What is the evidence 9 qs0dgvhr(z-1amf /sthat sound travels as a wave?

What is the evidence that sound is a form of enc7m; eix84rucergy?

Children sometimes play with a homemade iq 2eggfa uedh ;-i/ 3/po46vw“telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and;3q hp6i gv g24e-ef/aiu/odw a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air intrk- dofj b26d0o water, do you expect the frequency or wavelength to 2-jbf rdk0d6o change?

What evidence can you give that the speed of sound in air does nwafhb -owd9;a aes* .j ;m1 aizb33x5uot depend significantly on frex.as mi ba9-o 5a3w;1 feb;w*3zadjh uquency?

The voice of a person who has inhaled helif4jk:o9uy ,yv3 i8xwe um sounds very high-pitched. Why?

How will the air temperat.8x) glxzb oicc3 9oh-ure in a room affect the pitch of organ pipes?

Explain how a tube miglsy/6*ov a )l ry3zji 32mot)sht be used as a filter to reduce the amplitude of sounds in various frequency ranaj)o tls ls* 623)oy/3y rzimvges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move upup. h2jxy)2qlnh+ w5.0e oas y the fingerboard 2 e ox2yh.nuqjsawpyl5)h+.0toward the bridge?

A noisy truck approaches you from behind a building. I/pfnv9fw fsx:.g1ah3 nitially you hear it but cannot see it. When it emerges and you do see it, its sov.wp a13ff/h s9x: fgnund is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,”3x dfa4tzjw)od4 5wnt4e rq:9 whereas beats can be said to be due to “interference in time.o43:5x e ta4dwz)nj4qr9tfwd ” Explain.

In Fig. 12–16, if the frequency of the speakers were 30ur ku4x *w6f m(wtbxlowered, would the points D and C (where destructive a fwwut*3k0x 4(burm6 xnd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting thpou 9(+q/c)nxgq gg jib .5cg8e hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is u/g p5+ oqxg gbij9)c(c qng.8used 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. Eaccs,qu , 2vqlp k3y:qz-h wave can be thought of as a superposition 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.z3 pc-s,y,q: kqvl2q u
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thew(-o+qy eofr,5x5bgbsumc40 -cr7q e same direction, with the ser+yr40 7swgqb5 cc ob q5xmo(uf,--eame velocity? Explain.

If a wind is blowing, will to)cta5hnfpq7,5 me 5kj3tg1p his alter the frequency of the sound heard by a person at rest with respect to the sourc 5kg7nqet,1f3) paotpcm5 hj5e? Is the wavelength or velocity changed?

Figure 12–32 shows various pou+j7w*hp 0 mozsitions of a child in motion on a swing. A monitor is blowing a whisou*j0wzm p +7htle in front 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 kjpywqjz0m nd( f)(37listening 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 sh)fy( nm d07(j3w jqkpzouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thei)+evzwv)e665wv- xajk4ijq echo of the sound reflected from the ocean floor directly below 2.5 s lat 5)wvzxji4we vkviq) e-a6j+ 6er. 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 wavelengthimtt 4wf kav/8(v2hgde- 37kas in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. W2ny kjid 2ow.m03lso0.a 0wwx ithout warning, an enginn ydwk23w2wol 0i0 0xomj.as .e 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 strikbkm7 4tgczg0 7ing the water below is heard 3.5 s later. How hb7zc t4kmg0g7igh is the cliff?    m

