What is the evidence that h6pjwdfl1m ai7. 9f k1sound travels as a wave?

What is the evidence that .9 sozx;h x(avsound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string njfe2g9r97/):/tof xppgcl n 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 othjr/ng:p72f 9et o l/cxn)pfg9er cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect 4;f(r6syp1 vcsm5 m5zfevs 7bthe frequency or wavelength to ch(v7ssm 5;v1zme fyfc465bp srange?

What evidence can you give that the speed of sound in aaxgtx to.w8) (2ivec 7ir does not depend significantly on freque)i .oxx v72cg(eattw 8ncy?

The voice of a person who has inhaled helium sounds very p q 2;a8jvwjqep*g 2)thigh-pitched. Why?

How will the air temperal157:rrb5cy odn wa6f ture in a room affect the pitch of organ pipes?

Explain how a tube might be use7pruusl -ws /d4cn/b-wu)u w4d as a filter to reduce the amplitude of sounds in various frequency ranges s snrl-cbwuwd/ )/-4wuup4u7. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yo1 l-,f+gy 2 x3 dl6ojftmyg:enu move up the fingerboard toward the bridge? tg f ngdfll6y ,e :o2j+1y3xm-

A noisy truck approaches x:2m1 +akdgp1hc;r7,ev t;yh+ rw tif, rts6tyou from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency no+ r+c:, vhted;mprkfyg 1tti 7a2w;16rsh ,txise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sai -cz oc6xjhl s(68cxr)d to be due to “interference in space,” whereas beats can be said to be due to “interference i68 h-c6lcxx(rzso)jc n time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woul 93clr 6r zsahz(-see1d the points D and C (where destructrzeesh1a r96( l -3zscive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people ha1ev71gwo1xwho 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 1o ah17gxwev1 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 reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought /.v() -gz tjt x/gya6mu.cpkcof as a superposition of two sound waves with slightly different frequenc(xvc .ac.mg-jz)k/ /tygt6 puies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obs6ftx01 :xaxhrk8* rzgerver move in the same direction, with the same velocity? z0x*8txh 6agr1f :xrkExplain.

If a wind is blowing, will this alter the frequency of the sound hea6vgt;sdhsyb*2nvca( g *m// n,bhbh 0rd by a person at rest with respect to the source? Is the was 6n* (g/ dhbty2,shmgc/vabv*; bn 0hvelength or velocity changed?

Figure 12–32 shows various posbaj*wqx:rl8 .u0 7sybitions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on :qr80l swxbb yja7*u.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 length of a lake by listening for e j2q uay7w,5ou;i6p6 zduosz+dxy)/ the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengzy;owu5 /zu s2o,yie+d 667udxjp )aqth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below ll firhv9 *vu8nw+0/athe waterline. He hears the echo of the sound reflected from theavinw 8f0ru+ hl/l9 *v 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air t* pp.5zqvb) (gqoxn 8 m:bft(a6o/g gat 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 i s(s 4rj3ur4j;l;ii9kx qlx :es drifting 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;l: ( 3ix eu;qsjsrrk9jlx 4i4 is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from (tymijf-adv3t vv n4 f;be+:k a re503the top of a cliff. The splash it makes when striking the water below is heard 3.5 s lateffai-( n:td4vaty5b+ev mkv03 r;e3jr. How high is the cliff?    m

  A person, with his ear to the gr7v jnms8:qs1jkq1b/v*9t olyx h; 3ggound, sees a huge stone strike the concrete pavement. A s;mtvnq71j1h: k 8l9g3o*gb/vsq xyj moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance byp8p q)j+ pij5w 34hoce the “5-second rule” for estimating the distance from a5 h)3iqocjwp e48+ppj lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a so5uw n 4wjft:9 dr1hdxwt3 w*z3und 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 sound whose intibz*mi 0gy*.t f7 jg:w)*xdta ensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a s 5u xzypa5p4wx em-6:g w+s*fvound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]yuv eaxm-6g* zp+ws5:w 45 xpf    dB

