What is the evidence thsb6my7gu4 n/l at sound travels as a wave?

What is the evidence that soupsu4m4 ux6flo+pu5 6znd is a form of energy?

Children sometimes play wcxr6 vzjf) njs -0l2429uhnshith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–xshjl409n)jh2n-rszc 2 fv 6 u29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water,8kv.gb2akt87lg09xar j xdp )q :teo 2 do you expect the frequency or wav)tal88: bk29t7je2x.xr g a go0qvkdp elength to change?

What evidence can you give that the speed of sound k wwr/45p.uu,at-kk.ncj 9zh gbrw)6 in air does not depend significantly orkrbntc.w)zu9jkg p,a -. ukh w56 /w4n frequency?

The voice of a person who has inhaled helium sounds5mppy7:45dh d cuft+ z very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgaa .- c: 50wtoev in q,hzep4da:ihfw(:n pipes?

Explain how a tube might be used as w4 x x.utuyhc3np 1k/8a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufflerwtnh3x4 18 yxpc/u.uk .)

Why are the frets on a guitzbjj2d( ddv23 ar (Fig. 12–30) spaced closer together as you move up the fingerboard toward zd(2j 2vddj3 bthe bridge?

A noisy truck approaches you from behind a building. Initially you hear x+iu .8niw6bhit but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffr wi.8nihx 6bu+action.]

Standing waves can be said to be due to “interference in space,” wheres)xojy 9 z3d .2ve 5d9:mm11ynducdbeas beats can be said to be due to “interference in time3sd 9.bdy j2meme1oc5zd :u1v dn y)9x.” Explain.

In Fig. 12–16, if the frequo; caf:y)+pm*rjuz o. ency of the speakers were lowered, would the points D and C (where destr*)ro+f;zoj p. a mcy:uuctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who h nw-nh kq1,4d h-ph(,i1kary3hc3a fwork in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How -f a1k(a -ch3hny,hq3 1n4i wph hk,drcould adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave +l-oyfrz ;t)gh/1cx-4pkgzm 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 apart? Explain. -+zfr4co/g1 t;lh) mxkzyg-p
(12-31)
(12-18)

Is there a Doppler shift if the source and k88 l z-de(6tnj7pztc)ma5 rwobserver move in the same direction, winp8d zm -awk5c8r ez6l7t( j)tth the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard b) gbhj/fzd-t*y a person at rest with respect to the source? Is the wavelength or velocith zdbjf)g/-t *y changed?

Figure 12–32 shows various positions of a cx6/k i1gpa49d3kn5n u z cg9mmhild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. g p4993axcn/mnmik5u g6k1zd 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 length of a lake by listening for the echo of her shout,b xplk12)twt reflected by a cliff at the far end of the lake. She hears the echo bwpx,2tl) kt1 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlig;tq*z2q53 yu1qq;zydk yh( r 8bp) tnne. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary sqbqr*2dz ;nz; h )t1(yq3u yq5 gpt8kyignificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveic lgft i6yvpbj(5 .14lengths 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 vf4oaz*a:;-i +h;wqf i ebpqp0 8von 3a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–: biewqi4-8f ; 0vz; q3ovo*h aanf+pp33). 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 when striking th;enm yyrg24p* e water below is heard 3.5 s later. How;4m2 gny*ype r high is the cliff?    m

  A person, with his ear to the grou.,xgprukoav.)3ory/ lt (dq*nd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travelsr. )op*au(y.kl t,xg3dqvr/ o 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 dis 7stavyu :-ucmi.o 4:p5vcgtp kr06 .otance by the “5-second rule” for estimatinyk: suio- c7. ua40mvrtc oppgt:v6. 5g the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ikh ng e:.ah2op 53r*gof a sound at 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 soun ofg))27dnpxad whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired f3rz qls7:h1 wsimultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intenshlwq1f 3zr7:s ities, not dB’s.]    dB

