What is the evidence that sound travelsi8)6guh 9l5n*e rdih o.5n yva as a wave?

What is the evidence that sound is a form of energ hcox. mp,4r/dy?

Children sometimes play with a homemade “telephone” by attaching a string touf v1ss,pt) ,i2dkz/ljy 8w+h the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at ttvk8 ,)w,/sjsuy2z pi hd1+f lhe 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 into water, sc(tq( d/j9bz1 ,34 exzrr tljdo you expect the frequency or wavelength /e1l qtb9,st(xj( 3drj4zz rc to change?

What evidence can you give that the speed of sound in air does not dependw bh3ky1a.:g7f7drdo significantly 1 d:7wrh.7fakogd3yb on frequency?

The voice of a person who has inhaled h ;j6 5)y:( gaogx0xlxbvsv: ) ed7f,ccdii8kcelium sounds very high-pitched. Why?

How will the air temperature in a room af9utg 3) iz ooqe k7:9b:*kjinyfect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude2d2ow+461.wpk )gfkur 2v(wqgoykn e of sounds in various frequency ranges. (An n f+6gv o(k po.)r2yu d21wwk4we2qg kexample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as ywo051; yc9i )ibd61wey lsttgou move up the fingerboard toward the bri56)1gcw0s9itt e odbwy ; l1iydge?

A noisy truck approaches 9ka+ twg l.id1you from 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 moriw9 1gd.ak +lte of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be duex7jk5 e sn qvmc-/57kh to “interference in space,” whereas beats can be said to be due to “interference in time.” Explains ck5- jn7/xekqhm57 v.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointkz5 5ux;95f/ 6mq2rsjrfs ,epf*jxi ws D and C (where destructive and constructivrqj2zxwu,i6s 5mf9efsfk5 ; r/*xp j 5e interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in aom+58 mhbf*xwc)r vd v3*ebxq9(q*f lreas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headv+bvbq mfh*9*c x85ml q )r(ox3*fde wphones 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. 12–34 bc ,8f,0xj.5sy(fz p3 teyi g1fritk1. Each wave can be thought of as a superposition of two soun1 4f. ,0cjgs3ztryy ekbf,i5tx8(i p fd waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer moveurh8/ g,1+ ja jhjjjas1s4w 4e in the same direction, witah wg8s/1hua+ 4sj j4jr,j1ejh the same velocity? Explain.

If a wind is blowing, will this alter the frequency l)sj )nfrv2r n00;jvao etp2)of the sound heard by a person at rest with respect to the source?ae2rv)2sl0on np);f )r 0vjjt Is the wavelength or velocity changed?

Figure 12–32 shows various positiov,8l2,mhvf nuns of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A th ,v2m lh8fv,nurough 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 e5e31llbc.q j tcho of her shout r1c .qblltje53eflected by a cliff at the far end of the lake. 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 jtmz/w*/l:dk 9- dzd puust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at /mu-:zp*dd t /zkdl9wthis 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 wavelengthh 77 e0l6/pa:zjadn94p;9.uh/ iwji gowalbjs 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 drd4vou5 -zv :pvfevl** bsff2w i()q4lifting just above a school of tuna on a foggy day. Without wa2(4sv ope) 4lfwv-v*q u5z:dl*fifv brning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes 2l q;o)cmpu8m when striking the water cl8;mu)q2o p mbelow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strmxt a6f3yub5i44xg -iike the concrete pavement. A moment later two sounds are heard from xi4xfti 4 -b3muyg5a6 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 e 3;v 4rl(lb3fv2zqo fsib.y8-jmzqxz 3zf9 g2rror made over one mile of distance by the “5-second rule” for estimating the distance from alfb2 fjqq.3o3zv9 -gb3sm;8zlz2r fi yxv(4z lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity lw-hzf-a9 fjq 9,jl)o of a sound at 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 33o kjp+mwcp u0pvv ji3yvi s0-;b513qjced :$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produik)v (k acx,2 uw,,uipce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,(iix,kupa u v,w)ck2, not dB’s.]    dB