  A person, with his ear to3r2x34fs xggyd.il ho s8s 0p3 the ground, sees a huge stone strike the concrete pavement. A moment lalx3pfdss 8s i4xg3h0o g.2 3yrter 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.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mi9q2kd:6fg2 p8t tkhj an4d4ga; u 1quple of distance by the “5-second rule” fga 4guk9a4q:2 q1p8p htnt;ufk djd26or estimating the distance from a lightning 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 levefd( x okd*ob03t y-x3hl 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 (cjh.n6h+vts:5fwmqp+i (q ua sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers e rpt7t*0ktjk+c9 r- (n8riarproduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if onl9jt rn e+a0pkcr*t -8rrikt7 (y one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy - a /hiryu/kd7jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this 7/iaru-hy/k d person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said4yaryegg3 :kiw8o (x9 to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What iyg8:yw94raoi (exgk 3 s the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a peimx- 0eo o0pb)qkh (0srson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformls0-pbx)mi ( oh0ko0qey 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 strs,yp f)/md5tqotnv0 7 .ck h7oikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 Whoij : 7t po,x54hp2dzl f4un6, while 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 in turn to p2 lt nfo,45 oi4zxh 7p:h6judeach 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,p:bggn rj.83wpo2 fj registered 130 dB when placed 2.8 m in front of a loudspea,pnj:g3b jgpr . w28ofker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a differenc22e0ptz n -kd.1 xo.t+:o sumf.dgqpze in sound level of 2.0 dB. What is the ratio of the amplitudes o ot2.pk .1-dm z.e0ogdqu:szx+nf 2tpf two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wdjf 42u kt vs)0o ,l-a12lwdr fb3uok*tm)tl. ill the intensity increase? Increase by a 2fk4u)ddt tf,our0wvmlt1*)b3la.-j2 sk l ofactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tj/*h vn2hwxj3 w c( h(-zeh6(jmigmt6he frequency of the other. What m cwv(j3i z h(6 /htxw(6mnjh2je*g -his the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wij+c, ( sr,svwave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm s+ is,w,j (crvat 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone 9ct ac ul7i3+:yzf+uc that has a 50-dB sound level? (S+7l+u3t :ayccf c9 uziee Fig. 12–6.)    dB

What are the lowest and highest frequenciesba7 e(t-0 rsui1ddmm* that an ear can detect when the sound levb-e d msa1d*i0(tm ur7el is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. )5: klikf+gw)nlbw*xouvhy.zb0*/vWhat is the ratihb 0k* fzlw*+5/ y:nvu )go)bk.wlvxio 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 length of ts mj/bpl8ehayvdp8a 4 )9 qu*-he vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mael 8 /4dpa8p*qv b)y hm-suj9ust the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenta , .gu/tnk.htil and first three audible overtoh..k u tni/gt,nes if 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 across the top of an(s4+iq)grcy+n-fheit-s g,z 8su f - v empty8c-s+f-qz)g-4+gthsurn s,fy (viie soda bottle that 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 with1( yp5cq4 pnzptk3p25 3tij*a 5lxhtg open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), whatitypa(1x 3 p l 5*3pzh5g2t4tc5kjqpn would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string6j0sskx9t;) 4 lqp p1;yqi ple has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingllj ;96;0ie) pq pk1ss4yt pxqered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle v*zip i m9a/,mnzag9)C (330 Hz)9an9 vpmgi )m,z/ *iza.
(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 pip+c oc / 4j/;bmlonjf,ge that emits middle C (262 Hz) when fb/l,/jon4mj co+c ;g 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 20 i oc*ny2rdy,6$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpin,me pxxgd4 meq *0w:o1e+x1yece of the flute in Example 12–10 should the hole be that must nm1xg eepqe ,x0*dxymo+w14 : be uncovered to play 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 pij u dnr: bx5;8/fya40hc ax;rvpe can resonate 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 close4x5:f/a ; uar;ynv 8xd0r hjbcd 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 ends. q9ygb93 yurl.i 2-jca gaa-+y1*3p vervibb2It resonates at two successive harmonics of frequ-9ap+3q.iuv2rjcia 9 *y1ybbv e23 ag -brygl encies 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 3uya+xm2tp qitn:c .4$^{\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 fqf6)3n x )ypxkwk:+j+ ) dlwzior a 2.14-m-long organ pip) n j +x:wkf)diw)z+lk3xq6yp e 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 qn 5wqsc zq (;p9i3 j3zx7w)eeis open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standin(73) jz5 nsq9qwqz;i 3pxee cwg 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 0zi(jykwq42 eu/h a)ntwo strings, one of which is sounding 440 Hz. How far off in freqnywe i)h 2/q4z(a0jku uency is the other string? ±    Hz

