What is the evidence that sound travels ux6 k7.xt o;xdg.pr)(r.csudas a wave?

What is the evidence tqbv (lixl0 1m-hat sound is a form of energy?

Children sometimes play with a homemade “telephone” blbvf72 1*baa*nwvj e. y attaching a string to the bottoms of two paper cups.vbajwal2* * 1nbef.v 7 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.

When a sound wave passes from air into water, do y 3sx 9o ec(cehzi+g/c 66zp,onou expect the frequency or wavelengt3/ie(oc p egn+ s6o,c z9xzch6h to change?

What evidence can you give that thn .yhmxe8,s i (ynikj0uzq .2.e speed of sound in air does not depend significaj. qi28, z.ym(hinys.0 kenx untly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?uc5(nzl-7w2-jzwqf *yyy5 onu d7z 2k

How will the air temperature in a room affect the piteofnm 0l;edh0 5wc87ty) s4pzch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude ofgy yekz/8y6u , sounds ine kyg8 yuz/y,6 various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together5 ziue0d 64dk8n6b:,;batxxqz j fm6x as you move up the fingerboard toward the bridgf z 5 jezd,6xdbn :x 4axib60ktmqu86;e?

A noisy truck approaches youz05fqcobi 18(tf mcs) 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 noise. Explain. [Hint: See Section 11–f 5qocbc s) 1t0iz(mf815 on diffraction.]

Standing waves can be said to be due to “i*i* iu(o cpic+nterference in space,” whereas beats can be said to be due*p(ociuc ii*+ to “interference in time.” Explain.

In Fig. 12–16, if the frrv(y0t6x. t fd + lx97yksgp8requency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apartpx rt+r sk6g8tvy90yl.f x(d7 or closer together?

Traditional methods of protect7spq:a *rxfb cm3h1s/wbt.0wing the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the he cs xa: tw1 bs/3whq0m7p*f.bradphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fxehqemxe * )-1ig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, ah)1xemq-* e exs 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 obsep iobcsf)3 .i-u l/b0nrver move in the same direction, wuof nbip3).l0c-b i s/ith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a perswf):; s+k ggt(r.6olr x*mysmon at rest with respect to *g k); gmmswl:sy torfrx+(6.the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor hd)//-ok 78)evyoeyo n2smwsis blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the e)o / o7k8 dymhwso)yev-n2/ssound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by liste9 p wfkolx *ywf)p;y*xic*b3f m4f(m4ning for the echo of her shout reflected by a cliff at the far end of the lake. She hea3;l9 pwbmcpmxk*ff*f( w*f4yx4)oyi rs 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 waterline. He hearwqijby)hf r8n6+ .+w*ct+smd s the echo of the sound reflected from the ocean floor directly bel rt +*. yqnbc8wdw6ihf)+ j+smow 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 infbx ou8x)ff /hii2l4 1 air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy dayho(lywot:o/ 0nt;g q0. 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 y;gn:/ qw0l o(ttoo0hthe fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cli6r c*;u./fdr1v of .whlp(v.pkd 6bomff. The splash it makes when striking the water below is heard 36dbo( wu p rv1k./vpchff ;mrd6*o .l..5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrg,: 4nggneyuh xe6g70bg 4/wwete pavement. A moment later two sounds are heard from the impact: one traveh6 wgn/g, w x4gbguey4:g7ne0 ls 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 erro q qiry:*x j2eqtw2f p/md(ff;r(5j z.r made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) q:f m(j./r z;jp*df(i5tx2w yf rqqe 230 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 di,lcc:)rgp f5n/ p,twB?    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 whos55pnqjnv*)bedz1d z) e intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce * *jj;z8s j,qrod0fiya sound level of 95 dB when fired simultaneously at a certain place, what will be the so ji,s;o08j* qdj fr*yzund level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from anyv)3 wmfh roup01a5+u jgv10j airplane with four equally noisy jet engines is experiencin1wg uyav j531v)o+rj0f hpum0 g a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whermmo: t fg/3mvu*.l ci/eas for a CD player it is 95 dB. What is the ratio of intensities of v.fmt 3/mcgo i/:lum* the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpufzmn42uk f3*gn (0 geut of sound from a person speaking in normal conversation. Use Table 12–2. Assume the3zf*nuf uge n2 km0(g4 sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikesu;k8 k sg5) htu1rlms. an eardrum 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 modest amplifier B is lytt hc,n0. ;xrated at 40 W. (a) Estimate the sound level in decibels yh y.0 ;tctxln,ou 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 regisym:pq :fjz/; jtered 130 dB when placed 2.8 m in front of a loudspeake:jy;pm / zfjq:r 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 typic-oy* b0wvvtn z.1tv6qzyw;8 xally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels di-vzq8 ywv*; t yx0vbotn6z w1.ffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavrr: hy- a8rk;je is tripled, (a) by what factor will the intensit:y ; karjrr8h-y increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tws3uqd;4 52 l-+p:xj vg euajnhe frequency of the other. What is the ratio of their intensitn-xuj3a5;:q+dp l j ev42suwgies?   

