What is the evidencegs s3ge:e7:gr that sound travels as a wave?

What is the evidence that sound is a fi;3rek*wt qpqzh997borm of energy?

Children sometimes pl324oaeb pqlgum+ 2a5ho4cf4 o5 syfe83o n*rvay with 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 cleayo42 na roof3lo55fpg8 cuev +3ah 4bq2*es4mrly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect 0.h ie2 azf(anft2o3t the frequency or wavelength a nofiezh2a tt03f. 2(to change?

What evidence can you give that the speed of sound in air does not de ,4tzpl/f tgb.jfe7 1hxha+- upend significantlfbj/a lf p,-eg1zxh7 tu.4 ht+y on frequency?

The voice of a person who has g 6bl-oe1uuzdm*p 55t inhaled helium sounds very high-pitched. Why?

How will the air tem a/3afrgyzor6ya9j/ e3sw* *t perature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter tq*seoj+)a8ml qwjg; 0 o reduce the amplitude of sounds in various frequency ranges*e0gqj)8oq m a +l;wsj. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30)* xv1.ybqu4mw87 t uaz spaced closer together as you move up the fingerboard toward theytab8x* vw41 7qzm .uu bridge?

A noisy truck approaches you from behind a building. Initially you hear it butw*nwos(. p f kbf0mx69s k3zp/(vtkx (/j:apj 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 onm(x/ 3:szpp k v0(wjfo kw9pb.*(sa/t jk6xfn diffraction.]

Standing waves can be said to be duu;d uge8:i5 i e(56 iqiu v-zzd,-vvahe to “interference in space,” whereas beats can be said to be due to “interference in time.” E u(-5dgz5,;v ee6 uh-:ii vqudvzi8ai xplain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the point9rhoev9- mkd9 s D and C (where destructive and constructive interference occur) move farther apart or closer togerh9-d ko ev99mther?

Traditional methods of protecting the hearing of people who work in areas witv jgc/ rz15el5h very high noise levels have consisted mainly of efforts to block or reduce jr l/g5evz1c5 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 c miip+31 ywbzlg t1j; bj8xr3(an be thought of as a superposition of two sound waves with slightly different freq3tg bzby (8m;x+j i1w1jprl3iuencies, 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 s0upco 33qnso8 ah9nw/ hift if the source and observer move in the same direction, with the same velocity? s9naw3qcu3p/0on h8 o Explain.

If a wind is blowing, will this alter the frequen balv;4 *0r+i*bs4zdjm5 unr aes1cc/cy of the sound heard by a person ;+ ua4mjbv ln1bs5sec4r0 r dzc* i/*aat rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child i6clt 5ftn*8 t7f*mto cn motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At whichc*lt*nfm 8 fct 657tto position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines th w* +eg((v* *h.wj;aes jhcylfe length of 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 length el vcf* j*aey+hs (j.hw;wg( *of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his sift1-* 6 ks;wtsixnu2t6rlh6 hip 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 not vary signi it*n itsw2 f1usk6x;6r lt6-hficantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atic0vusdm. , db*am0zzm o-vxz 1x6;0s 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 foggyzs+hs** 2-6 u2hlwkyq6evazo f78 xsk day. Without warning, an engine backfire occurs on anosv7kwhay * hsfozzu-8ql 62e6x+2ks * ther 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 toushi/a-scu . 1d-2(1krdw5kwr.ar ifp of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hi s/- iard du 5k ca(i-12r.sruhwk.wf1gh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cgeoqq59 ,9z6gzl*nul f7 + xuyoncrete 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 du7nl5ze9 lqo*y9u,q 6g xfz+gid the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dista8khgb-l(.*b sq 6vnxye7 yom3 nce by the “5-second rule” for estimating the distance from a lightning strike if the tko-qv.xb 3m 8l 6b*ny7g(sy heemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the) p6 )b,bqciu2a:):tuwn uyye 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 ofd d4hpx/m/ b*l a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously l0r *))a;6g/ *pqjrphbbiaovat a certain place, what will be the sound level if only one is exploded? [Hint: Add intel*bvrp;a rq/bh)joag0*p6) i nsities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equaq9ytg k ) km: 0ey;a+z2j)odjilly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut downyd +9iqygej)2j):zm0 kato;k all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hav s-fd*b q6flv)e a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device sv)ff6*b -dlq? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norm2thwq6v4*yb5x1f gw1lpx -(.se wp ob9arth9al conversation. Use Table 12–2. Assume the sound spreads p2bl5wxt *19oes v( .hx -wra4gw69y1qhb fpt 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 eardrumq,yivfyha *y/1;m 0xf 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 ir3y6nh75ni 0 jcgg5bx.jgl 4zs rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in tur gglyjgr4h5 n 75icjznx6 b30.n 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 re:+si/ wg 02m)ar yaewvtj2y9pgistered 130 dB when placed 2.8 m in front of a loudspeaker on thew ypv +s2m:) ti0a9gwyear/2j 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 typical-;rrk2 id+z zu-van2q-4jj gfly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudesavgfjn;r-duq2 zj -- 2 4kzir+ 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.jxr 3x e(idcyu-5gf u)ej *-r what factor will the intensity increase? Increase by a factor uu ee(5-*yij3x )c.fx- rdrjgof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa*/d 7ga f5przgcement amplitudes, but one has twice the frequency of the other. What is p7grg *zd/fa5the ratio of their intensities?   