  A person standing a certain distance from e9hp4k8fxsk: 5wn 0fxan airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this per98fn5hp xe0 ks 4w:kxfson 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 c)r (l(:hkjq 5kf 6bo+ign4fl 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 backgroun4bf+j ifc5:g ol(nk(r h)k6ql d noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ojo0x3: //ges1 msj ihautput of sound from a person speaking in normal conversation. Use s/ hma:gj1ox3/e0 isj Table 12–2. Assume 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 eardrum whose ark3lsc22hg3i a ea 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, whilekl*qi*jxsp9 0ybwb+.bj55iu x p ki.6 the more modest amplifier B is rated at 40 W. (a) Estixby0*kp95pw isbi.56. +j *u jxbiklq mate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frongj-m) a imqr5r3g wmz6p4i+(ft of a loudspeaker on t5r6i43+gm) am(q m-irp wfj gzhe 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 diff.glsyc-ad k )6erence in sound level of 2.0 dB. What is the ratio of the amplitudes of ty)-.dkl cgs a6wo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) byb8 cj.6djsh/y what factor will the intensity increase? Increase bydc. yhb8sjj6 / a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equat5 7me.j sg/mu3hn6tmmpd j,*l displacement amplitudes, but one has twice the frequency of the other. What is the rati./jej *,dmgusmttm p56m7 hn3 o of their intensities?   