  What is the beat frequency if middle*k7) ny aeaar* C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whil1cb:c 6lymc)9tk+d f re 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 simultaneot9d+l:bfkc6c1 m cry)usly, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with ax h v+ c*hteo(uw)v+6p 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational he+vu oxv* p(wh6t)+ cfrequency of the string? Explain your reasoning.    Hz

  Two violin strings a52 .jo kyx7f :ap(zqvsre tuned to the same frequency, 294 Hz. The tension in one string iss :7.5xo(qyvjfpk a z2 then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes etuxb7ffp78aw 9pv;z ,4 cs bn1x-rb2 cach try to play middle C (262 H8xf 7p 1 7caz9nruw;t-p vs2bx4cbbf,z), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B,kt op7n :t+yba7;v qk5 and C. Fork B has a frequency of 441 Hz; when A and B are sounded togethp;k 7 nt5tk :+yb7vaoqer, 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 persd8:urfys;xh hz: ) e73 c;wxoion stands 3.00 m from one speaker and 3.50 m frrxf7;):s :cd xoh ;hw3 u8yizeom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pee 4ag2(g) kmh7n. c/bkg-lpriano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrat2gl 7kgg4ekmce.hr( p/ )an-b ing 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 (4 .:5ftm ipggw;hsyjin air. How many beats per second will bm:ys i5j4gt(;fh.w pge 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*3aryf. mpr.rd hpl4i jg*0x 2.bv:fvnd4w: l Hz when at rest. What frequency do you detect if yl.v p4:yirf:2x glw **bmf rjna4 dh3.dv.pr0 ou move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What cy 89a/ 4,c xtqmdqq)dw6qfk8 frequency do you detect if a fire engine whose siren emits at 1550 fc869wq),qq qadcd m8 k yt4x/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 moving toward you 2dkf -6wdlym;at 15-dlf y;6 kw2dm m/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 5+pnph3ur c;u. p i0gpzk6+yrsingle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hearsrr6u0 +ung;cpiz p+pyk3 5hp. 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 ult l.qq;egql46h c,9ai vrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/ eh9 vic.l6q;lg4qaq,s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall aj2h5ac n6xas:mq kz-. 4c*k iit a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequenhczk4c q6.: i*ai2mjx-nk5s a cy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppu7u.rr9viwtezy my ;pp;:(d1ler 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 restpi9; 1vz7u.utr ed;w(rpy my : in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supv7 fc+sojh2pdr+o4 gw/:g ght n6+8ltpose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large lerh6g c g2n+o:whl t+7 vg4f tdop8/s+jg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasb3/g bs mywt0:onic 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 5ex;8h1dp uh mh4l0ki;70 Hz. When the wind velocity is 12 m/s from td hu4h ; ehkli180x;mphe north, what 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 moving on land if its speq6ga:,zfj6 uuxbrh n6i,6l-g ed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whrp e cc1/rshd x7o)nh6 7,gyy:at is the angle the shock wave masd)p1 h:roe6cy/, x7hr7yg cnkes 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 atmospb/pvrx yt6 7q8here of a planet where the speed of sound is only8bpyxvrq7 6 t/ 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 the 49z:i yzd) lmim-xd d+e x8pxh:dh (4yshock wave angle lh+x:zp9dd -d :4)imh(yi xze4y8xmd it 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 r kzsk q7(o fz1m-956pb r/7urptkt-e$/theta$ 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 dib4)b/ ad046 p8fkmh.btb ph above the ground flying faster than the speed of sounmdtb)hh 04f/4d.a pb8p b6bkid. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses down arx n9pk6; ;w3 /nbf1(khfbgcward from the bottom of the boat, and then detects ecfbw;/ gxcknf3n1;( hk ba6r9 phoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are hvs 6n n3zu9;uthere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy :kp0jdk*c:vwmphony. It consists of many plastic pipes of various lengths, whp*v ::ckw 0jdkich 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 persooy,k 3.kz7dglz *z: dw- aohh*n makes a sound close to the threshold of human hearing (0 dB). What will w do k*.3lg:oadh-kz*h 7zzy,be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sous 4-h2gnh o32v u6cfolnd level when an 82-dB sound and an 87-dB sound are heard simultaneo4noh632l ofucv s-2ghusly?    dB

