What is the evidence that sound travels as a wosb0zon*kz 3 4ibdcx8x82o + cave?

What is the evidence that sound is a form of eo, ld:q tfh/4e1),wwzhar bc q*7mbi* nergy?

Children sometimes play with a homemade “telepl 6h2t9tk2d jwhone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to tlht9k 22wd6 jthe other.

When a sound wave passes from air into water, do you expect the f7uzy, ( donfam(i:u8orequency or wavelength to c:u (o8d 7nimyf(o az,uhange?

What evidence can you give that the speed of soundpgr+*zid0l yc)kt *izv. u32g in air does not depend significantly on frequec p+guyvikti*r)d* 2.03 z gzlncy?

The voice of a person who has inhaled helium sounds very high-p.lkn /i+bxyfw o,s +4xitched. Why?

How will the air temperature in a room affect the pitch of organ pipe8 jjr 5-dqvy z)y+*6x2vb bghqs?

Explain how a tube might be used as a , a xnr/uo+g3 yoxw0;pfilter to reduce the amplitude of sounds in various frequency ranges. (Axr u/+ yxn,;a wo3p0ogn example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tfma-:mw ,qdk83m * 8yxqnig:n ogether as you move up the fingerboard toward the bridgfw:k:xqqn-,*g8 mmy in3 ad8me?

A noisy truck approaches you frveynr13vo s..u 3ot4) hn di5dom 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:. 5so3vr4eh 31uitn)on vy.dd See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats w,y0 , cf) qwqr;:mnelcan be said to be due to “intc q, qn0fwm:ley) rw;,erference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wx y s t+tz,18 )na ktdxn,+chbh,mq((nould the points D and C (where destsxtnx (t aqhn+mh(d 81kn,+,,ytcz) b ructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areaszw)vs0r 5 swufi /c,w0 with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn thatws5c,uzriwv0)ws 0 f/ 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 Fig4e * :r0jmy m4q2ptwjdjju 0-o. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly differenjerdu jy0m wt o2*4pq0jm 4:j-t 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 and observer *z f0 7.sxo,dwc3xwrm move in the same direction, with the same velsmwxcr.7* 3,x fwoz 0docity? Explain.

If a wind is blowing, will this alter the frequency ofi.1 5iu-bv -shs p/iycf-1orc the sound heard by a person at rest with respect to the source? Is the wavelensp1.1-c fh -soyv rb/uiici5-gth or velocity changed?

Figure 12–32 shows various positions of a child in motion a8aeqq;o:ylvp6wn8 * on a swing. A monitor is blowing a whistle in fro8a:8olapq wy6nq v ;*ent of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the2-4jaefa d eu+ echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s a e2ud- e4+jaaffter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears tz41m)v-y biug he echo of the sound reflected from thgv m-z)y4uib 1e ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in mdd9h riot6,p 3d hu7.4ginu5i s 7t)qair 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 8jm,yaecpkvr2 r 2wu;0m8c* z a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elca;m j*u 8ry2vp m8ezw2kr0,c apses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frocmi9mi2+6 w x6 vin9rmm the top of a cliff. The splash it makes when striking the water below is heard 3.5 s lateim+ riim9nxw9m 66 cv2r. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the n 6vjoqjx7ff0v( gi 3my oh nhy6h(-40concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concre- i(foj6hgfq0hn74omn 0x vv hj 3yy6(te, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance:ts 6nvh:bh iv.6brb 1 by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 htvb.h6ri: n bb6:sv1 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound loku6*z5 oo p9at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity is ucnv;,t3 5qzm$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired si7jz39 ti ( ctkvj*:jlg+x2 jremultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensi+j:lec i7g(3vx9t*rj jk 2tjzties, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equalq t2yqmhv i0 (3oi)o9sly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captai9 3ioty h)s o2qvmi0(qn shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have arijm(h +ytg y9m+ ua5/ 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 dh ygat/m5jm ++9i(y ruevice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outp()4na)e;ta wtdl c /huut of sound from a person speaking in normal conversation. Use Table 12–2. Asalc d;)/)wa4tu (e hntsume the 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 strikes an eardrumo xt;-*spll1o rdla,; 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, whih,1r wna:; tzple the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected inp n:z;r wt,1ha 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 plafoqygo7f2pmw/. bi;n/7 k ge2 ced 2.8 m in front of a lg 22;qgwykfeo fp o .//77nimboudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically d3u ob y2:)vvhdetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ b3v yo2hu) vd:by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sxp.pobf:m8rn. qbx*/ u t+qj 0ound wave is tripled, (a) by what factor will the intensity increase? Increase by a factor of:/fxumopp8 *rxb.0+nbt .qj q    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa9hc8togy. p6ab4t(p f0sy)jj cement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensit. yohbg86c sf(pt t4yjj0ap)9ies?   