  A person standing a certain dis6se ptpvrkv,y -: /*whtance 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 captain shut down all but one engine? [Hint: Add intensities,wp/ stp-ve ,:r 6k*hvy not dB’s.]    dB

  A cassette player is said to have a signalajzgef(9 fvh2rv*-b3 r(vf) m -to-noise ratio of 58 dB, whereas for a CD playff)zr v(m*vbgh(f-a293 jv erer it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spea-:sao:ny:b* xh wcnq4 aygvk t(t) 9(eking in normal conversation. Use Table 12–2. Assume the sound spreads x*ycshtqgv-): ot e(ay:w(a:bnk4n9roughly 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 e3dz puyxo wsez 3n,:n1)c+upz4 hz1zlx 7ob2 :ardrum 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 th+f s(tifv -0g8qf;s lce more modest amplifier B is rated at 40 W. (a) Estimate thesglt -i+vc qsf0;8(ff sound 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 registered 130 dB when placed 2.8 m in f6pm gtxck(03 0vka0slront of a gmkx0s(a0 c 30tkp6 vlloudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Wi asr6 .a*hb0uda er+(e s+4yxhat is the ratio of the amplitudes of tw+rixdbye+.*s6 (ar0a4es a uho sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a lvnha(oqw.k/ )qo1 fl5)e4803pi; d ljqq cix sound wave is tripled, (a) by what factor will the intensity increase? Inc.4;qldolx0p/q)a wv)ie53j1(q 8ci fnk lqo hrease 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 1qm7x2txuo/l-db ;bwf: - zepthe frequenc /7z1 xtdwb l--:px2ue ;fobqmy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thatyd9k3 p-xudu8 mbn1nu f l.22z corresponds to a displacement ampxz d 2u3 fy-2d 8l9pkbnmn1uu.litude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must djf9f ,8 20y,k.ihubebk2k2vam o9uvhave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) uio ua f9ykd.9v2k8beh0m,2fv j 2,bk   dB

What are the lowest and highest frequencies that an ear can detect when the soll65zi .nh97ptwt +c jgt)0leund g. l 9n)cttlj 50izt+wh7lp6elevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounzm.o+o;v o*,olpf) lbd levels. What is the ratio of highest to low,z o. *vol+f;mpob)l oest 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 of t+ xmqx((w8oujud/ vk4w*z7 kr he vibrating portion is 32 cm, and it has a mass of 0.35 g. Under x74muzwd *uxokq 8+jv(k w/(r what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three auz;ez)j zh64,uuuw1abaoy) .(3ko gd j dible ove3du)yeohak4 wbj z.a1;,ujo)zz 6 ug(rtones 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 you ds-5g+ grt; b)yuj6y rexpect from blowing across the top of an empty soda bottlg)bjg u6-+try r5d;y se that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe ok t *13ig tpvr2*h*p;sdh0v q0ebi*forgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 iv *k h ipv *10opers*h3tgb2qt f*d;0kHz), 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 f4gouuf 81atbgs4*r a ;requency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 8gatf u4rb uga4so* ;160% of its original length?   Hz

