What is the evidence that sound travelsxsfr*j zpz y w2qi-kq6 60j,.l as a wave?

What is the evidence that soundfxu:t59tp1a qh79gxq is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string t e1osu14bqa 6ga.u7oqo 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 cuuo s1 1 aaq6bu.go7e4qp (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 lqhd3.4 ) opa: bnemmx71r:8kd3xizy you expect the frequency or wavelength to c. 3 8lo1b)k:m4ar hz 3mdy7qenixxp:dhange?

What evidence can you give that the speed of soun x 2so.jq f.p2bcl((ued in air does not depend significantly on freqf.soe2x bq pu.((c2jluency?

The voice of a person who has inha c1,i1+ok2 vt,5wbrxibfwgplw-: r2 dled helium sounds very high-pitched. Why?

How will the air temperature j0./ficehf x2r j8yx/ in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplijpgmgew 2)i;6z,c1 oe8r mk glkh 1g65tude of sounds in vari26g,lh5rzp68gem;j ki1 )go wegcmk1ous frequency ranges. (An example is a car muffler.)

Why are the frets on a gu k l.(uiid8uoix* bm3)itar (Fig. 12–30) spaced closer together as you move up the fingerboard towardo( ud xb mu3i)8i*.lik the bridge?

A noisy truck approaches you from behind a building. Initially,bv / d:elub1kps l;2i sn5q:q you hear it but cannot see it. When it emerges and youk dbi ;pb:,2n1q5e lsuls:q/v do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spaek oh */w0rrgl-qf*ob jf.*7ace,” whereas beats can be said to b7lr.*ofrg 0 bok jfh*e-aq*w/e due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wea1c(hr.)a(yyft * tzore lowered, would the points D and C (where destructive and constructive interference occur) move farther apa hytoc)t1a r.z(y(*f art or closer together?

Traditional methods of protecting the hearing of people who work in areas wi5/(g7g y.x8t 7.r4bjfv szgj1ff ut xbth very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reducfyv gjxfr 7.5g zj 7.b8ufb(txg41s/te the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a hy1 -4b4s/po; pbrqgfln/+i hd u. (mrsuperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b),q ump /;rb44d.o/lrhb+1 -yfgphis(n are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shiftbfmdsfyp;8 r2 .zn12htkj9w .n8zy f/ if the source and observer move in the same direction, with the same velocity? Explainhy;ny/2rdpfz. 1ws mn. 8kftfb9j 28z.

If a wind is blowing, will this alter the c f:k9.dkbf :gfrequency of the sound heard by a person at rest with respect to the source? Idkf9 .cg bf::ks the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swni9 6qy d(iog-ing. A monitor is blowing a whistle in fg iny6q(o-di9 ront of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ecy.1vyb tnt9q - w 4tru: z-f33ulreji)ho of her shout reflected by a cliff)zujbt rn t-9f3:erviq.yy tul41 -w3 at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the s:+ew0lnve5q waterline. He hears the echo +elnwe: q0 5vsof 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airrj(a z1si vjyjh06m5 / 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 jus3npomv c 7xbps3:8zl) t above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,p)zmsco33lvxp7 n8b:    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strik9/hjrxd x 0crt; mm81lg6g3 lsing the water below is heard 3.5 s later. How high is the cliff9x1;r3 g0mmhll6r8/gtd sj xc ?    m