  The sound level 12.0xqkh63d u3gh9 zuz b+0 m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally b 3+guuq6xd93zz kh h0in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power p7 9o)ceutfrr0n6 t k(kzsb9t468q m ooutput drops by 10 dB at 15 kHz. What iso(sr9zt tn69f 0p ) ukok8e6qcmt74br the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicallyggq-,p7e lif o6*. 97f yafwcp 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 2gqpfef7c, . -l6yf gpwia7o9*.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,qt 7abxg 773bafdmp m)1 709qwkmpc z7 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 isy88f5x/0bmtt/9)i ssliy hp1muxz ; z tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fua cp8 (y+f2nkyndamental frequency of 440 Hpy(8a y+2kc nfz 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 e1;0(pv x sg2wwoy(u d n(1rvaopen 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 watewnux(1(pwv yrs(do aegv 012; r 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 tube37 e+atho4sc v that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) saot vc4 73eh+with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed i ,vs4l yl( qrur*bpu.1o,/cbto resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in 3nuy jb(aju cb(r1i0c/sv3 *jthe 500–1000-Hz range coming from two sources. The sound is loudest at points equidi av u3jy cb3/1j0 ((r*unicjbsstant 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is sli/mh /teod3l 5nlm)lt-u; gl/ ,bz f;tationary. The conductor on the stationary train hears a 3.0-Hz bed3utm/f,) hlg l;lio/t;/ mzlnb l-e5 at 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 dnd;+n5 bjngr2u1cj1approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinj dgu2; njdncb15nr1 +g (assume constant velocity)?    m/s

  At a race track, you ca9 ukv8f*r egu20w6,r:jnbc eon ,t3pon estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the strafp,egun 6 oe8b3wjrnc0o t:uv9k2r*, ightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a bealmo,zg5) h +dwt frequency of 11 Hz. The shorter one is 2.40 m long. How long ism 5hgz)w do+,l the other?    m

Two loudspeakers are at opposite ends of a railroad car as it yjpswyk(5m*8 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) he hears the speakers after they have passed him, ay(5*pj kw8msy t C?

  If the velocity of blood f7btw :ash0d j-/ao emr(7b:vqt9wez(hhm 2 f )low in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speederav7/t-: 2omh(bf7w0edj(h q bszah)m:t 9w of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 mj. zuporgu 064ia0m2a /s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequru.m04z 6oag02upj i aency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mothiz x mik2/ca6tg,d* t3. The pulses are approximately 70.0 ms apart, and each ikt itz,a*x/3mi6g2d cs about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sip8xqrg.u oo sl: eqq/;hvmd+:r,:k9 zgnals from one Alpine villaghs:r:/ q8kmod+uv .qz,oe qr9;xl p:ge to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can b3 -vmoa /c8js(;ot ojte compromised by the presence of standingtj ja;/(co voso83-tm 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 frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves aqvz5f(d hgsf) )/id1 bh- 6snz 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 tg61)) shfqh/bsdvfd (n -z5zio “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a fredad;*9jr2 y9ws s2gn 6h/91ze8ykuhj u( pwgxquency of abodw9dnsgg8uhayw9hy1j2 / x r 9 kpsu*2jze;6(ut 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. A macq;+(eqbec k.0qf1 n observer on the ground hears the sonic boom 1.5 min a+q qf;k0 m (bcceaqe.1fter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatni 7g1fjj)+7 gnnwm i0 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