  An unfingered guitar stw3me+ y(5xq4 qtk uso2ring is 0.73 m long and is tuned to play E above middle Cm2+4qwku te5(x yos 3q (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 H4 mcfnjy7v/6vk ibx6 d)+zfa)z) when the temperature is z)kv/4fy6x+cm)b6nfd a iv7j21 $^{\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 7ic j8pu,v8 xlat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Epq4j(: :aptzuph4;a sxample 12–10 should the hole be that must ta( paqps;4: 4hp:juz 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 catol mj ./tp9:*xlffmlv o t urh-359+en resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in be l htrvl9x9mo- epuj.3ft/*t5 +mlof:tween. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two su i ;wcc ap ,(g,fpk5-)ki1buwyccw, kcfwy b (ig1up;ca-5),k piessive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 idmv tk : 5-lo2)un,cq$^{\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 organmir)+ yrv7q2i pipe at 20y ri)i qmv+r72 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outs c: 3uv/dhzo8side and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the/:cdos3 vz uh8 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 everwp18xl d0d b)6hz- blgy 2.0 s when trying to adjust two strings, one o-xlpd)l1zb 8wgh06db f which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat fretabj-q7omy+bihb9y9f m +8ve -r u.02 gk dsi7quency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whinje.ow c3hf1 za /k59gle another (brand X) operates at an 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 ko9ze5j/.hc a1fnwg3brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 bewym1j+8rc 4ur; rw* beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency om8+rbceryuw j4 rw;* 1f the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29l tpgla -5icf-gcd9.8sckx98 : o +xbw4 Hz. The tension in one stris :5g8 aki o-9cpdclx+8-c9wlt bf. gxng is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hear329 jrm.j wwxcd if two identical flutes each try to play middle C (262 Hz), but onejmc j3xwr.29 w 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 B hqk5cfl n1 pngzssx0)m e)a6 :.as 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 A and C? What beat frequencies are possible when A and C are sounded togetkx l6fc)aqm50s ep)n:zsn1. gher?$f_A$ =    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 ,j)eqvx( 1y/(qkgo u7dx um, s5fx2mp 3.00 m from one speaker and 3.50 m fd ,/ qf(7qxvy2 5p) jmkmuo(sue,xgx1rom 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 suppos u-(pzdx2aguh tu,m / ej6;f+sed 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 the otheau- dmx/,2hge+;sjpzt6u u f( r ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Ho9rcq24tkkxl 34- fc xbw many beats per secot c9rq4k 2-fk bx3lcx4nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sofp7d6 7p3f1;tmq qgmiren is 1550 Hz when at rest. What frequency do yogp t; opqf7q367f1 dmmu 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 detectp .m-6tt yaa7w if a fire engine whose siren emits at 1550 Hz moves at a speed. paat7y6t-wm 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 toward3- , udr+afha.lyzwv/ you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Ar.zylfrw3h+,adv a /-ue 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 frequenc89 a k6btn1e 8/vdmz,uvv8jv vy horn. When one is at rest and the other 8 8k,bvavv6e9jumv1tvd/ n 8z 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 and receives them rey)est f1jn 30fajs(xd,.zuy6turned from an object moving directly away from it at 25 m/)zjf1d6 xe3jyt,a0 (f. syun ss What is 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 emy.ohkamhq :trihn,.1ou0 .:iits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectekyuh0m.:htr a,:.i1oqio n. hd wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was3xw:z i p4fod9 played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a w4i3:zoxf9pd speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedn8b 5bg7y)3kt b r )kk.9uwhrykdaz03s. 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 blood is flowing in large leg arteri8rkkry.nb30w ) 7)zykhkubgb9da5 t3 es at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wc( fua2wrq,2eaves 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)g ,q6rtmxfbi- rob +/ is 12 m/s from the north, what frequency will xt+bmgifr )ob -qr,6/ observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20 9hrx4p9gdsw 5vwsjke f,b;vn*k :;u ($^{\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 ata*95nrv : -a85kc egwhd kgrn3 Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes witg5h 9w na3kdak-n er 5cr*:vg8h 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 the speed of soun8hy0 t8xew nc+d is ox8e +ytnwc80h nly 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 st3j /f3 c rrou3*k+b m(9ydsyltrikes the ocean. Determine the shock wave angle 9(+rucy/s ojf bmldkry33t3* it 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 ig p24tes8nu ;j qlr)3m8e-ue$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grou. ntrqh/ekw :+7u 9nxtnd flying faster than the speed of sound. By the tir w+tq7ht e/.u:k9nxnme you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward :xn0+3 oo5rn na+sowp(csit 0from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to5 :0+n stsoipwa( rn3 0conx+o work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audign*cl/s2 hb +dble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cx v+.quq ;o*bggyks ; la83mu8alled a sewer pipe symphony. It consists of many qy3;kugl8;ug.m + vsqx8*baoplastic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the s2zocg/o;-ee o3e4+7ok 6, nqvikjlw threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitkgsjo 3oe 47 kzeo6ni,clev o;+/-2 qwoes?    dB

