What is the evidence that sound 4o20w npwztvk:y0o-z travels as a wave?

What is the evidence that (9lh in5v ; qjsqyz;w2sound is a form of energy?

Children sometimes play with a8g hlzhvp3b0*-d2zcp *:fin z 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. 12–29). Explain clearly how the sound wave travels from one cup to the other. 83 2pz-iz hbnc * *z0dfhvpg:l

When a sound wave passes from air ;6l:ucqh/eb cinto water, do you expect the frequency or wavelength to cha ucb6l/ec :;qhnge?

What evidence can yom ,zggl7 ah6(,y2 e umg,ajgt74, mbtcu give that the speed of sound in air does not depend signif2,zmum g(at,t 7h4gm7 ,ceg 6ajy, lgbicantly on frequency?

The voice of a person who has inhaled helium*z1um*3ozls , r)vyv,c /uy j *nxvwo, sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch pdutd0z6u b-1zh(6wo vp/ 3vcof organ pipes?

Explain how a tube might be used as a filter to red. l9k)p* rwq(yg jcyb7x(da * 0wquwz8uce the amplitude of sounds in various frequ b(ldczkgy0ju*.r) 8 7wwwyx q*p(9qaency ranges. (An example is a car muffler.)

Why are the frets on a guitarplbj2w6.ev1(zd*7h . t pz. f8q wklzx (Fig. 12–30) spaced closer together as you move up the fingerb.zkjd8(v2le.wtwz7p*fpz1bqhl x6 . oard toward the bridge?

A noisy truck approaches you fq. mtl o*m9 snpoo-z23 cyy:9lrom 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-frequentsy yoc.:l*olm-9q3 9z n 2pmocy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inter/5 c)y(b orgfjtq7ta6ference in space,” whereas beats can be saib atf(5)6y t7ocj/rg qd to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsfq/ .r jeisg,vhl,u*.z97+q 1t bgc hp D and C (where destructive and constructive interference occur) move farthertj fs1bgu q,* e,rqg vl.+7h/.iz9cp h apart or closer together?

Traditional methods of protecti5jwn -,3.nnhunu*pv1cx. ;wm l te/e wng the hearing of people who work in areas with very high noise levels have consisted mainly of effort5.nnc3we nnw1xu,u/ephv. wm j-t l;*s to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown 9xe 9a g8 sipv21n.-elorngw;in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.i 1l-angxo928s. ;ev9 ep rgnw
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sai,7(6-5 zg5s o q/utlcsqw-iu7c avpvme direction, with the same ve(7- u7 vuq,gosciqcw 65spat/l5 v iz-locity? Explain.

If a wind is blowing, will this alter the frequersn c75lm5fu.mw +vmj 9aka 1(ncy of the sound heard by a personam r1w (a.lsmf cm7 +u9jvk55n at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chihv-de ,6vmzf91n2ohqld in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At whi2fv zhno,mv 1-eqd h69ch 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 f9q (zrkq8mb7- bghjly(i*. f hor 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. Es(ibk yq(hfj- *gq7r lh89zm b.timate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bel rruz mw4ic8e-: 9t;asow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with 4zs-8rmi9 uc; a w:retdepth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths sgqvl3(x3itwc *w u1e em68)t 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 schow6 . - 2ynjiyc 7j*hii*en+tazol of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much t y -nyczi*.ji*e6iath2w7 j+n ime 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 whene; h/lxqk(i f 1t;b4mk1w pmy2 striking the water below is heard 3.5 s later. How high is the cli4k 1qelhmm;kytw1 /xb;f 2pi(ff?    m

  A person, with his ear to the ground, sees a huge stone strike; aa;4ybh5md0yk :ogkl7svh.*e)fk q the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and thb*: 4;g.lv0 hy hka;5myd aqokef)7 kse 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 ove 2z.pmy:(yv2zs wq8n jr one mile of distance by the “5-second rule” for estim8:swp2q2y n (mzy. vzjating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB?1h(tudm9a skd+p3uu1* ydd/m    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 sounf4k vtdh/;b .ed whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneou p:rfw8k j,x8-dbf 2ifsly at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not fj-dx :rwf bif k8,2p8dB’s.]    dB