  A person standing a certain distanceb fro+5:j +mxegvr,-k from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captarv+ jfgermk,+:ox - b5in shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to haz,j67abd6tkhq(g) e snjro; ld9li7 dll97p1ve a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sz, 1e (jlddlo)ldqpk9i gtr7sa6jh 779ln6;b ignal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe0:t v 67nuias)rb6y bmsdh.5 xr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound sprea6t)hiv.b:r a0bn6s mu5dyx 7sds roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum who(khsxlzkg+ + yzl 5)d*se 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 amplifier lz.6;j84pg k3 ujx skuB is rated at 40 W. (a) Estimate the sounlsu j .3 k;ugxjkzp486d level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter r l cs8 3xaq49vq7ankf7egistered 130 dB when placed 2.8 m in front of a loudspeaker on the a3fs 7lx4ncq798avqk stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a dijzio3i8;q) 1w;govwj qh pv,*fference in sound level of 2.0 dB. What is the ratio of the amplitudes of two 1goi; 3*; qvvqz8pwh,w) ojij sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor -s 4b kovj/k(fwill the intensity increase? Increase by kb ovs-j/4kf (a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equk amoo75q*y3 bal displacement amplitudes, but one has twice the frequency of the otherok*37 5qm yaob. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air t2of 0zlekm5:-5rlwja;+i vg mhat corresponds to a displacement ama-r0m+ wez5:5vllg;k 2 fo mijplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level mclg/y7l 6e c a-xqvol2s96h4 to seem as loud as a 100-Hz tone that has a 50-dB sound a yclo gmql x-v46/hl9e6sc72level? (See Fig. 12–6.)    dB

What are the lowest and hicr;2:kc y2 ca569wi pemesax ;ghest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)9wik6 smpac :ey2xrc2; e5 ;ac

  Your auditory system can accommodate a huge range of sound levels. What is thes 89/ekxhj,fv-vy aj0 ratio of highest to lowest intensity at9s /hxy-ev ,jk0ja8 fv
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamj 9+)h2lqx:ydjz c 0heental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass ofqh0j y2hl+jcxde9z :) 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fw9h;b+i o/c :cysd/t tirst three audible overtones ifc s;htdb tyoiwc 9//:+ 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 you expect from bl-b:xqbku9g5tq 2cl.d e7of5x ,l ;zuxowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube?9 q2uogb:x7e .kcqf, 5bltx5l-udx z;    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 rangpn:ui f 5555qmca,uuke of human hearing (20 Hz to 20 kHz), what would be the range of5u5km5uf ni, a5u: qpc the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has )64 bufgm3h kecg5p* yix0-q da frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingeref0q*- mg ek3ihcdu4xg6yb5 )pd at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and z u0ja+-nr*j/kvgp4vhyqpwxcy ;/7 /is tuned to play E above middle C (330 h kvwvq* 0gpry4-;n/j/xzc/uy ap7+j 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 emitly(oxp (fg94z s middle C (262 Hz) whenxzo (p9(4gfly the 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 oz0k3s4 brqi9wei;/ sv :(ph b20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece6dtmxsm k,,iu4h)j. b of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at iu,,x)m6.b 4htsjmkd 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 Hz5nb5y7, x/g 2lb nr lw)jq5vmc, 440 Hz, and 616 Hz, but not at anymj2l5g)cnx5b bl/,yqnv5wr 7 other 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 v0dlt7:xbg.3:h b;cfs ha)xv8w s )ksm long is open at both ends. It resonates at two successive harmonics oat x7 ks shgc0)l;bh:vx.f)w dbs8v3:f 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 bmv, d(,8 )uc bl spe2iys(lm2$^{\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-+t*m,.e8z : sh qyttc6y 5mg zpqhl(y4m-long organ pipe g+8 qh,m mzyq (pthe4*: yszytcl.t56at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal iz40/ 5b qa4ck,mgoihqs approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the earzh qqgk b, a0o54mic/4 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 evern) m 4enenz7h+y 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How fn hm+) eeznn47ar off in frequency is the other string? ±    Hz