  What is the resultant sound level when a4 8jsay(jnc1c6ffzb -n 82-dB sound and an 87-dB sound are hear6( s b1-j4fzfj ny8cacd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed ipsvps3lltkt x 7*f,4ihng58hr9 v-o8n the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates eq-i ot4kr 7t8gs9p8 *nl,lpvxfvh s35 hually in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hzo1t (khw:b1hs hjhy/i ziv u8j;,g65r . The power output drops by 10 dB at 15 1u hbih/g; z6 1it sr,( 5ko8vjwjhyh:kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically m27 uxuagm.6gwear 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 a6um72x ugmg. be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationsojf1tbdh70ohki)-v h4q 5) zn f ./ngq 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 tuned to a frequency 1+*x pi pove-;bp f5wd($\frac{1}{2}$ 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 fundamental c6 i )b)(g gmbd5pchd(fr (bd )gbhpd g5(ci6cm)equency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vert 9,9 speinjge12bpk 2lical 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 when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is th2jge9p i,lpb 1s9nke2e frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that *e3. ( +c/njssjbacqmis open at one end and also 75 cm long. How much tension should be in the string if it is to pro.jss+*j c(3c e/bqnma duce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wasd-3xyo ;h yu,u observed 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 tokazs5 /d;moyej- *tz8 ne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one-jate /;o *8dmy5szkz source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary 5;f)cxavp.gx7;pa qt. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the sp q g75pa;.x);tvc apfxeed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is j1ho so(ex nn5,/l.u l538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was theouo1 /nhenjx(s,l l5 . train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis 69ckhv3gpdo0 :r6xs itening to the difference in pitc0d66cpgs: orkhxiv 93 h of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce andeg788l z7r+ dq afbj743mwgt4y8pt beat frequency of 11 Hz. The shorter one is 2.40 m long. How lontn8tgl8z 8fq47+gadb4ymed p 3wj77 rg is the other?    m

Two loudspeakers are at opposite ends,/5mve8j hhq.0d n lc iyt:o:bxs6,d c 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 frequhs5, e /dcjb:qv6i xn 8d.l,c:hm0toyency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.fhei.7 xbdi.3idd) d,32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the wfd3,i. )hiiex db.d d7aves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.ga0/8wxiersdvxjrc ); 6ky 845 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 xd06w iy;kgjca8e s /rv4 xr)8is 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 pulses as it approaches a n4b-5 :nr tmerf ub4j/moth. The pulses are approximately 70.0 ms apart, and eachr-bnt5/: mr4nf ebj4u is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wafb3:c et/f fqf2obrr4.li0 -h s once used to send signals from one Alpine village to another. Since lower frequency sounds are les4h rqr ol: f-eft3 fbicb/2f0.s 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 12–3.) Model as an open tube.

  Room acoustics for stereo listenqmytgg ,5;+ f1o2to 11mu9ltfmb 5mxling can 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 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roog1 f lqytmu +o bxog5 11t;l,mtfmm592m.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing k/x wnjc;+p(ou ;fr9b 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 (fx;;/p ojuw9br+ k nca 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 human0 zgkmhtsy0o9c50w 2s ear at a frequency of about 1000 Hm9g ksc0h5t wzy0so0 2z 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 grou+x mkrdrsp:l0wx .: -tnd hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plant0m.+w kxsp drlxr-: :e’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 1b (k2s zcye;cis 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