  A person standing a certain distance from an airplane with four equally no8j (n ok)umpj0isy jet engines is experiencing a sound level bordering on pko8 ) jpmnu(0jain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rhq.1 2anrdmv* mro h7+atio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =mho*aq1+ m2rhn.r 7vd    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speak,yfc owhoa5x* m0(;st ing in normal conversation. Use Table 12–2. Assume the sound spreads rouc,sytox w;h0( 5of am*ghly 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 eardru /-,(s6do*alvibnytrb 7tvpl bf,t56 m whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modestv;zc l78ufm6bg;l -lr amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poing ; ; lzlrl7u68mvb-cft 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 meter8x swa0h a4oqxvb1jg4b)l08x registered 130 dB when placed 2.8 m in front of a loudspeakera1hx0alsj wbv08oqx 8g )b 44x 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. Wha gjp-nvy n f*zu9oj0tj69;z6rt is the ratio of the amplitudes60ju;gof tz-j ypvrj n *699nz of two 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 will the intensiy+5mkj 5p+sj qae21okty increase? Increase++ ys 2kpj155 eomakqj by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amko9p v+kx dm10j2 yoi5plitudes, but one has twice the frequency of the other. What is the ratkp9j1m dx5ky oiv+0o2io of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspo v( 1s-ln kzj5z*phk3qnds to a displacement amplitude of vibrating air molecules of *z-vl1 zsp53 qkkj(hn 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-H ;;hus -sdid8,q agv fkd*j:g9z tone that has8d;gui jd- av;f:9,dsqhkg* s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest csduip2 exq)il2 a uj 9(+,w(ocpr*3 jand highest frequencies that an ear can detect when the sound level is 30 dB? (See su9id*+ (2j3r ji2oapxwc(e)lc uq ,pFig. 12–6.)

  Your auditory system c(xh8h50obl ,hhi xswymr+q5 0an accommodate a huge range of sound levels. What is the ratio of highest to lowest inteq+ h5x ihlrs(5b 0,0how 8hxymnsity 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 z-sm(puk d1svqb4u10 8m hx k.of 440 Hz. The length of the vibrating portion ( ukkuh qvmbsm-d.480 1zsxp1is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. l rauk08dv-3:*jdc/nlo, pq b What are the fundamental and first three audible overtones if the pipe is bpd0n vl,u* dc:a 3-/qlrk j8o
(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 blowing across the topsqe:j1. a vt//qe 7ynj of an empty soda bottle that is 18 cm deep, if you a :yjq1q e.jt7nve/s/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 organ with open-tube pipes spanning the range of 6)fg3x shp; spm hj 9ae zqht72+guc56human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes s6s ;7ggzx h ct6pf2)5j ph9ehqma+u 3required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third haz ,ty,jif )vg0rmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of v,)g t0ifjzy,its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play2p4 c6 nt+q(rrzq;mdy E above middle C2(cdqprm;4rqtzn6y + (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 g+x0c/97mdldfmm e w 7an open organ pipe that emits middle C (262 Hz) when the c0eld79d wxm+ 7mgm/ ftemperature 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 z(0 j jj9e6inq20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthp ohu.;*a5dzf hiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at.ozu fh d5h*a; 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 Hz, but not at am (r:us1s82ded6/mpj;pg 6pog k y+aakpcr:(ny oe(pkp;m2du p6 mpsrg( aak/c6 :g:s8 1jd+roy ther frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both end770v hq 1ndmh0m ir/nds. It resonates at two successive harmonics of frequencies 275 Hz an07 d mnm i7n0/dhrvh1qd 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 kwfv,jet)q * ($^{\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 organnk+zm;mu djv2u (. j(z j(kzu;2m m. vd+nzu (jpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open- /4p gpvt:p-4k rucet to the outside and is closed at the other end by the -up t /r4k:pvtp- gec4eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust 4cp -m98 w.n zrckgw(ytwo strings, one of which is sounding 440 Hz. How far off in frequency is the othwp 8gnc.mw 4kzy(cr9-er string? ±    Hz

