What is the evidence that sound tra9t- 0e8kag8u6+oce)z boembw vels as a wave?

What is the evidence that sound is a form of energy?tp( t2iy++5*exyt1lv uqsc d 5

Children sometimes play with a homemade “telilr r4;dz5f;6y 4 yfmkr/s3u pephone” 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 4 r 5kr/ f63isuyprmzf;y4; dlthe sound wave travels from one cup to the other.

When a sound wave passe:z wm y 8dzu8qck0o-i0rsj+o*s from air into water, do you expect the frequency or wavelength to cha oqdo0sy ck-8:z*+80zujmi rwnge?

What evidence can you ge6g .bb1qgxd2ive that the speed of sound in air does not depend significantly onbgex.qdg1 b2 6 frequency?

The voice of a person who has 0 xdwsbz- (ahs0(4nb ninhaled helium sounds very high-pitched. Why?

How will the air temperature ink/f:3tc jtvq9p5 ym,i d:ia ;t a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce 7d f- o)n +pwl;/efmvzthe amplitude of sounds in various frequency ranges. (An example is a car mufflf v+p-mw o7l ;nz/f)deer.)

Why are the frets on a guitar (Fig. 12–30) spaced closer to yg(-5vkec5d gcrl 0(mgether as you move up the f-gmcr5gc 0k(elvy d (5ingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear itlbtk wun v*7n.k0bq:+ but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diff.v 7*kkn: bn0wlqtu+ braction.]

Standing waves can be said to be due to “interference inl /d s-12 kqp4s m/hrahi(ebz2 space,” whereas beats can be said to qk(-m4ssz b pl/ hrh2i 2da/e1be due to “interference in time.” Explain.

In Fig. 12–16, if the fr)e 9 irk0stwkn*s6im (f/ms0nequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) me/(90r fnimknit 0ssk w)m* 6sove farther apart or closer together?

Traditional methods ofi s:39yg +hlwc protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new techny3 l9 +hcwgsi:ology, 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 w0l;exqm )3qmv ave can be thought of as a superposition of two sound waves with smx mv0qq3 );ellightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directio(0q rw2))ar;m6m7 hlrn duq hon, wi qhrnom7);lrrm)0wu2h( d qa6th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pcog3t.iu-(zd+ *kvg)*upahp erson at3*hdoip* k)gg+ u(u a -vc.ztp rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a aja9nw20xq5(*d zlle z) nyn1swing. A monitor is blowing a w0) z1nq9dax2nwjlln (a z 5y*ehistle 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 listening for the echo of her kcafk u0305ab*7 id7gehu) p. h jf5nilp6r-eshout reflected by a cliff at the far end of the lakebkh3e7-.igdlu* 5 inpaf0a)0kfp7h5j r6 uc e. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hcvfa1 +dgit5 9ears 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 ic1iv+ 5tg9df as 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavele zg8 icf+b6ya vo 0o0tm90b3dbngths 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 drv2:j,n bk6mg qifting just above 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 elapses before the backfire igm6njq2v, k b:s heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cl nd7 h*dt:1q+1b cjtlhiff. The splash it makes when striking the water below is hearc hdt q1l:j+t 7hdb1n*d 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge s.3 ua(wqaxz1 hc 6c5 l12kcoigtone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occu3 gc acu2a.5h1oq6z w(1ckxlir? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secondl p pxmg-it:su97krs)a8a4 5m// doqm rule” for estimating the distance from a lightning strike if the temperaturdr8 ta oal9m/57pgm/-mupi:4ssq) k x e is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thj2; g o ghf(kiu6hg0 ,5bf0xahe 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 intenk ,lxkrg+nw3 -sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fir+ vw5a+mc(g+)dp;l,e p;gforj rnl,eed simultaneously at a certain place, whatv5+,pw,lrojnm;le(+ a;)+ gp cgdf re will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wimm9 t(tvpgt zk2-6 mj.th four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound .tj6vz -tpm9ktm (gm2 level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal2l-uit btzm4+ wpvfn9 3-gt,u-to-noise ratio of 58 dB, whereas for a CD player it is 95 d3t-lbf u294+- ntwu,tiz vpg mB. What is 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 fr gz 8.smync /7obw:m (ni8 qno4fybp.9om a person speaking in normal conversation. Use Table 12–2. Assume the sound sprec s zbn:n pmof9o .8/.inw84 m7bg(yyqads 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 eardru7ypjyb9v1 ) c gnbqtlbs)jp0:7-0w 1+rkl fyx m 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 2nv0hiok 2e x+c;efbwj0; 9ai 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 tnb c+;;20 9 fiwhev koex0aij2urn 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 whxf:ay: jgo oto /2m8/ uyrhy66en placed 2.8 m in front of a amo xuy:8o/g62 :yjoth6fy/ rloudspeaker 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 typi8o)lc; snk8 ,z,rbj glcally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this a r n8jb ,;lc,)8kzslgomount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will qc cp 4wo.i)j,;o/wq3* xqsjrthe intensity increase? Increase by a factor oj .j cw o 4*rq;/wiqs3qo)pcx,f    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal ieb;spjo.:p)/ 4 aj3jzw* stxdisplacement amplitudes, but one has twice the frequency of the ji/js aop . x;zejw4 s3pb*):tother. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wam:9 iwl uh1;zwujs5ce-g7 t4ave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm atw i-a;w9mluj u1s7 5gze4htc: 300 Hz?    dB