  What would be the sound level (in dB) of a sound wave in air that2-l o7fb ;sbuw corresponds to a dilb s-o2wb;fu 7splacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem qz8k*yw )d s3das loud as a 100-Hz tone that has a )83 sdyqzwdk*50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest amwshdu+ / wohf sw3h0+*k7pr ;nd highest frequencies that an ear can detect when the sound level is 30 dB? (See Figs w*;u/m w0+pfhkw h+3 dhor7s. 12–6.)

  Your auditory system can accqq 1zhnwf6jmg (g)dn ( )*7dyhommodate a huge range of sound levels. What is the ratio of hig w(qfzh dn*qh))mn7y6 ( djgg1hest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz./8 anrrg4e* fk The length of the vibrating portion isng*ae8krf /r4 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. What are the fundamental and firs5ixpcq 1 *lhxp9dfi1 1t three audible overtones if the pipe isp*dixch1 xi 1q f1pl95
(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 oen jh(b2pl l;4 s/er9blowing across the top of an empty soda bottle that is 18 cm deep, if you assur4j o92e(/bsnl ;pelhmed 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 wiqv, j2vy ou)7rth open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes)vjr,yqov u72 required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third hp.yo+q .m8b 9b6pk4d dumci8earmonic. What will be its fundamental frequency if it kddbi8u mpceo8 .mp+yq.4b 69is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar stria 82gd )om*p 5qsxco iebx;8ltudd74 0ng is 0.73 m long and is tuned to play E above middle C (330 72xatmp; dx 5co0 b4dqsui8oge*d8)l 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 a ov )o7tdi7 hl5pf,ra:7tyla:3ahrr4n open organ pipe that emits middle C (262 Hz) when t ry,37vr ohp4dhla t:l)oa:f7ai 5tr7 he temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune atk1 n2q zdh4*;re hvm n+z-yyq; 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpish+ 4qjv0/m vo:uix g2ece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle jsuh 2:4gv0qmxio+/v C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but n9 x7q48kkc3efnl fall*( y-lkot at any other frequencies in between. (a) Show why this is ana kl4yn3l7fk (q-98l*le cfkx 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 euw. myc /vopz9hat4;*h2ae3at both ends. It resonates at two successive harmonics of frequw vhz/3hp;toacay9e*u 2.e 4 mencies 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 dizqum.n 7*b6ko/)ia 7wl jmn1il x85$^{\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 tplnd1bzq2dy9)j torn a x3 n( 7939plohe audible range for a 2.14-m-long organ pipe at 20lpoq(ar)3b7n3 nj1 y999plt x2on dzd $^{\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 outsidk4z/xacg kh/x;gx 25pe and is closed at the other end by the eardrum. Estimate the f h gxkz5k/pxxca/g;42 requencies (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 ev 5 vd0mw)it:;nyn;2dv jj,w(t eprk7very 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strin0 d 5p k,ywe)(nm;v7ritnv tj:djv;2wg? ±    Hz