  What would be the sound level (in dB) of a sounhub- 21gl+xf (ivyt:/pyw0 mrd wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300ymi1 :u0-p(xfg yh +tlbv/w2r Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lof+ t r5u psn66 ktxf:bl.n-m,cud as a 100-Hz tone that +66tm5k cbl. n-sf:pnu ,txfrhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencty 1b4f kql(+sqvz z+(ies that an ear can detect when the sound level is 30k+sby1 zz( l(q4+vf qt dB? (See Fig. 12–6.)

  Your auditory system can accommodate ; 90 azrezk5hzyww g0yg f37c2n)ygmwv: .6qva huge range of sound levels. What is the ratio of hhyzk )fgwr6q:073y zvgnga.0 y;c29zwe vwm5 ighest 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 b8hh fvr8:hm ;of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be plhh hf:;v8b8 rmaced?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible9v o/5d0 jofnnalht 8/ overtones if the fj tdl n/98ohn5o /0vapipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from bl. ondnvt6s /i yblfai; , ecmo(,-5z+gr8i/bb owing across the top of an empty soda bottle s ( bl.ty6o v+b;i,-5gr,a/m / doenbfcn8ziithat is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tub2 ok8i3tyahx/ j35aiv py.cq7e pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengthtv i h3i 5k3y.qp 7/oycajx82as of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has al d*b*vgr0s o+3q rskn+n2) jr frequency of 540 Hz as its third harmonic. What will be its fundamental frequenss+ljr kq*vg*ro3 +)r0b2dn ncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73u2eyka h u/ i28yg4b:b m long and is tuned to play E above middle C (33hgubbu / ae2y24:ky8i 0 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 that1:g vg4 n:i ywf2pkz3u emits middle C (262 Hz) when the temperature isif z:gvyku3g:p4n12 w 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 azx t)g;yn0n;tp5dn1 lt 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 should the hole ad94*2if3*oql m (piok5gncq g7ioq,9 nf f2ybe that must be uncovered to 7( m lf9, n op9i*g*qgiq2 35oo4dckyffai2n qplay D above middle C at 294 Hz?    m