  A 6000-Hz tone must have what sound level - ol;cinq2hdhpxr+ 4; to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See F-c4+oplnhxqh r;2id ;ig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wy/47 )rpm * agcr:soajsjo3 )when the sound level is 30 dB? (See Fig. 12–6.rp)w73/ mssr*j4 g )ocj yo:aa)

  Your auditory system can accommodate a h1o1k e(:p-h.nilslma uge range of sound levels. What is the ratio of highest to low.1 opi l(ma:-nsl hke1est 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 H ,1noil ,obonjk2fdq( o.6kl1z. 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 placed?o6 f( k li,12ok.o,qnjonld 1b    N

  An organ pipe is 112 cm long. What are the fundamental and first three audi:pzb 8vgyt :y0ble overtones if the v0 yy 8:g:zbptpipe 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 e .t vhpq0**jnompty soda bottle that is 18 cm deep, if y*n.o h tvpj0*qou 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 ok,i n*8lt/ec otr(y)x rgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the rangytl xnc)(t*ko8 /rie, e 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 third harmonic. What willxklgx.9w*jh 4 be its fundamental frequency if it is fingered at a length of only 60% of its originalj.*g 9xwkhxl4 length?   Hz

  An unfingered guitar string is 0.73*vg :q +yxg f*ox:r53bm*qd oq m long and is tuned to play E above middle C (330 Hz).mo :x*f x5*3qqvqyggr*b d o+:
(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:vnh ns )yw49s of an open organ pipe that emits middle C (262 Hz) when the temperature w n9ny): vss4his 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 vie.r1+l*k.d y d bm5m$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thqsoa(ra e z z41bfm2,6e flute in Example 12–10 should the hole be that must be uncovered toaqszm (6 oe1a,r42bfz 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 pipe can resonab 8r v *xoc-s;mq* sak,kva0(ite at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequcvqsk ;kx0am8-b*r si v*( ,oaencies 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 ends. It resonausq(.6ayo( lytes at two successive harmonlu(o. (6y yasqics 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 -ui bbn6nnvw 4-b1d+ 8pikj p3$^{\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 are2wue.m lmykl;6m o1,v,0x8 nh6vuvlh present within the audible range for a 2.14-m-long organ pu1hek, lom8vy ; lwmmn662v0, u.vlx hipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is opey8 (srpcida 18n to 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 canal. What is the relationship of your answer to thyar8cs18pid( e 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 trs-.hio1 )pwzqszi h0oi,7g n6 ying to adjust two strings, one of which is sounding 440 Hz. How farh 7sh i q 10.)-s,pzoz6oiwnig off in frequency is the other string? ±    Hz

