What is the evidence that sound trt2bnnoau4s /pfe8vo6/r 2 vp +avels as a wave?

What is the evidence that sound is a form o sq uc7mzd 8t6c/tu56gk ;;okxf energy?

Children sometimes play withk3 h6 a 8qwsuh n6ent0;d0tf9i a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the soundk0tdue8f h;ht s6n3n60wi 9qa wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frewsyx:izz :/v9)ga .l s: zl5n.aev e2pquency or wavelength to change?l vian)s/es.zz:z 9.:gey a 2x:lpv5w

What evidence can you give that the speed of sound in air does not deped16xmivioxo-5)tw2g8 .d)tqgq* h g lnd significantly on l2goq )6ix*m t-w ihxdgo.dg)q158vtfrequency?

The voice of a person who has inhaled helium soun 1xs/ t.k c3pu34*b 3wkoccgazds very high-pitched. Why?

How will the air temperature in a room affect the pitch of ognvn:h 3 qf.n.rgan pipes?

Explain how a tube might be used as a filter to reduce the ampliti)s,c -tkcdosb5 v)t)ude of sounds in various frequency ranb t s)5d,vks )tco-i)cges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as vuo)7xxbda f/(u u5s 6you move up the fingerboard toward the bridgx xo7ad6u(ufb5 suv /)e?

A noisy truck approaches you from behindzz+ .v((jnfbp rw5i7y 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 11–15 on diffracti5zprv(j. b(+ywif 7nzon.]

Standing waves can be said to be dun5 kaj2xks75x e to “interference in space,” whereas beats can be sak 7sn5xa5 xjk2id to be due to “interference in time.” Explain.

In Fig. 12–16, if thk+ otoj ,hr*jxlo7p( .e frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or co k+l, (rp hjox*.oj7tloser together?

Traditional methods of protecting the hearing ofbx fcd:1y ov82 people who work in areas with very high noise levels ha8ydo:f2 vx b1cve 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 reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as x9-e, nmjwkz8 a superposne,9x8z mjk-w ition 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.
(12-31)
(12-18)

Is there a Doppler shift if the source anekb,efr+7mde s+ 9j3q d observer move in the same direction, with the same velocity? Exrbe sf,+keq93m7+d jeplain.

If a wind is blowing, will this alter the frequencf7/:, a lmy,xpfei-bmy of the sound heard by a person at rest with r ,ix,ap /ff7:lbmmy-eespect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a cpk;ug /8 pk+:rto)yo0uel r+ 3invae*hild in motion on a swing. A monitor is blowing a whistle in front of the child on t++n *rg tu:3u) ok0ka8ppeyo/;v ile rhe 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 o x gz;e3kh-l6yf a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengthl6eyzk; gh -3x of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of elcux 4pp i pb(.xx,( q//wh0ahis ship just below 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 notaec x wb./( l(hpx40,qpp/uxi vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 204xrxx0fwyx(v7kbm9 -nbt g94 $^{\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 gez zsf8j:gx11f ;( shtztt.uhb(q(a;m l(:his drifting just above a school of tuna on a foggy day. Withou;zt:x (a 1q.(f;tbtg z8lz h1:mehh((gus js ft 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,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when stripelyi* 47k2es king the water below is heard 3.5 s later. How high is the clls4yiep2k*7 e iff?    m