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

  A particular organ pipe can re9w8/g uc)mwugsonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencieg m)uwugc9 w/8s in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both etmmj+v*4xh .6idt0uy/d 7 z ennds. It resonates at two succe ty6m40mdeivu7h+./ jt*nxzdssive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 ux *e rqp;0k9pi1hgs-$^{\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 pr*c(p(c6(qp jf pvfxl pse b5qh o1,ddd2:1xb9esent within the audible range for a 2.14-m-long organ pipe at 20 hqj(pvp(d(d p cfpsd bcx1l, boq* 2:956fex1$^{\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 toh yvb,:5jsf0c 0mqxdhu( xr+6./kq l o 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 s+my0,:/klfu (xq.xr qov0d65hch jbcanal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every r 8wzg8sd93 vcxm9l6n 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far9rs xlg 3mv898z6d cwn off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Cl2 2awu-k 2th9kdqmxa/dn+j,6 wm jz , (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, w f (f c7rto4a/9zeyyb)qx;+ tshile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of fre(tx y4)cy9f t7o/+ ;frs abqzequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/sr- 4nnntkofl 9 gyqj5rq.,2v m)y5q7 g when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What ir q9qo). -q y55n2tv g7m,g4fryl njnks the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tpdri,bga(2vymi j )3+y*ulp ;ension in one string is then decreased by 2.0%. What will be the beat frequency heard whej,(uvayip3)p*2+l;yrmi gd b n the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical f5 ahtymu1br(n;wly c ;920rb olutes each try to play middle C (262 Hz), but one is at r( 5a9um;;nt 2lb0ycyrowh b15.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 tw ltt 8s1fdmz.0 e6d3Hz; when A and B are sounded togeth31sw.t 6ft0l 8zdte mder, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaaixl f(+ z-,8: lhpatsx5(wmo ker and 3.50 m from the other. -t(f is: m(azxo+ lahxl w58p,
(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 bed waw-;jk wz /8h8grm6sf0y 4a vibrating at 132 Hz, but a piano tuner hears threr;8mhjs-gfd 08 k6w/wzwaay 4e 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 airdo5gcx nf ca:)x1b80w . How many beats per second will be heard? (Assume T = xn85:wfoc0b d) cagx120 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren1l 3l9 a)dptr8 roux)x is 1550 Hz when at rest. What frequency do you detec d)lp18lxxa 93ortur )t if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire l2xwa 9cta /f/)lcrd6engine whose siren emits ataxc9a2dfwt rc) l/l/6 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 ,s/vum 3mn,vy2000-Hz source is moving toward you at 15 m/s ve ,vsn,y3mu/ vmrsus 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 with15 )g mbbht6bc the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequen b)m6 b1cbh5gtcy 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 rec; o xfzyj)(yi;-apfk16 kcu /turned)cpkf6i / ( kf;cxzu; a-yj1yo from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, t2tpr8 ly fb5bb4sg *0ohe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the refl*f5o4 ygr0pb l82sbbt ected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on h6 jvx(u*h8x+. egayd a moving flat train car at a frjv*eh a.+g 6y xxdu(8hequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavel k78*iddyxaznxt 3 2-p 0y/qbs to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if bbz/qpkdy x0 dn3y2*i78t-xa llood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency a*7.kb*kze idkuyg 6 +$2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12y4q+b;9g9k b pb(gbe x m/s from the north, whatbxp9bbg9+k(;b q4ey g frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object 3 czxjew6qy*1os oz,( 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 them a-cttcfus6he*, /0f speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s m0 ucas*cf/m ft6t ,-ehotion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wc3+1wj n6 7c4yh y.dqqyk vp (2iu4hpvhere the speed of sound is o2yv4p ckh 1qc. yiw3q7d uv4j(p6+hynnly 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 strikes the ocean. Determine th 67 izj9v +kbt7ybzl,4gf0 -tlenz)y se shock wave angle it pjzk n bbts zl64y0tlev7z97,i y)-f+groduces
(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 b7qm3v*mbi * p* )mqlb$/theta$ 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 exactnm1 dqu(r.c4 kly 1.5 km above the ground flying faster tha cun1mrqdk .4(n 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 sendshgjbgf +4c rf0apg+bi2qcm bc-q.6 -; 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designedgr+ bm0 cfcp2fh;4bb -g jc6qa. q-gi+ 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 audible*lghmg9i2 yt, range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal,5d (, wh(mux1lm3r9gshxge kled a sewer pipe symphony. It consists of many plastic pipes of variou, s rk,ul3wxgh951me(hdg mx( s lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes+h*t6ojad zaj9xb2 ec l 4q9lf/(rm.x a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mooqarx4bl/9zc(6l*x 29 m + ajt.jhefdsquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-c2yvz hq0amn3v1-1a m dB sound are heard simulta231hc 1 -mnq 0vavmyzaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105ukqyt1(jiv l8fh3ru)ur 2m0)/ms ed* dB. What is the acoustic power o/8mu0ty()u ljqs 1*) miruvdrkhfe 23utput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The evqb6m ./e o169xcl.h ;qqkakv2:drppower output drops by 10 dB at 15 kHz. What is the power output in watts at 2eqv.;ep/rv1l:q 6ko baxdmq9 c6h.k 15 kHz?    dB