  A person, with his ear to the ground, sees a huge stone strike theh-bn+wshfgh6 6 fxl0c7 -qn5a concrete pavement. A 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. Hhg5bl6 n-0-f76 sqn x a+fhchwow far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile os 4jby z5+hje.f distance by the “5-second rule” for estimating the distanhy.ejj+ s bz54ce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound9r)pxwk/,vfwassz0p9h r6y5sd( g z3 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 8:.ug3znrt nr5 j5txka sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaj6c7 5n(wgurrsyu/.ive j6 q0 neously at a certain place, what will be the sound level if only one i57j ecijsr0 /qn u6y(wu vr.6gs exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nos6ln okbkqa 2,,o:d1 0x/ inqqv2 jzr,isy jet engines is experiencing a sound level bordering on pain, 120 dB. What soundrzqb,n q0,xio6/n lkv o j:k 1qa2s,2d 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 ha(7+mou9ydty 1v+od p cve a signal-to-noise ratio of 58 dB, whereas for +o1uvtdyd+ y97(c om pa CD player 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 speaking in n (7zs gh,8y6a6y qijzmormal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly7g z y8ya, ms(6zi6jqh 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 whose area is:o21nvfrupk*vye:,7ebje v o s.a87e $5 \times10^{ -5} m^2$ (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, whi ufq :da u842kit-tq8fle the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a l8tq8k -a uq 2tfifu4:doudspeaker 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 me+m;4 lr yff8)b l)ms8mvsy;diter registered 130 dB when placed 2.8 m in front of a l )flmm8 ybm4;s 8s)+ifydvr;loudspeaker 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 d6qd1llg/l1 ndB. What is tdql ng/1l16d lhe ratio of the amplitudes 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 factorwzx 2u i) ;sh8i*np;yi will the intensity increase? Increase by a factor s i;w ) uzn*xyi2ph8i;of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement a6qr4 4-l akodqmplitudes, but one has twice the frequency of the other. What is the ratio of theiqq do-r4l ak64r intensities?   

  What would be the sound level (in d/z9omid+0xc .s + c3 o4wyipkhB) of a sound wave in air that corresponds to a displacement amplitude of vibrating a+cki/opy w4 +oz h9cm.3xsdi 0ir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound le/h/nyef k)z2o vel to seem as loud as a 100-Hz tone that has a 50-dB soun)ho kf ez/ny/2d level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can defc p-2-uny1xa tect when the sound level is yac-xu n-2fp1 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hugej8jnbv0 l( j1z range of sound levels. What is the ratio of highest to lowest intensityj8jl(b 0jv nz1 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 lengebt7/ na/.wujeb 1j 6t28kojhth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension j2te 67b. ae1jk/wh b8t/jo numust the string be placed?    N

  An organ pipe is 112 cm loeb5tsqkft0 :hz,)u9 vhsie84ng. What are the fundamental and first three audible overtones if the pipe 4zhb,q58 ittsh e0:u)es vfk9is
(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 exm:92gcr/m 4mcxdvq jtj 7xi;3pect from blowing across the top of an empty soda bottle that is 1q3r imv/gtx72mj ; d:4cx9mcj 8 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 organ with open-tube pipes spmppt8v.d6+1,sbkbg h:v hrd):bwzm 3 anning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pivk v tg +d,zmd.brp :3hm1)b:8hs6wbp pes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third vmj1vdwav:8,duk 4*k harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origina:,k4 kdu 1vjm*a8dvwv l length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E aboxkml8 4huq (rcfkgnjw -0+ fb (/0hzn/ve middle Cgfn8n(j0wuh hbl 0mqck( k /f4-z/xr+ (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 08s)wv -vldodopob(6 (262 Hz) when the tempb dop )sol-6(8vod0v werature 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 20okz83/d oc4b1wktxq r6sfo4 2 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thejqt; ukj,+zh id29o n+ flute in Example 12–10 should the hole be that must be uncovered to play D ;d ijz9 ujo t+hk,n2+qabove 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 c0y 2:f 9z9ornr:pros zan resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this ir oroz9n :rz02sf:y9ps 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 ov r 5vivf ts.1x78d)vwzdh*4r pen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whaz*7 .v4h)t5vrwxdsv dfr1v 8it 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 soxl- zt40 b .ie-s-xn$^{\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 thw) a4nuz k y4814 hi /lnff3kjdonyi/4e audible range for a 2.14-m-long organ pipe at 208l /uanj43zfyw o k/4iy k)nn14f dh4i $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. Itf0n3kt )0/nua((p)1p wd,re hxdxs c s 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 ear canal. dp stx()0u pr3canwhk 0 d,esf/1x ()nWhat 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 tryin3m,dwj:ltxh nn m63jgd7.l6 cg to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otxn.hmd cg6:3tln j6j l,mw 73dher string? ±    Hz