  A person, with his ear to the ground, sees a huge stone stx.4),i n xqaqrrike the 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. How far away did the impact occur? See Table 12–1.x )4i aqxrqn.,$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second ru/5fg ptbb7: ma)-zg.qbupz r*le” for estimating the distance from a ligh bpqzb-:ba*m) 5r.g7pg ft/uztning 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 x 8kgk jtr/(m(sy(+ip68eio tlevel of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose int *8a6j5cf uc2uh k)r2ez0miv uqrv .j*ensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslyr-jkq2td0rz 131lbi1m kx0l t at a certain place, what will be the 1tm02qz-lbt k1rd il103 rjkxsound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four yk/ ,bq:lmdj06w,uh eequally noisy je0, hwb j6 y/ul:dq,mekt engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB*f2w k a2p3bf gjix)p7g,+p -uvt j+cd, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise f +g 2+vw3u)bjtg2f7p dka-* cip, xjpfor each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fro) m)v6uyy wu5:z 7ysydm a person speaking in normal conversation. Use Table 12–2. Assume the sound sy v))5ywuy 6uys :dm7zpreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an n +mlofdjt xejq21c(( fn-yx5k95 5 oxeardrum 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 6h6 4s milrx5w rw.7cgW, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in ww4rx 6gi l7rhc m.5s6decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when s1tk15x1+ pdfp,bmasplaced 2.8 m in front of a loudspeaker on the stage. tpf a51b,d1pm 1xss k+
(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 typicuow/+9e e ,zopally detect a difference in sound level of 2.0 dB. What is the ratio of the e,+ /pewoz9 ouamplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, -rkq6 t ;qxyn d55s;gi(a) by what factor will the intensity increase? rgxq5-ny 5ik;qs6dt;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 the freg:31 kf(g/va l .na6ofzj0q2zhj zu m*quency of the other. Wha*3f21ov0h (fkzm/ gag q zza 6:.ujlnjt is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wa5 m.bjbc ;3wpmupg1*ive in air that corresponds to a displacement ambbw35pm g* j1u;pci .mplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that/hu: 1njhg4wilx ,e)t hah:,/)t1u inwgl h4xejs a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest myt ew24jnwet6c )ggl+ 879c qand highest frequencies that an ear can detect when the sound level is 30 dB? (Secw 7ctwngj8+2)49 6e qt ylgmee Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thl :gds;7 - vh*p4gweo/ s9zrei3 -chgse ratio of highest to lowest in-9ge r z-3h ;w4vlsod: *sghgcpes/i 7tensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has ayg k 11jd3fdil2nodzb ,277b m fundamental frequency of 440 Hz. The length of the vibrat2okzl fy1b b2d,nddjg137 im7ing portion is 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 first tia .jv:yd s 5jfh/v/g4gucq( 9 ,uj1sxhree audible overtones if th194fu ( y/s/uxsg:vvqadcj,gijh.5 j e pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would y 07dhsj2g9 hcvou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumsc27 dghv09 jhed 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 re4zr1*nyko; u ange of human hearing (20 Hz toe4*;zk1yn r uo 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of z +gcuwyu*f* ;540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengt guuycz*+ ;wf*h?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle cw5hx) ue )2m2o/arssC (330 Hz). x m /cu2sw)es 2a5r)ho
(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 mhg:hvl/r. 42 2; bn gqtauefj1iddle C (262 Hz) when the te2 2quf ;btgl hhjra/gvn:4.1emperature 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 am3i1 lic3zko3864mw 4psna;l+ a urgwt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shoul:6g rfbo;i:w ud the hole be that must be uncovered to play D above middle C 6:g;u :brw ifoat 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 r* of*hd 5msbwf )4ubi2esonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed p)s5* hub2fifowmdb4*ipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is ope( wxwzi 1g ekswrw+.50 x)val:n at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What 5rl.wz(v1gx ka+:x0 eww)si wis
(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 ie19vm7/laj p $^{\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 atm(*,h l: jac .3zfiise s6r-o8f lms+re present within the audible range for a 2.14-m-long organ pi(cs 3:o 6erhf,-mm+ l f zl8tis*a.sjipe 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 eslc/-r*mc1a to the outside and is closed at the other end by the eardrum. Estimate the freque mc-r1cl*/aes ncies (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 ever47 *xs1ivtraz y 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stx* ztv74is1ar ring? ±    Hz