  What would be the sound level (in dB) of a sound wave in air that ca:2bb;2 ) uiyymn6q zn yoj7:corresponds to a displacement amplitude of vibrating air molecules of 0:uj2o6qc yny:yib2 zm;7n b)a .13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what s wb3 qf- dr :(;cp0udcruw)4evound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? wcr3qdr0)pd; u c w eu-:4fvb((See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sou/uo0gd j;)/gxwj y a9rnd level ij/j/o9; r adguw x0gy)s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the b(n cwra-xs :1i3vx+k rationc 1x(3bv k:i-w xas+r of highest 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. The lengthpv.)x/a5i b b bkn29os of the vibrating portion is 32 cm, and i nsvx.ba 9)k/2op 5bibt has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whvpi1cyj v72/ m4vczux5z, t(mat are the fundamental and first three audible overtones if pvc4j v7mtcv y/z521zi ,xum(the 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 you expect from blowing af/aw 6sj4r9svcross the top of an empty soda bottle that jw46sr savf/9is 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-tube pipes spanning u)k vl3r7 *8ypx gu/ebthe range of human hearing ()pv*3eu/yk xu8br gl7 20 Hz to 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 540 Hz as its thik.r7p2 ps(j qs3 qcsf-rd harmonic. What will be its fundamental frequency if it is fingered at a length oq 3spss-7f2j crk.p (qf only 60% of its original length?   Hz

  An unfingered guitar string 9 +uab)qyp7 lfa 01,g 7,vsfs+cckivsis 0.73 m long and is tuned to play E above middle C (3+gs pvl0 1fs7 vqk+c,u7b,a)yic9fs a 30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C dn l*ezxmfbd5 z0 7np4/junn; 8n9 p+m(262 Hz) when9npdx+n8m;z p7m40/nlj*dzuen n 5f b the 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 at 2y k3oh1:s**miho 1 d 3evwifj90 $^{\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 shou0tl wfb 7va,wqwg:- ,jld the hole be that must be uncovered to play D above middle C at 294 H ,wjqtvwl, 7:af-bgw0z?    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 notu bjc. n:kk:mi3j9z) o at any other frequencies in between. (a) Show why this is 3jc ko 9:.ni)jzu:kbm 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 rr:e qk.fbewmnx/af(*h-h :r(8 +npc is open at both ends. It resonates at two successive harmonics of we b-hnax:h. eprk n(*rq:fr+ c8f/(mfrequencies 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 f ak02g+4m qkpyq hjz xz9a)s0)2s/eh$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.6tjsd(1** lza8y nvj l14-m-long organ pipe at lls 816*jvn*jtdayz(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 to the outsid7b: dbllc7r+ia7f nb9 s,qtsa n4nyd.(,n3kje and is closed at the other end by the eardrum. E4cksa d. l73y:itndln7s+fa9,n,j7 bb rbn q(stimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two (yg ur0k nho6r5y u9 :8b (fvhc5/okonstrings, one of wh cugk9:(oy5 buk yh(f8n6o5n0rvr/o hich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) eds.m ef)r h)8and $C^＃$ (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 whistlrv)sei3z fxl 7.x:kllq frl:,m ;m*7 ;l9dg zve operates 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, estimate the operating frequency of brandlklr:xfvf77v;le;:d9*l. mixsr ) 3zqlm g,z X.    kHz