  What is the beat frequ 7fxat+8 no 7be1lux/zency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X)31 x0x he tu7:pa(ftxg operates at an unknown frequency. If neither whistle can bx 70texufh a:t3x 1(gpe 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 9 v1,7g p/p 7bry8l fh5,kvapvtbeats/s when sounded with a 355-Hz tuning fork. What is the vibrationlpt r/1 k h7,57ygap, 8vfvpbval frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The zg,o0n+i9 jenjp7s (dsj4e 0ztension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: R jn +,p9es7j0 i4gnzj0deosz(ecall Eq. 11–13.]    Hz

  How many beats will be heard if two identical hgc/m ;dv8cdj zkr(47flutes each try to play middle C (262 Hz), 84(/gm j zd 7rchdkv;cbut 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 B habx*nu )2le50w6 2upzfh4y mtk s 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 ip u*2l ehk56wybnxfu)t m0z24s 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. A person stands 3.00 m from one sayep3+ ;x :lnec2. pr+ 7gdeyhpeaker and 3.50 m e2eye 3y7g .lap+hdc+rx np;:from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano texvdz, gy:u80ue c;uw1 hm* o,uner hears three beats every 2.0 s when they are played together. (a) If o, u0woeg,h8 zm ec:;u1uyx* dvne is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound ofh +e1 zobq65kivdlq6 , wavelengths 2.64 m and 2.76 m in air. How many beats per second will be ve bd qlz 5o6+h,q6k1iheard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ojf6(cpnlr (2eh8n p1tf a certain fire engine’s siren is 1550 Hz when at rest. What frequency pjtrechfpl2((68 nn 1do 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 x xqcd nm;.;hwh ub8 7wfk;y15detect if a fire engine whose siren emits at 1550 Hz moves at a 5xw fy ;b.d 7hcmxn1;huqw8k ;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 mov8q1 h /htu89ump;1az/efni dying toward you at 15 m/s versus you moving toward it at 15 m/s Are tdq98h/1me;za h /1uyunf8tpi he 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 frequenc) 4sla2 tem:x*f fks/xo2n 0ujy horn. When one is at rest and the other is moving toward the first x ulfn/xstj20f *4:m k ae2s)oat 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 50o55s x vugfojwzi289 ).0 kHz and receives them returned from o)xiv2 gszj5 ow 859ufan object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As4d0aa erm*5ehx5jja4 it flies, the bat emits an ultrasonic sound wave with frequency 30.0 ke xahmd5a 0je5*r j44aHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentg gw4w o6m0g6*/uyko qs, a tuba was 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 speedmk uggw*66o/y4 wq g0o of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoa+uha0c2qgh.qf8o l /und waves to measure 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 the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source2 c8fo+0u.alqaq h hg/?   Hz