  What is the beat frequency jaa3vi8vbiru/c m2,/yv/ q 7sif 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 ,+acoc:+ezqt76e wuqo2:jrg at 23.5 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 played simultaneously,z:tuc qw+r+67goe2a: o,ec j q estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when n l*4+k ;n.n7ozur eft n23ip: q(llmusounded with a 350-Hz tuning fork and 9 beato+u *(pr :l2t7 nem;.nl inu4qlnzf3k s/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned au4eq c(qzd;.to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toget.d;4qq(cua ez her? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pr5 1td s2pl9rplay middle C (262 Hz), but one is at 5.0°C dl r9rt1psp52 and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.by:2 rdfi10 vd Fork B has 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, t20 d: yb1difrvhe beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m e7s20qs/)kga2zp 3(puesmyk 7e67o :knnk rofrom one speaker and 3.50 m from the 7ekr27pgoe:z2 / n7 skpyen (ks0k qu3a6) omsother.
(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,ozh- 7f8z) wzyvjn,mr, m+u2q but a piano tuner hears three beats every 2.0 s when they are played togz8-n,ufzyom2wzjh,7vq mr+) ether. (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 mn/aw0q f7 -vey and 2.76 m in air. How many beats per second will be heard?0f7a envwyq- / (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine , nyn;a3o f(u/ju/nbe’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30/jou3ynun;be/,afn ( m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freq/ u5a4+f*vc+ csk feyiuency do you detect if a fire engine whose sires ifc*+ +u/ cefka5v4yn emits at 1550 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 2000-Hz source is m(umhm1u57nlhz x+kv ,oving toward you at 15 m/s versus( u l, khmmh1unx5+7zv you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency hornj+apejh- *4, 2kd4fyt(jp nm e. When one is at rest and the other is moving toward the first at 15 m/s e, +f j(e d44nt*ma2h-ykppj jthe 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 w, .: so 9pi3zukyr/ghand receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency:s3pygr i.9wz,ku h /o?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat enc g8ax:dssm.a2 nup 6y w66x:mits an ultrasonic sound wave with frequency 30.0 kHz. What frequency sxu6ag66y a w.n smnd8:cpx2: does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba m0 cnn0wmf*( fwas 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 *0c (0mnwfn mfstation at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves 2s song zcb9sm (vr/((to measure blood-flow speeds. Suppose the devicsv( (oc /bn2 s9z(smgre 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 source?   Hz

  The Doppler effect using ultrasonic waves of fredryz: p yvtit(;154ji.bw 0fzquency $2.25 \times10^{ 6}$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 emitpc 8(;yc i ez b +ldkzqbk2k*,2bk:ib+s sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, bz82+pi ky2(k qbe:+kz*l,kc ;d cbb i
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2/g )xkltv*7es oyu4u50 $^{\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/s (a(igxa*far0hy4rq)x8 +c5 df z fa0:yo) What is the angle the *aa aff8:d+xc (rx0hg y5) rz4y0ofqi shock 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 vh15y1iyykts 1zs3 )w; xrbh,atmosphere of a planet where the speed of sound is ,z;xh5 1v3tyb)yhkw1y s1 isronly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikeo ,c iq.-phhz0 c2bjn3 1rte-rs the ocean. Determine the shock wave angle it npo hhrj1z-re c t03cb.2q -i,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 j ixl i+ pu 6u800rsxlm/p4d;w$/theta$ 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 kmly3 ky8e y3-q,vt 2qffc,urivuv e.9v, g:ug 4 above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontavyyqyu vklfq3cggvuf9,8v 4.t -,e,3 :i2eurl 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 b 1gidy8yg 6j.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 between pulse1gi6db g yjy.8s (in fresh water)?    s

