7j/w9 ,)k(5hbrxkzj zls3 tnals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 1z (tz3l5r /lw)x9sk,7hb jkjh2–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by+ 7 irl m25eokj:toc0 8vra75obc.vgb the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing wavl8r5c7e0ovt75jc:+. ivm bg2o baokres in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv-u fpw-t d1w .:xla-7+tor lxuz1c0vfolves a long, slender aluminum rod held in t 1-uaxf7t 01-d:p.ctzxuo-w +lrfwv lhe hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshwlb0 hvb 2wda68/4ou nold of hearing for the human ear at a frequency of about6n8 ol/2 bahvwdb04uw 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer z/g;s3k/o,; wkjrv cfon the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alt;cw;k/,3fosrzvk jg/ itude?    $ \times10^{4 }$ m

  The wake of a speedboat mtr)kx+pf) 5uis 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