  The Doppler effect using ul)gl0 69llp* lt kbdil1ons91ytrasonic 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 570 Hz. When the wind velocity is 1i+ walp2znfqxjnt+d+1,6s4;u6x vpk2 m/s from the north, what frequen n6,p xt 2ln fj +4apz;+s+dqukvi1x6wcy will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spei cxb 34irp 5-b2rpmz5ed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound ,4gb3 ujfq3lcis 310 m/s (a) What is the angle the shock wave makes with the dirj43g 3,flq ucbection 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 atmosphsqbpxl kj(cn0yb p +4(k5y p;;ere of a planet where the speed of sound is only about 35 ;csp4kjbxlq(ykp+(5p0 n ;ybm/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 strikes9u p1nljeb:d +hizr4 1u*9ofp the ocean. Determine the shock wave angle it prouidf oep4r jhznp l*b +u:1199duces
(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 p 1wma.rix/.z$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pl 5okajyv*/ 4oeu-y, u7v 8zzhy2e(bhwane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal do,k*uw o5-2e4e vyyhz /7bu hav(jz8yistance 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-H6 3fy d te(/4ttaq,mfsz sound pulses 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, what is the minimum time bett/ yqftf 6 3as(m,e4dtween pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?lz 6ym bth )c 6f4o(49slk g( (iaog:vha-jin. $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipev6q95op+g6i +c bb af +3hplpl symphony. It consists of many plastic pipes of various lengcb a3+hppo66q+plliv+gf 5b9ths, 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 5ws46q h,;gnrd dfb6y;mws*zthe threshold of human hearing (0 dB). What will be *;5,6;dmzdn srhqbwswy64g f the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sounwn n dw6/3pc9pr 3v2y i51zelwd and an 87-dB sound are heawl /cydnv125pw p i3z9r3n w6erd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker,/v oa9wei7ft qz,fl 2, placed in the open, is 105 dB. What is the acoustic power output (Wal ef, f/z27i9tvwo,q ) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is ratewwek6j o,7m;pyk,2wc6jb 4pt d at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whatwejobwtkpj, c,y 7kp ;wm6426 is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eary u aev vg*f9xwmn*x h5:-gq7+s. Assume that the sound level of axumfg5ex- *wvga97 *yqn:v+ h jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatie*t*u 5 hizo:ylq3r2c,,id4ktpk,nfons 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 oc3 mj(h zq r.5dot( 3q)05ztxihi(og1$\frac{1}{2}$ 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 vi rom hd/b/ a1qz :b 8ik1)6xu)fsiez,xolin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a hforba 1zd)mq k/i )u/xe1zx,:8 s bi6mass 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 uc/l7 bpn -y2yinto vibration above a vertical open tube filled with water (Fig. 12–35). The water lev/u bnc-2ply y7el 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 op5ir e2piy(gjmwba 0 pi).e15xen at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the ta0p2. epi 5wm i1ei5(bxyg)j rube?    $ \times10^{ 2}$ N

A highway overpass was observed to + uop+do 1zho6resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from ta.tatd t7dl tlc /. f+k)q ya3;aw*a+hwo 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 hadta t+f;)3 7a c/q.ykwa*l.lt d+atthat 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 stationary. Tmetk )77ie2um jgs7 1ohe conductor on the stationary train hears a 3.0-Hz beat frequeeimo 7k1gs77uje2 m )tncy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After i97lbp6wa 8 yrvr x70h5h8uvuit passes you, its frequency is measured as 486 Hz. How fast was the train moving (assumriw5 6uy78ph hrubx0l vav8 97e constant velocity)?    m/s

  At a race track, you can estimate the speed mcrkf .tk+/5icj3p/z*xt r/tof cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppo/tfi p+3rr cz/cm/k*j.t xkt5se 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, soundsu99hxp;2a yd ing together, produce a beat frequency of 11 Hz. The shorter one is 2ys2;dp9hx u9 a.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as yx*)lcvk1qykk(5cb7 )8 dl xf it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer w yckk7)8cf( lxykqvbl1*) d5 xhen (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 aboeyf4kzyz)4g9 jauh)qe *v- 0nut 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume tha4e)qn0ejazzy g- y)f 4uv9h*kt the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at xuup8,mpl.w v*:spx3speed 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:*x8sppm ,3lv.uux pw . What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a x2vd2pevh77m moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that tvdv7xmp 27 h2ehe echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1) if q *od-6q7dyomwbi06 z9au2–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flaiodb6 z)0uia7mq - fw6*dqo y9t) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised byvljd by /1z c i)gw1jqp6f-:r* 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 roomi -)1c j6yjbv rf/g :dzwq*lp1.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing+kz nuh j;l;7h 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 pkl;;7 njuz+hhractice, 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 hearin 7. zk*pn+l.h4m pjdfhg for the human ear at a frequency of abokdpn* h.fjzlh. mp 7+4ut 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 gr*z4xl; fs *rcwound hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane*lzfs*w ;4cx r’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 155 jgbq ,ks79ad+ 1z joy*falk7 $^{\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