  Approximately how many octaves are there in the human .( eo 5vh5cbgo3xk.st nsb6tpp *tm5-audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sypjd2iioo zfw5*gpl / 6.j v 9q5fdi4u:mphony. It consists of many plastic pipes of various lengths, whiv5figi l.2ufqo / ji*6j 9zwop:4d5pdch 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 persg8ws*e0j) cce v7k4 zbj9s/ wmyxe )f+on makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000w7mc z*)bsg 8 k ecexwyfe/+v0 9jj)4s such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sous r/h+2u.xc rvux47la nd and an 87-dB sound are heavc sx lhu xuar2r./+47rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 gqkv;v i)4im 0dB. What is the acoustic power outp vvm k4qii)0;gut (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 10p z51skuia1*lk:)/avkbu :md w, ab4h 00 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts a)1aaz5p/ kad 4:hb kvs b1uk:,lm *wuit 15 kHz?    dB

  Workers around jet aircraft typically 2 fxk0 e5au az82an1l m5gz5wtwear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would bet2 a25f k1u58ml xnazge0 waz5 the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communi w(3ui1rk dsfui+jl(k+g3a o1cations 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 tu(b51ocz3u5z gyj va/p zt*l t(ned 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 fundamecysc ns *xc .b3(ty*6intal frequency of 440 Hz and a mass per unit leng. tsby cc*isc36n* xy(th 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 vr6qv3bs//ho+ gn nii 1ibration 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 and again 3or g6h+/s1nnii /bv qat 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g i9 ( c2h;e;ht8pfb9jfh m;ey mts near a tube that is open at one end and also 75 cm long. How much tension should be in the y emhe;mhf( ; 8htjc9f b;pt29string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fwgvpi r.y npz;.,tr2x,ik;n ( ull 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.g3i/8 z2 q oy ia(qswsywz-oj.ta5 /5v The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. assq5ajg w 2-i5 qzy3(o8wi.y/t ov/zWhat is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationacq eg+mm9t6+/0.c x ymsdk2lrry. The conductor on the stationary trainmgts+ yqmk2dlm ce 9x/.6r+0c hears a 3.0-Hz beat frequency 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 Hz6qdf25t ,iypy-7.evsx a m-ym. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocieatm qiy 6 yf-7 ypdm.sx2,5v-ty)?    m/s

  At a race track, you can estimate to/zb93 em:f6z.r/ cd ix3gzb mhe speed of cars just by listening to the difference in pitch of the engmbzz/g6 fmxr 9/ezi:3c3db o.ine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togeterd3sif6u9s; as o mz x4w//2sher, produce a beat frequency of 11 Hz. The shorter one is iro9zef6m/4;2ws u/sas3xs d2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past j/jc 5 tgxi3r 94at/ 7thbnrr1s8ch5f a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakrrh8na cf/g xj9 i3bc71j 5tt rs4/ht5ers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) 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 th m-+wqi1o.xg u51aw ly.w1eaf o,3rche 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 3.11.qxi a ycmor- aw5 w,1gf+wueolhfrom 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 thecvn, d/)v5 h(:yhrtap bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by/p(v)rthvna,d : 5cy h the bat after that wave reflects off the moth?    kHz

  A bat emits a series of h qt1t7(oz4 tzzf x7q5oigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How faz(4 oq1ftztox5qtz77 r 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 used to send signals frombav)vp6m o7akkf z+81 one Alpine village to another. Since 1fo+pavk a b)z867vmk 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 is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence m jb3owmj,f.7a p5-;yg0e zd mof 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 2b m70;wz,g j o.jp-fm3mya5ed.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv z9+opik)5f oxn n ,ys*i6gyn1olves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, l9on), 1yz px 5fsgi onni6k+*youd, 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 ofjv))pcjz7z 4 e +o7 mgz4k0mvx aboutpjjm zz)4gc7z xomke07)v+v4 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 groatnb, 7rlqn;ry ;:e gq3e; ok;und hears the sonic boom 1.5 min after the plane passes directly overhead. What i le ke3g7oqnn;br;;qry; at:,s the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is s7kot16mt g rmx2)3q5rxxi e ,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