  What is the beat frequency if middle C (262 Hz) sa.-*0pslfex 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) operatx8 ru lf 5/*bi+d)ofafes at an unknown frequency. If neither whistle can be hbox 8d +la)ru/*f5fifeard 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 producep,(ba4 4k:dxlb ipsg7x: k fy4s 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What isxad b (4sykfgpbp k,i:7xl44: the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in on.sptuuw7)mb9- g +fzee string is then decreased by 2.0%. What will be the beat frequency heas-7g.u bz9pw t+ feu)mrd when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two u 7ekk/v h4gg;identical flutes each try to play middle C (262 Hz), but on/74kg;ve kghu e 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 has a fre/ban7 njw4cnn 6*u4jh +bu7sq quency 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 frequenc4b /j7+nwhbnnu nc4uqas 7j*6ies 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 onea06c qgswf g-, speaker and 3.50 m from the -0fsq6cag,w g 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 vibratinzxpyw3sqo ag.i- (dt31gn6:fg at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (ai13wdyfo.:(36qxg stp -znag) 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. Howvp4wa; d //vrf many beats per second will be heard? (Assume T ;/pfv wvd/a4 r= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15ur y 3i +)n:dl2k7eeht50 Hz when at rest. What frequency do you detect if you move with a speed of 30 m nd)r3e+k:iy7 ht2ue l/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine2k3h2ngzw8.+(3kz bxtwp; yco 1glre whose siren emits at 1550 Hz moves at a speet nhy2 k2x lgw.r zb1+;g o3epk3c8(zwd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencs+e d5 l2d6yony if a 2000-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 same? Are they close? 6n +e2yosdd5l $f'_{source\,movine}$    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 on5c4n* tcceo9 ue is at rest and the other is moving toward the first at 15 m/s the driver a*cnue tcc4 59ot 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 rq za 3pp)ag4ra(c e+g2eceives them returned from an object moving directly away from it at 25 m/s What is the received sound freacpraq2ap+)3gz ge 4(quency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/hcc5bg 8ilh+kxu +1c 0s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Wh+bc1k805ghl+uxhcc i at frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplef:lj:lzmzlld3-l/n4vhd; fa:5d fm5r experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba ph l : zj:4mdff:lf /;3llva-5ndlm5dzlayed the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supfbw.tq dey/.5 ;7 l:ao6 ted(ch s.jnapose 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 lsny d(q oc76fw. ; atl/d.e tb:ae5.hjarge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usingh xx*;vl (v dsnx50xe7 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 sound of frequency 570 Hz. Whenosynv2 -3jci /8 :rwir the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, - ji8i/r cvrsn:2owy3
(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 objectv/,y0+ gjb tnu moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/yp3 2; icqm/krs (a) What is the angle the shoqc pm;/ryi2 3kck wave makes with 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 planev 3xw0. r3z*rzskyg2k t where the speed of sound is only about 35 m/s . yk30k wr3vzzgrx2*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 stri2r1*f d6i5 /c vlulyjvkes the ocean. Determine the shock wave angle /u2v l 6fcrjy1lidv *5it 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 we *mzv0 -oo*-h+ydd n$/theta$ 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 ground flyim*-b(e4sv8z p kqg)a fng faster t q(b-) k4gfs*8 avempzhan 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 sotrz.8via 0,rjj fam s o.* i tn4z6.zv5zd1(bfnar device that sends 20,000-Hz sound pulses downward from t5.trz( fat. 0d iz a1ibsjj*6vf,4von8z zm.rhe 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 between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audi jo3o3 b9c -jj+o)dupr8jrhw;ble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonympqvrb+f4)ahg7n4 9 4ybqu6u. It consists of many plastic pipes of various lengths,qab4f67qp4h9mbg )+v 4ruu ny 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 5.0dg yme eg26fx:++ypa5 m from a person makes a sound close to the threshold of human hearing (0 dB). What x2ef5ygg ayp:mde6 + +will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound anr7cdtp8jk e/ah3-psm2r sz m* u4;e3bv v 4zt;d an 87-dB sound are heard simultane; jakvmsdpz3tves; c43hm7/ubr e48-prt2 z *ously?    dB