  What would be the sound lev ygc ho emp/((1ol0pv0w+ze bx8vn*,cel (in dB) of a sound wave in air that corresponds to a de m8* p,oxv(z0o0pel h /gc1c(bwv+ynisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud a 2f2 m9q)ghvs, zkflc5s a 100-Hz tone that has a ,l9c2qfzmk gs)52fvh 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when th8w1r cp, kr06iia,o.xi k pmh+e soundocr ,0+pxr h8w,k m6k.1p iaii level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangeot(-w5f sy 6zm ln i,(uwrqus3y*tjb 2 */4xte of sound levels. What is the ratio of highest to exu(mit*ytyst- fbozw 2l*6qj wu4 s, n3 r(/5lowest 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 l fn9wag)xv 1-bength of the vibrating portion is 32 cm, and it hag9xv f1-nwa)b s a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What ylfj( -k1wwz( are the fundamental and first three audible overtones if the pipe is (1yfwj zw l(k-
(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 yoirmcu +q,v aq,/5tyg3 u expect from blowing across the top of an e,yuivqc,rg +ma/ t3 q5mpty 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 with open-tube pipes spanning the7as)ndflb1ub4 g+c nb:v tt 4:,a0dtl range of human hearing (20 Hz to 20 kHz), what would be the ranavlns4:)acbbt40t+gd b l17ntd,uf: ge 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 Hnffv)c0 g x n4bb.)/hcz as its third harmonic. What will be its fundamental frequency if it inb0/gf4)hnf.x v ccb)s fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to playsqa8i )2872t6rh;l/w ts x2 qwmjyu yb E above middle C (330 Hz). tw 2ht;qi 6 rsmxs)82ab 8quwyl2 yj7/
(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 middq o40c iul.etqq*9i a3v1)cj gle C (262 Hz) when the3q)jvicqul c*q to.4a0 91eig 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 acc3x;r +5qqrdeu* 3nf t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the 2 om + +xf6ti10qtgd .qvn4apoflute in Example 12–10 should the hole be that must be uncovered to pla+v4x12pnog 0qtot if.6d m+qay 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 resonate at 264 Hz, 440 +pi/* fa6cavq ak7ni )Hz, and 616 Hz, but not at any othera a+fncq/a *i6kvpi)7 frequencies 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 reso;bny/rvgtj n:vajv )-3f*) uonates at two successive harmonics of frequencies 2ofvt;ny)jr3ub) n gv:-a v*/j75 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 5z xqu+ndl 1h)$^{\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 prb +y9n: ih/gesg0t nk7mx ,/uuesent within the audible range for a 2.14-m-long organ pipe at 20 / htuk0 n:big/s9u 7x,gey+mn$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5hll gt*stq2hvz.3pxc ow*3p.r o;q *) cm long. It is open 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 the io lgvtozshh .l)3.c2tq*3 p;q*pwrx*nformation 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 tw223.2 ; wgyu v7/nv1ikxdygcugj:jt go strings, one of which iyuw d2cg gk2. ;1g2vng:tijvyujx 3/7s sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Ct9 5dlgn y0orj2xx, -l (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 opera )vunu7 bh(pt wh+ 0/.fnxcs(ktes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played sepaunwh0hn t(). kspb(+ f 7x/uvcrately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork aa dt)b6tz,x pq) c,e1cnd 9 beats/s when sounded with a 355-Hz tuning fork. W, 1ctxzp, 6 ))caqbedthat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tunedmsqmdng-; 4p/ 1ga0yf to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are g4ad-0/pf ysgnq1m m ;played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle wk l v0u5cvx 1hfi 1mk/7a:*bhC (262 Hz), but one is at 5.0°C and the othk0bhav1xlmf7 wvc* 1 :hi ku5/er at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequjqly+o0l v08uency 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 l q0y0o+vulj 8possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands09 mgy web2p t)wn7r+h 3.00 m from one speaker and 3.50 m from t9 bw7wthegy)m+ n02prhe 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 ejba.dg9qv 5x7 5e6zh to be vibrating at 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 frequenv e gq7hx5dj5az.96 ebcy 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. 3d:)bu )hzsf7m iuld5 How many beats per second will be heard? (Assumi u)slfu3h b zd5d):7me T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s ut1lzmw9e++qb c rkxn0 .+n: gsiren is 1550 Hz when at rest. What frequency do you detect if you mrln1gxc.wnt 9ue++0bzk : m q+ove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. W(f pt3lf:xma9 hat frequency do you detect if a fire engine whose siren emits at 1550 Hz mfmtfl9:p (3ax 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 2000-Hz source is+vjaj;va e(* h moving toward you at 15 m/s versus you moving toward it at 15 vhvaj+a*;j( e 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 single5 ux/ *.fhytwg frequency horn. When one is at rest and the other is moving toward the first at 15 m/s fyut h. 5*/xgwthe driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recgx :a5gmpg 86qeives them returned from an object moving directly away from it at 25 m/s What is the received 5pgq 86gxm:ga sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an0( iohvalmop: 0 c-ef qw9v,l5 ultrasonic sound wave with frequency 30.0 kHz. What freque ev l i-cqh0pvw f59o(:oa0,mlncy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played 8n ztn.p5 761 ycxyg.1hlsft ron a moving flat train car at a frequency of 75 Hz, and a second identical tuba played 1 1lxtnh 6f.yyn7rp5.z8ts cgthe same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow s*7k g8/ j6g.objubhn :yx wpx.peeds. Suppose the device emits sound at 3.5 MHz, and the speed kbujg/ox8nj* xy6.pbhg7 w :.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 using2g: hj 0yn0wxhej u3r7 ultrasonic 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 frequen3,c :6h mb 8)lyyu lcfgy*y)w as8dk;gcy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wi ylym3 y, lg)88kugh)w;dyf6bc*: ca sll 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 on4co -e mk-8npr 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 spe b:hq:i 4v.ddtkm9)uv7gr 4uaed of sound is 310 m/s (a) What is tkurd )97b qit4:v .ud4 v:hamghe angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet w8j 64hj)myvlyhere the speed of sound is only about 35 v4y jml) jh86ym/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 m7funt3 kyh4 x2+t+b/m ht ffs+/s strikes the ocean. Determine the shock wave angle ts7 b+f3f4xkytth+/ hm fn2u+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 f;b,+n f* rkgws26tfq$/theta$ 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 1.5of-c /3ewk e6otmmrf0 5 .rmr0 km above the ground flying faster than the speed of sound.e rme3fmm fr/6rwoc5- k0.0to 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 20,004rr0f 14j;o 1nli z xgp81buzu0-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 ux1f;4z prz1 g8 10unljor4bi 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the8r-+lf*po;fhk o +rpqkxbv 64 human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal/yt;d4hhkwl5vq j0x le77n*oled a sewer pipe symphony. It consists of many plastic pipes of vhn7dktjl x5 ql47e vow;h/y 0*arious 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 f+sfhs+h )7-*zvlnudz rom a person makes a sound close to the threshold of human he*hhl+nd)s7- +vfz suzaring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soun-h;c0786 owy aq3 jntiorw)z0m 07asqxh- ft zd level when an 82-dB sound and an 87-dB sound are heard simultaneously? zz07rn o3wh xf) -m at-t8 6sqy i00wcq7oah;j   dB