  What is the beat frequency if,fq1m34m m-zw(*izq9 vwv(u l8hjers 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) opera k a0 0zfcca9woc8*o/ftes at an0o8kfa0cc o w*/9caf z unknown 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 produ-5uzlaznfui 9 l :;lxwkq;zgd687bk,ces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stringz -nl:u7z, ;qflgl9udb wk68a;k5xzi? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension inqo0ug.r 2a, bs one string is then decreased by 2.0%. What will be the beat frequabrqu g0,os2. ency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flute(l,ej3ulfz+o01 b kc;e. apxgs each try to play middle C (262 Hz), but one is at 5.0°C and the oeau.(1 , egf3x z+l obkc0jpl;ther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequr8dawj+y .cp38 ntq- rency 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, tha.cw 8 r +3dyn8tr-qjpe beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart.as: g6j b7wf95y 7uql*+zodru A person stands 3.00 m from one speaker and 3.50 m from the6qlrw7 9of7u*z 5+ adjub :sgy 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, but a piano tzd; g9kn9ju 9puner hears three beats every 2.0 s when they are played together. (a) If one is vibratin duk9gn9 pzj9;g 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 and 2.7k 22urm7(g xzd6 m in air. How many beats per second will be heardm x7g( d2r2zku? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550i9yu6g:z 1rgl 7qzkb1 Hz when at rest. What freq69g1 z7zuk brgqli:1yuency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire e j4:su-a r ;9v0e y0ydzck5y/c:slv wtngine whose siren emits at 1550 Hz move0v yw-ta/kszj;vclyd r sc u:y:5940es 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 towardb3g ;ez nqa.(h you at 15 m/s venh;agzqe .b( 3rsus 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 single frequency horn. When ol)v +d97egq f*cbyx/k 8y xlc7ne is at rest and the otherf)xv8kyqb 7lecc9 lg / *y7+dx is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anuf+q64dqf omv7,0 olj d receives them returned from an object o70,f4 mojfqu q+6lvdmoving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a e86dd/fb*i(og cvl ;zm:7bxtq1c4 go wall 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 reflected wa1/gc (ev xiolc; to mzf:g*7b dq468bdve?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen p3 j6vc4cs x mf3agra6hb.3i5ts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone6ba3f45 3hvgi3c cma .xs6 pjr 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 measur,/xv+f-zmql qe blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is,-fz mqvlq/ x+ 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 wa fonfvp,y v4 zc7z-i/+ves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity isfn-iprv4 v i e3n.(6pt 12 m/s from the north, what frequency will observers hear whot3i.n -nevvi pp rf(46 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 i f3j5ef 6l*wm4bl,fkon 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 wxk ypa9s5ht 6jeo w,k07a*-mw here the speed of sound is 310 m/s (a) What is the angle the shock wave makes wi50 -w* esm p,xyk7wkt96aa hojth 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 plan77 +s55ox9 sviynfdo2p ov s--/swhgcet where the speed of sound is 9sico- y7nv5sof+7-owds /gp hx2 5s vonly 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 stov5u uebjj7dve 0q2ps s(85cbf(-dt:*nsn y2 rikes the ocean. Determine the shock wave angle it produ(cn j 2q5s2d: 8uv beo5b f7(-jps0etun yd*vsces
(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 u ta,zz,scb5b .i8c:i$/theta$ 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 exactly7r yt 4;*y-y2cryaliiu we 45b 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travit54;cy ryiy*ub 2wl 7ey- 4raeled 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 pulx+tu- lnph3o 0ses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, ph0+x ulo- n3twhat is the minimum time between pulses (in fresh water)?    s