  What is the beat frequen4imr3sw kov:4 cy 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 23.5u6x/z s;8cvxk kHz, while 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 playuz xcs8;xkv6/ed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounvuenw9 m :f ;72qa-9+jihdynyded 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 swfa j:9udnvh +m7qny;-iy 9e2 tring? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency,f9 -73qnqn8 )ru ,0xzooni gxb 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strib7 z83,orn- ni9 x0xq nufoq)gngs are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two ident7:nyi,k+a uwz ical flutes each try to play middle C (262 Hz), but one is at 5.0°C andu: ian ,+wk7yz the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, w/c,lz +e9) - 2ptpsigh asp1wB, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz1wgpepshs2-) c pt+ iwl,/a9z 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 mqeage9r* p)ld8tkg (; apart. A person stands 3.00 m from one speaker and 3.50 m fql9 (rg8ek)de* agpt; rom 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 s )z(oxevhp8ab/7sfa3u-dhx, upposed to be vibrating at 132 Hz, but a piano tuner hears xpfa/e ah3 )8bsd 7o-,zxv(hu 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 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 2.76 m in air. How many beat2h9 ;pysjjsb:-qd x.ts per2jjsx:- d.9hs yb; ptq second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencyg5sj)7 ;u r ;svj(w,7jhxvag x of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speej(hv)vx5a; 7j g ,gsj;urs7 xwd 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 engine whose sireoyenep51w :/ e n+uz8en emits at 1550 ez:ye/eon e15unw8+ p Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20gbn 2im1wz(kp o,z5j:sw)pg 400-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the s4opwsngw( ji:)1z5g zp,2b kmame? 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 on 7 dhy)7bjvfb8e is at rest and the other is moving toward the first at 15 m/ yb8bdh7)fv 7js 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 49ip t 3df.lvg/ ao8 tje 1pzb:r6,bmbreturned from an object moving directly away from it at 25 m/s What is the rel39vetzt6a f8o. pbbgdij/, rb: 14pmceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, th6a6stzsqds5;sp : o6pe bat emits an ultrasonic sound wave with frequency 30.0 k6o :zps6spqs td6s;a5 Hz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pl k)xa0)xsv wa8ayed 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. Wx aa)0wkx) 8vshat 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 ;rfhk3p onry70b)8/5 / m m jtqczzk/xto 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 ar j8hrk3r/pyx zckf7 o0bn 5)mzq/m/t;teries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usingoo+n: m: (8xzfk lkegif/z4;w ultrasonic 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 souaspjk.,4jl.x j5dxa (nd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, a4jd (sjal ..kxa5j,x pt 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 +b3,xbj .hj oeon 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 o.l .ogpb9z8fMach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motiongz8f lo p.9o.b?    $^{\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 the3ref-b-z epa+f bqgq*. + yvs7s:a5l s thin atmosphere of a planet where the speed of sound is onlssef3-s+5z7b*r q:ablfvpega y-+. q y about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling osaa47. k0 twcx-l*,:ge lfjt8500 m/s strikes the ocean. Determine the shock wave angle it produc7x- csa.ket l*j:fgw0o,a t4 les
(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 q ,yn; bnaxgn1-n:/ve$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plae; zw+p wzo+ v9dhidd3.0si+qne exactly 1.5 km above the ground flyingsdh+0 p z.ei3+w+ vd i;9qwdoz faster than the speed of sound. By the time 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 doig b9po(gyu. 5bda0 d*bi8i k25/c puywnward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is kuu( /p p5y5y2bidg0cd* ibab9g8oi. designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how manrou *vml cg5 91hqd ph,g2u wn962il6ry octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sxdl tc,khk(x )r gy i..qg.pv-o.q4n5ewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bot hckontvr. ,k dxpq )g.. y-(i.q54lxgh 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 threshold c,;op bkwl3 o9kk6reih;d 67yof hukr;9cl y63 6hwp7okeoi;,kbd man hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB1vh6eh zf/ck+ sound and an 87-dB sound are hea6fekczh/ 1h+vrd simultaneously?    dB