  Workers around jet aircraft typically wear protectivea50 :x(o-hkmckgz g3n 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 wouldax:g50kc on(- hmg3zk be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicati sex 7y6tb ez;g a9a)1yb1cbu.2g.eat7j bti5ons 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 9edfzvq7n s,jd5:wv + 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 lo yhtjc589vi4 ing between fixed points with a fundamental frequency of yv 4ic9 8ithj5440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube a r71jyn 0wjb)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 frb10n ) 7wjarjyom 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 4 m2v x.bzuw)lpds ,9ystring of mass 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 resonu94p, x 2yd.b)zwmvsl ance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loog lo*n6 z: 9(i.wr*ra+mcd dupp ($\frac{1}{2}\lambda$) 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 pur/l9z yb/oo a,ie tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequen bay,o/ /lz9iocy of the sound?   Hz

  Two trains emit 424-Hz whibuq t+r 4mi0f3stles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving trafu+rb mq43i t0in?   m/s

  The frequency of a steam train whistle as ikwxbr 1v;d o5x a4qw2w mg64/mt approaches you is 538 Hz. After it passes you, its frequency is measured as 486oxdw2xw46m451vrqgmw/k;b a Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate thv3h o s,6gz0*jy2hrbx e speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suhvb3j0x6h*r,2 gz os yppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beatbez r9+jm/ hsmtfo0*c8 r2b( p frequency of 11 Hz. The shorter one is 2.40 m long. How lonor9t 0ecbsh fm(m2rp/bj8z+ *g is the other?    m

Two loudspeakers are at opposite ends of a railroad 4,n6t,rm4z0plbhu pk car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) h,bltz60 mphknur,p 4 4e is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what 9y, nzndgb5,69xsiqcq3g qj;beat frequency would you expect if 5.50-MHz ultrasound waves were directed als9b3 ,y qg dz5gjx;9in6 qqcn,ong 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 spe. wls89s nmc:wed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.ss9 :wmwc8 nl.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 so2be ,jh7jfx,s und pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat fh j j,2b7,esxso that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was+sps+5p cjoe, once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss,eo+,j+5 cp pss 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 thee nm awi(;ysvyaw6p6*k3ien7t.e ) ,l 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 frequensey;7 a (n6 tl)kpei,ve3.m6n *ya wiwcies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, s :vw5sgc fff1*hzz72plender 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, loud, ringing sound. For a 90-cm-lonzzf*7 1v 2s5h:fwpfcgg 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 hea i7s;lg3ovfb*s,ra 7f,m4qjcring for the human ear at a frequency of about 1000 Hz is fmba,4cso7*;vf qs jgl,73ir$I_0$ = $1 \times10^{12 } W / m^2$ 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 3k nxhbyq 8ia) 536. pmqwvstj4k-c*zobserver on the ground hears the sonic boom.a y hqvcw8k-* 4px3znqm b 5ksti)63j 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ikdpn*j d7 ,s*ss 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