  The sound level 12.0 m from a loudspeaker, placed in thl+ n) hhpqw/8; :efezbe open, is 105 dB. What is the acoustic power output (W) of the speaker,+f:e p zh8enl;wh q/)b assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 101: a ro ot-a/jwjjyi::00 Hz. The power output drops by 10 dB at 15 kHz. What is the yrt:oj iaj/- wa :j1:opower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically w ss)4hh; lc7.p tgyujq)hbf0xk:f ,2lear protective devices over their ears. Assume that the sound level of a julht7xh;g)b jsy hf4lcfq, )p20.sk:et 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 communicatio 0m+4 )oi8 jnvjpevv,rns 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 x)ram b/+l,biis 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 between fixed points with a fundamentcmjrsku 1 pez4catzd9 9i,(4/q: (xxyal frequency of 440 Hz and a masa9c dq( e1c,/ys x: tjr94zxk (4pzumis 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 v:8: cmrx o,zhyznn m+fo-;, qhertical 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 +h zoc-nr,n h:qf ,:ymxo;m8z 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 m5 tcy:ztsy3 t7ass 2.10 g is near a tube that is open 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 stt:z73c yty5in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fupzml(44ygb725u/s/+ c cco oh zoluo.j2b b:cll loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Th(u yyzyf0h*/ue sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the persoyhf* y( z0/uuyn moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the hohtu*jyg921stationary train hears a 3.0-Hz beat frequencyy9 h12uj ht*go when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle ask(edmyzx n p4(c,;sy0vx8 h d/ it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velymd ,dz(8v;n xphk/ ye sxc4(0ocity)?    m/s

  At a race track, you can estimate the speed of cars justlgu; ,k3w: m+gqrnt3:9vibwt by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it go+lt:g quktb m3:w;ivn3w,rg9 es by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding to ef1a*m*j bx2bgether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the *jxbbe21a *mfother?    m

Two loudspeakers are at opposite ends of a railroad car as it mb xfd4cic.5i+ oves 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) he listens from the position A, i 5bi.c4fx+ dcin 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 th46m,f,ux-9wmsba )bq zj) nh2h ohvw2 e aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasou62bnbah h, )qsxwz)mjmfwu -,h942vond waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the bpp3moa,h0 kbeow10 : hat at speed 5 m/s 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? 10 3o: wphohemkpba0,   kHz

  A bat emits a series (tu5 463 bturzqwh.3h)oicyxof high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and uthuwqoi )h(bz3t5x4 .3y6 cr 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 once )4,pe)0bwgg1u30p hbsu bm:sk xzii ;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 flat) horn. What is the fundamental frequency of this horn, and which overtone ihwip ,gz; s0) mbkxb:4)e 0s31biu pugs close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stzm d,82smi)b yaep 2,qereo listening 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 f)p8 aye2,z d qmsbm2i,requencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing 8 ubcxljm,ws 3;ja39grods,” involves a long, slender aluminlwcjgma9u,3s;j8x 3 bum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. 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 ear at a frequency of 7/;lfv)u ivim about 1000 Hzivm7u lf)i ;/v 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 on2e /zj wus pfg8+u)f4z the ground hears the sonic boom 1.5 min after the plane passes directly oveugf84)jwz2us +f zp/erhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is r-vkpa+6vk,x te 4kyc ;pypsy* ) 8qy515 $^{\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