  The sound level 12.0 m from a loudspeaker wgv y.k n2n la4e;vh6qy8**mw, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all e2lkg 6 ;8yav nvh*m*qnwwy4.directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hr *+ fnq (g65qleevfj;z. The power output drops by 10 dB at 15 kHz. What is thj*e;q56v+ffn qre (gle power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eaqd90;x5 xv:hf)jzkjo rs. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 d h5od9jjf0kxq;x z )v:B, 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 communications systems, the gain, c8l* nztu7b58 j; ekxs$\beta$ 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 tuned to3y cf2w asq8jqviz:z g(on- +1 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 m ,pww/(p6yrufundamental frequency of 440 Hz and a mass per uniwyu mr6w,(/pp t length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with i8pr( l4ui vir;w:oe5b. m5k 09oloxhwater (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuninbil i5er m;.u4p(9o 8whv 0koxro5 l:ig fork?   Hz

  A 75-cm-long guitar string of masat jx6k cj fm 9yc jr-d5cv9cb441bg,(s 2.10 g is near a tube that is open at one end and al vckmjg 1tj4,x(jydc95 bba9 c4f c6-rso 75 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 l 8 v0s uug4*(mi8nh5j9qlaijto 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 the 500–1000-Hz range coming from two sources. Tid/ rsx ey+oznc:h.;)he sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source th;. idyr enos) :x+h/zcan the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whi-k3b z2 5-lcnsp:g0(i -0jbxz q igkjxstles. One train is stationary. The conductor on the stationary train hears a :z(bkxzxkgp- -2nsi0jb- ci50 qgl 3j 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it a1pfp;3s / ,tyiszru vg +82urrpproaches you is 538 Hz. After it pas1v8rzu3i;grur,fps ts y/p 2+ses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars justq *3co.az dd-d -g.hqcl1xi 2jk7t,vi xua55b 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 stra71hi l,q dd5ak .b5.v tg-ca2d- o3xqzxciu* jightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetherwoqmty9ar5 6 f7qh25 /nwybe*, produce a beat frequency of 11 Hz. The shorter one is 2.40 m ymqq59nrb76/aft2 w 5e yh *owlong. How long is the other?    m

Two loudspeakers are a. 2y j1jvitnx-t 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 position A, in front of the car, (b) he i n.t1ji2 y-xvjs 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 vnmbfo8twq)2v:).or7 i j3gp0.32 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 travefvno:82 jv)3o)gqm. rwb7itpl with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a 4uvf ta..h2;/afhnlr moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat 4ahf2a;.nl rft /h. uvafter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as trp85mvs y.8 s47updqit approaches a moth. The puld7 .ss qyv5m8r 8p4putses 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 returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sef5nm o;qfitpk .;dtx o44,l4and signals from one Alpine 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, the alpenhorn must be blown in such a way that only one of the overtones is reso44x k5;at.o,nfim;q4l d p ftonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of str*cloa clx5 19anding waves,9l o5lxra1cc* 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 a long, slender alumztghxkn; 31a .inum 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 t ah.zg1k;xn3to “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-qv krzk-m,iqg3 b7p o2:)o*g s 4pdeh w49oyw the human ear at a frequency of about meosi zq3kgvhky49 pobp g- ,w:-)dw2o *4 q7r1000 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 hears the son+vrc u+u54e -i.xbhaj ic boom 1.5 min after the plane passes + bavxe+h .uc 54ji-urdirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 159 oq8iv.qgifc wchnwb.: f ):- $^{\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