  The sound level 12.0 m from a loudspeakerucvko/o*t+un 1/ c6q p t8d.ob, placed in the open, is 105 dB. What is the acoustic power outpudtn. qk+8u/6v *p co1c/ouo tbt (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier ico slqnif4c*j o(.7rhn10 l9hs rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is o*h4 o.1q(lrncl7 jinsh9c 0f the power output in watts at 15 kHz?    dB

  Workers around jet aircraftab0m 4bb o,k2g typically 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. Wha4abmg,2k bo0b t would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, a nfmtt43m8rr aca*0( 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 viobas:,q /hz 5f1nx mq+tlin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betw: 5kh9h qv ;(2cmstan(dz43llkso ze3een fixed points with a fundamental frequency of 440 Hz and a mass per unit length a (4q3z2;3k5el( sd tzlhnhk :cs9vmoof $6.1 \times10^{-4 }$ 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 vibrationb , 2,81iozvpfwu 3 e2yhl/d nsil,9wg,4 ofti above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m an ufvw2pesfi ,3o2nidohl1l,,/b4y wz8 9 tgi,d again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar w/ujzjke-. - r:gdk( gstring of mass 2.10 g is near a tube that is open at one end auw-j.:gek -k(/jrzgdnd 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 tube?    $ \times10^{ 2}$ N

A highway overpass war6k ov2s a80 *mtupio4 *a2ugx:m1djo s 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 tonian8fkz l(xs,qp4s480qni 3) s 1cr auir+6 jse in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources.i0),as643zs1sunn a+jxc4iqr 8rkli 8pqfs( 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 whistles. One train j-trk g3an 0l)is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approachat nrjg)k0l3 -es. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle al,lf s7,es5qchy. - rgo0y3xes it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train mo5-3yl,q f7sel0 egy,crx. hsoving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of carsog llw511v,2bv evc c+ just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequebvvv52c oe l,1 w1+lgcncy halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding tozedc x 7h:5ecik 67(ilgether, produce a beat frequency of 11 Hz. The sh(x l5i: 7edc khez6c7iorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movewu:l mbku/e7+s past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a)bku+7:ewm ul / 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 bl)6u0xwll5fku ood flow in the aorta is normally about 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 that the waves travew0lf6 u5u)kxl l with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6gwu 2 7b63vb bp11hy.n*kpkup.5 m/s while the moth is flying toward the bat at speed 5 m/spby6ppbvnk1 u 2gh b7k3*w.u1 The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ap5fn 1fy+grnn q0r*;5k9 sacydproaches a moth. The pulses are approximately 70.0 ms rn9g cf1 ank5*qrysy 5;+f0dnapart, and each 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) was ob jk9s wa*skc2+9 2byance 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 tsks* ab9c92w2j+ kaby hat 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 c( k5- fk,4em a3 o82e kuwhaf5iwijww2an 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 tj2- 5wfumo2iw ewf3 ak45,k8i(aew khhe fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singingu)pdokf5bwl, n1mt 1: 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 cleapfdlo1,) u51wk : bmntr, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human earmu2 twtxjw h5z5:a9+)9ryvql at a frequency of about 1000 H r5wwv+:qat5 2lt9) j 9hmuyxzz 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 groundm l9c tusp749m2mc+xb hears the sonic boom 1.5 min after the plane passes dirsmxcu m+2p t clb9479mectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbofi98:m2 hcaf8tj- rqzat is 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