  A guitar string produces 4 beatskx v;6gqzxdq6 cs9o,: v; r6hb/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reaso,qv ;6xz:9rk;s6vchbxd g6 q oning.    Hz

  Two violin strings are tuned to the sa2dshalm, z*z (kq,5tmme 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 ps 5, mmz*(tkqdzh,la2layed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idenpyqx+ttvv3l 146n2z s tical flutes each try to play middle C (262 Hz), but one is atl6vnt 4z2 3+qsp1vxyt 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 akvz hv4u j iwdic3/r;v s0m)k 5 ora4k5a5-jd5 frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C kdr5c5io /ds 55u ajwkv 0j v-4;ikhmv3 4ra)zare sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.mh gg8 ro+pjs; )2fv2qing 52wtuv -9t80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. v2)gwm8rt29sij ;u5gq+g ph2nf o tv-
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tunl,rkj 2ci ,n ma1:7jnxer hears three beats every 2.0 s when they are played together. (a) If one is vibrajj,rn:k 27nla1c i,mxting 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 5r/ e:0advd+4ftkr539lf xmu e zn2qgm in air. How many beats per secondxg/ lezd 2q54endr f5:f3 r0t+uavk m9 will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz w v sj,9e):krwjom-l67)olxj rhen at rest. What frequency do you detect if you move o:jl-ke jr ows,7j6 lrm)vx)9with 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 engine whgz.h/ +m p(wbgshur9lw5. d 3eose siren emits at 1550 Hz m/ hzd9..w 3l+u hepgr5wsgbm( oves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a acig((rf qm3 j3b2v:zroke.e u18y hg.2yy) j2000-Hz source is moving toward you at 15 mr38g3b ek2ec1 jj2yog() .q:.vafhzmiry y(u/s versus 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 hor8xiou /( 0fmcd2be* sdn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What02uf x/i*sd8meb(cd o is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends ou4l7qc1yo-kl+ jgep ;pvqlg/ 6 t ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the pl cl7g+k1qy-/o4q 6ej plvg;received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s bx-bm; py,/ ryAs it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflec ymr,/-bxbp;yted wave?    $ \times10^{4}$ Hz

  In one of the origin0 2)vt:hxtx/vzzi/tni 7 bw 0oal Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if0/x/ )vt7 0ivbtzzix n:oht w2 the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves/: lsqqbl 1ay7d7hs/h to measure blood-flow speeds. Suppose the device emits q7d/l1lqbs/7 shh:ya 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 ultra)o ;gax4)2 jlkwcj 7mh-jpd,asonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocro:n blt2y9dc v i4;6mity is 12 m/s from the north, what frequency will observers hv inc9yrlb2 : d4o;mt6ear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if itsj((o lr* -fba(p kgh6f 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 speedl*7fivp)*13a xgw0h 2h rdlijaea9 0d of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motionrva a30xf*2ijdgaeh h l1wpl )*9i07d ?    $^{\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 -8;s0x pz+mi.jq nrirv19b gp02q m qsa planet where the speed of sound is only ;i-rrsqzg qp0mn81mx. vji2q+0 p s 9babout 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 lhu cdc4zb 2-5v;s dj,the shock wave angle it produces bh2djc 5sczvd; 4-u,l
(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 wo;y)jws4 5 z8rd)c ay$/theta$ 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 abovvr; w:)usiiy s sz-/6ue the ground flying faster than the speed of so /ssruws6 iu-;v)zi :yund. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20nhf 9fpe5 4 b7ig05xenw(opcro 1.y4q,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to workg4enq190hy7.b ofp pfnriw 5(o5 4cex is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rav/o;0akwb y)qggm,n 8nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of ma:ofwk8wddh26 : je8 ttny plastio: hdw8et k:t f2wj8d6c pipes of various 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 a sound close to the thfc t(pr+v -;0xj)vh,j e4rba ireshold of human hearic,hf-r)xvai +0e4j (jvr p;btng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sk8uh,x,ln/( be-zk 74rdp+w aps pm ,yound are hearmb h4 kla,ndzsp( u7 p,rkx-w8/y,p e+d simultaneously?    dB