  What is the beat frequency if middle;uqf:qym b+z - 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, while another (brand X) operates av3(m9gww (ya1ed; hx( skq0sgt 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 brand gdg(w0y(q1s vs w( h;e3xa mk9X.    kHz

  A guitar string produces 4c vo6(2 fh,4b p 4,f7: p+u y-ghgskrygpgi0iy beats/s when sounded with a 350-Hz tuning fork and 9 bb(6rg4gcg fvkp ih40 ,sp+7u:gyy-pifo hy 2, eats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenc xsl p o7qzv).dam5d5 2eo.,gay, 294 Hz. The tension in one string is then decreased by 2.0%. de.op l ,)5qag2o5v mdzx .s7aWhat 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 each try to play 63v0 ic6b 45 g5umkpthk3phynmiddle C (262 Hz), but on6h gmi63kbcp4ntv3 k5h50 puy e is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a gy6:;a(nz/ l t fh-ut 9vm7rdnfrequency 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 are sounded together? v7damufln(z6 nr;-hg9tt/ y:$f_A$ =    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 speaker1slt+b +:gu g ;f7 yst5zwqh1e and 3.50 m from the other.z1s +:7welg5gh tus b1q+;fyt
(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 am*mfm9o ,qc2v t 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the fre ,*qfo vc2mm9mquency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats peolyix7j*wb 5/r 0 qe(ur second will be heard? (Assume T = 20 ri qb*(lx7y5/ju0 w oe$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of t 35xcq t6bw;d*bd9e va certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detectw 5;9d q*vd 3xbbetc6t 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 ifxzv 4ii(xx i95 a fire engine whose siren emits at 1550 Hz moves at a si 5i9 (i4xzxvxpeed 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 movivl5dq xft3w fzb:81ua1r 1ixszg2 s19ng toward you at 15 m/s versusuf1r5b3xgwzl szva1st1q9i 1 :df2 8x 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* z/afgruk 9:o frequency horn. When one is at rest and the otr u 9kgozfa:/*her is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soun5d m anlebvaj799pw;;d waves at 50.0 kHz and receives them returned from an object m jn9a;b amdev9 5l;w7poving 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 flieh5w-gz z dup(n 76skk azfgjb.t465 v4s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected w5k6 zbkz6d ah pft75.z4(u g-4 vsngwjave?    $ \times10^{4}$ Hz

  In one of the original Do8 24*/rdsihtro gess-d iuq:( ppler 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 hearh/*tr:ri-4giq8s s(2us d oded if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to 9nrisll1hq/9(nxl ya+/pe3 v z7+ qihmeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound nl 7l e9/1iqpv+lhyq(/+9ran3 hx zisin human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequem 0h(i9 w*gjnvncy $2.25 \times10^{ 6}$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 soun/h,riescwok12 vcw 9 (l1up /pd of frequency 570 Hz. When the wind velocity is 12 m/s from the norwpve92lw1u(/ r chpc1o i ,s/kth, 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 l.p 4v3kdn lca*7 0 xr/gprn,con land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 31uenj-v )f610i*lc4d vxa c3dr0 m/s (a) What is the angle the shock wave makes with the direction of the ane c-larv6* cdjx 41iuv30)d firplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound z0t2z8cjlpqe1kn4i 90 gy9dq40 ybvc is on4gknyy0e c028p 9zc04i qv 9jd1ztlqbly 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 thepe4ewet tr* q0 8ls7r)dd4of + ocean. Determine the shock wave anglep*7tedo qe0ldws84f)r+ e4tr 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 5 ,1zg rkrq/yt7 2huav$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground f 0 )yue2cu.z-t5 dwtnblying faster than t0nttd ey) cw2uu -.z5bhe 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 senrzs 24kq--mn mx2 )yzax-qw9jds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, whqxx -y q-wz msn24-r2j9azkm) at is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the a ysm.ld 6rb8:yvn0(kash (0ohuman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a 8/o1yrpgziynv s;vo6;/ m 3hohxh4 7zsewer pipe symphony. It consists of many plastic pipes of various lengths, which a ozog/y ;46viryh7z /h 3nomxv1ph8;sre 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 threshold of husv*5 o/.bt5w4lsjj/l bgrq9cman hearing (0 dB). What will be the sound level of 1000 such mosquitoes/jsqs/grb jolbt . 545v*w9lc?    dB