  Approximately how man b 6aopwo8uifp3.4k .bz0 c*voy octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. I w ws0 co;shh:8g2f upy.n7mp/t consists of many plastic pipes of various lengths, which are open on both eyuh7wspwo :h;p./g 8ncms20 fnds.
(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 persmu/63 kfx24q0m zp rdv5*w ufqon makes a sound close to the threshold of human hearing (0 dB). What will be the sound level xrqd0w/fpvuz45 3 km * fum26qof 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound o .i .:qb5yw.l ooxr)care hearoi o.5bc wr.qlx): .oyd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opbpg*2enw* *ke en, is 105 dB. What is the acoustic power output (W) of the speaker, assumineg *ew2b *kpn*g it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 3t4 m(ql gr5zaW output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power ou(tg5r3qml 4 aztput in watts at 15 kHz?    dB

  Workers around jet aircraft typicalrd,ib4 yhwrt ux9:*86n evy7 1(nv nvmly 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. What would be the power intercepted by an unprotected ear at a distance rv*yh4dnb 97xe, :v w1t6(i mnnrv uy8of 30 m from a jet airplane engine?    W

  In audio and communicatm i.g 73xs 8ri6yud.nxions 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 tun*lf) 6jot l68mbyvg loo;ve 0(4tzt y7;mb(pned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundament3azr.ic34 zmjal frequency of 440 Hz and3z j.3a4cz mri a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verticalthzw ,5i-s8v0 n j7d*xjf aas) open tube filled with water (Fig. v8ithj ,swn05)d *aazx-f 7js12–35). 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 level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open atpgveium v;6uy :kmb r5.1f q9( one end and also 75 cm long. How much tension should be in the strin1 ;vmi.m:q 6 (vkegbfrup5 9yug 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 resonatezt7m53h.x1 jj sxqa3w 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 cominsp o(gv4n7n0d /:cyffri3 t) cg from two sources. The soun tsgdc) v(rfc /nn0y7p4 ifo3:d 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 the frequency of the sound?   Hz

  Two trains emit 424-Hz whis0v75 0/ ek) 0exuficl2wfcqkbtles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when th2kk0/ li w vq ebc)f0xf75u0ece 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 538 Hz. Aftmb,qn1c/x*,pgxa 6 yder it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume nm,ypg c 1qda b*,/6xxconstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeni3,jjo92 2ghkimrq p *gng 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 straightawm3ip2qgg h , 2jorj*k9ay. How fast is it going?    m/s

  Two open organ pipes, sounding together, prodl, zultp d7yo 8wu;p(7uce a beat frequency of 11 Hz. The shorter one is 2.40 8 y,ldz (u;7luppw7 tom long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stattho xec yfwz:6: va2)qx6q9, uionary 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)wcva6oz6 9h qq,uf:tx:2 y)xe he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normaeb-z k d*k40 fvnxb:7qlly about 0.32 m/s what beat frequency would you exd4nk kb- *fve: qzb0x7pect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward faq:u/m*au5l vdr4-srfn 2n+: evr0rthe bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequencufe*/rva lr 2-v0a:du mqnr:nf s+r54 y of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approache 9 e888ppgzykb6vunm7s a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. 8 8vnuzpbpg9mk6y8 7eHow 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 usedc5j63 gjn;;osr h9jac 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 waysjg6n;hr95j3 cac o; j 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 nih/1oiv :gog/(;m 17f .g4lftpxr pbbe compromised by the presence of standing waves, which 1h/iop x; gn/1p mo v bitl(:f7g4.rgfcan 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 demonstration, c2 6lzyj:vk7n s1 .fl3s g;3tp:goqm ssalled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound.p:3 f:vs61;7ts ngzsqog l2s.ly3mjk 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 :zcr/ f 7 4v c4iqj,azj0yto*;yp hto8human ear at a frequency of aboutc i 4:7ot jvqych,ry8tp*4fa0/jz ;zo 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hearsw6e+ sgw92.tv5d: jviedetm; the sonic boom 1.5 min after the plane passes e6 92. wsgedv iv+5et;dmjt:w directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat izs-sfr 2 xc:t5s 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