  The sound level 12.0 m from a loudz. he1 7gb0qtlc/ y -*fl3osxmspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) off7 gem -o1z tcbq*y /.llsx30h the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output ac wfr:y;:q /f 2mwdd1zt 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output i2 ;w/zqw:yrmf: fddc1n watts at 15 kHz?    dB

  Workers around jet aircraft typv305n8,ogkls h rgg0z ically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an 0lh8k 3szng0 vr 5go,gunprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain. cghdq8 yng2zo)*v2 r, $\beta$ 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 vio be- 5fnn+f zpwt3:6c7pzx1j))ggsxblin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32q03 f klopmf8n/t;/te cm long between fixed points with a fundamental freqfq8n/f03ko;t tepm/l uency of 440 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 vibra:3s nc db31*5rem uwx8 g+tygmtion 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 fo8cd 5xm+: r33ggbwsyu* en1tmrk when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one )b-u6l *p ctkcend and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundampc *kutb)-c6lental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as oh22 ol(m+icdr9nm( tcne full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in a j9xdquhyd/hd g(2p5dfh9 b*)7 jqx+the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant fromx dqbd qhg)ajfx97p5+d/ j9 h2(h*udy 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. o, d3sjwoib d /-n,ud6The conductor on the stationary train hears a 3.uibn-/ ,o6,sodd wjd3 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 whist,rml6ziwqj1xby yar g4bb55ej r91*0le as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume consta*r5jg 19qre, yl4 axmb0 zr5bw6j1by int velocity)?    m/s

  At a race track, you can estimate the speed of cz(l izha*-f (hars just by listening to the difference in pitch of the engine noise between approachinfh*z h-(( laizg 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 together, produce a beat freqhq85w qtx1 qa)uency of 11 Hz. The shorter one is 2.40 m long. How long is the other? ht a q81x5w)qq   m

Two loudspeakers are at opposite ends of a:zt ;ht l1afl- railroad 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) he is between the speakers, at B, and (c) heh: lz-ta;ft1l hears the speakers after they have passed him, at C?

  If the velocity of blood flopmn:,mbk 1d12g zuk1pa, zwh;w in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along tzgwk2bmd ak,;,mu1h p11:npz he 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 th1bdhj w-s:vh0 u xnu4:tq(wl8e bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detec4 lwd-hhnxjv:s(uuq:10w t8 bted by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound7oad spf9sk6m3j 20 vbx2e1,dwglo l, 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 so that the echo from one chirp o,1o dp,3b7lve j9fd as2lx0k2 6gswmreturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpb/re:h 7ot+nwine 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, theob+ te/wn7r: h 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 compro100h0qeihp8h7 ts lhg mised by the presence of standing waves, whi01piqsh0 0lh geh8h 7tch can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrati/b., bmde5c5*qucjpyon, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the dm qjc/ uye,bb5.p5c *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 oqj828z5qkac a( d+.:ylm wc zqf hearing for the human ear at a frequency of abl zq 8q.:acc+jd 5maykqw82z(out 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 ground heaj5a)e/e7 g6f kb99 ul, eqkdwlrs the sonic boom 1.5 min after the plane passes directly overhead. W979auj, b5/dlgl eekqw) f6ekhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ew 0bi7g iji.*is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h