  What is the resultant sosdl od7p:a cfdu+ r*)4und level when an 82-dB sound and an 87-dB sound are hear f+rd)74od*sapdc lu:d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What ihyypi) mvrx ah;v0s7 rc0ea8+v8nv 7,s the acoustic power output (W) o7ryxirs0vp;av na y8)8vcvm,h07h+ e f the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output ;df 8-z(40raq2p hp a1sk wgekdrops by 10 dB at 15 kHz. What is the power output in watts at 15 s 2pakrwez;4ah(8pqkg-f1 0d kHz?    dB

  Workers around jet aircraft typically w /t,:/v o/i ; a n)r+s):a/witbloewjyonruw2ear protective devices over their ears. Assume that the sound level of a jet airpl/ro/ww;yi o2)s/)/ +a nntjiutba,o:levr: wane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communiegps)vl 7ns6gb /9u ;xcations 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 j* mh-40k70t jrlbn smtuned 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 8g :16h tg,h0vhxqysba fundamental frequhtb ygx s,60g qh1vh8:ency 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 vibratidd0b)rg ;3, .s+xt 4bghybzj don above a vertical open tube filled with water (Fig. 12–35sth3 bgbd0 );bx.gy 4djd, +zr). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar stringgw l2 0lfl oyl)l(2d*y of mass 2.10 g is near a tube that is open at one end and also 7lldwf ylyo(l ) gl220*5 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ps;*gjd m:axh1ebom w mv -d,*1r/nq+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 the 500–1000-Hz range coming bgf3 u+v5 v5rpfqwyyl0hftd.8,l1a * from two sources. The sound is loudestyv f8yt5 + f*5.gfbaurd3 v l0l1,wqhp 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is nm0jsp;3-pwhe7h b h:tz 3f2qstationary. The conductor on the stationah7t0:2 hsmh p-3zf;jn p3qeb wry train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a stw )qekrf7-bug.+ e2eceam train whistle 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 constant vec+7w)e-e bk2 eq. gurflocity)?    m/s

  At a race track, you can estimate the speed of cars just by li0*el.oxu eld2,. vgs;ew j5p g ofxk2;stening to the difference in pitch of the engine no .p x2dgjf*,leo s;2ekg0l wx.ue ;v5oise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequer oj2r8.zl7n bncy of 11 Hz. The shorter one is 2.40 m .b rn7lor z82jlong. How long is the other?    m

Two loudspeakers are 0v894;bkdf3uknm(9e ch h i fjat opposite ends of a 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 posv (fu3ijde kmhn 09k4 bh8f9;cition A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s wh,i iu9.w:ohgp at beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bloodowiu,p9. gih : 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 flyubjj,cq hn8 *ig) *r2 lnbq1a4ing toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by then2i8jrl)j14q q*n a *ghb ,ubc bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freque,cp2hdi pyyir; 6mx3v(voea tgy/,a v;bq+23 ncy sound 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 mop 2gadb+v;t yx yq;rih ,vp 6,2ic/vmeao(3y3th 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 signa(6i40dqgew;uwhru kv3w w01u ls from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long0;w 0rk uu i6g3uwqwe( hdv1w4 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 listeni9g 1c9 uxjd09vth5pd fng can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing0hd 9tf5xv gdj991c up waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration,qy/mi1sog f20 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 rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long romf /1i gy20osqd,
(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 +; ig il6ylbfkcxoy759h0 ,pcthe human ear at a frequency of about 1000 H5ifi+l kpg y67,oyx0 b9chl;cz 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 groundp (++exwz9vo2.yzot y hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altiyopt. x(2zvzw9y+ o+ etude?    $ \times10^{4 }$ m

  The wake of a speedbo k2t,b f(5pmrlat 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