What is the evidence that sound travels as a wav mox3mii9e2m,e?

What is the evidence that sound is a form of energy78d2fkrmrbyqe 4 5 ps.?

Children sometimes play -9 zdl 47*jhtfom or7 2(jcoam2hf x(owith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretco7 7fol9x m2tra*4dc-mojhj of (hz2(hed and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from fbia;+/f-5 w(ajin*d dkqj67q-qouz air into water, do you expect the frequency or wavelength to chaw7j oi -+ qizfqn5f(*6kjqu-ad;b/ad nge?

What evidence can you give that the speew)7wkw440 hfzh cm3wfd of sound in air does not depend signifiwh f) 4kfwz 07chww3m4cantly on frequency?

The voice of a person who has inhaled heliumsa qi: zs dd-ena0 5d*icp4(3o sounds very high-pitched. Why?

How will the air temp7 zf**q 3tb7 xsc+iieferature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplit (adx0 -ha,.o5aqjw sgude of sounds in various frequencyxjd( ashw.05,o q-a ga ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog;bpu* lellvhu (.kb8 4ether as you move up the fingerboard toward the bridge? * (ul4vu8 bh .eklpb;l

A noisy truck approaches rxssb;e7b -/ zgib53v x z)lf+* xgfw:you 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 more of the high-frequency noise. Explain. [v x+ zr sxi)xgsf*b w 5b:;b3e/zf7g-lHint: See Section 11–15 on diffraction.]

Standing waves can be said to be duedcb1ox)hq 8uf,y)3 sn to “interference in space,” whereas beats can be said to be due to “interference in tim1c) 3nyb fo8, uqdhx)se.” Explain.

In Fig. 12–16, if thek1p pv /(z5y6mp j(cvn frequency of the speakers were lowered, would the points D and C (where destructive an /(6vyn51czkpp mp(v jd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with8, arok zqdzfcm3 ye20l 4.5ih 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 used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambientchlqm8ia3ed54k y.0 zr,o fz2 noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown 2)ilo788s2ky kjlm s dk;iol+in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with sliisd7lily+2;mo l k kko)sj88 2ghtly 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 ann4yw9. +sxc cbou8e1x d observer move in the same direction, with the same veloc c+xyso.uxce9 148nw bity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a 8/ +ters1c fsj 8h v*bmcrr.v;person at rest with respect to the source? Is the wt*r+cfrjsh.vs1e v /m88b ;cravelength or velocity changed?

Figure 12–32 shows various positions of a child in motion o3 yl6skt(*bpp)8lyqb;a k8 xbn a swing. A monitor is blowing a whistle in front of the child on the grb8lk p)aqx3p6bb*(t s yylk; 8ound. 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 tup yf4cb +x /oq2u8g/rvf;v x8he length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the up +/2ourx cg4 b8y;fvfq 8xv/lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wvidorg -z(t7v1g 5z: yaterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not va(zr v1vd7ogyti: g-5zry significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelenyd rr8a8 u68onh78ojqta0u pyj y9-c3 imi: 6qgths 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,6: bw4pe biuixpso 95 of tuna on a foggy day. Without warning, an engp6p w, beo:bi4xui95s ine 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 mabpo qsb,d- nz/+ i6)jp- ghyakw76r- gkes when striking the water below is heard 3.5 -p y6nbab igrzpgwk -s 7d o-)h6q,+j/s later. How high is the cliff?    m

  A person, with his ear toq 9ck9q (4.qpb)esp oo the ground, sees a huge stone strike the concrete pavement. A moment l4pq)9oq (ceo.9 psbkqater 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 mile of distance by the “5-second ros x(o u(zr46fule” for estimating the distance from a lightning strike if the temperature is (a) 30o6 4rx(zo(su f $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB?n4:x edbzqqe/6n i,(c    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 whdu; g )p;s q4bh.ust rj*2.mbiose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta. qao5.m b)xriie)u0 3c11jz4mqjt nk neously at a certain place, what will be the sound level if only one m m) kai)3q.ob11xz5e cqniuj 4.0jrtis exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane;ne/irtsdtx- q p 2nspp 3v ,2ny-+e(y with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add int,ptsyn pdey23 s-2 rpi/(+xnev -;nqtensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 5 g1bn2w .hnmoxi-q(ow: po l+)8 dB, whereas for a CD player it is 95 dB. What is the mqo1g wh2o-+i (.p: )blnxwno 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 ofe)u0:x bqp l1e sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly un0bx:p ul eeq1)iformly 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 wh ncf4*r rsdaz wpu h*xm,a+22-ose 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 is3n95sow-cti( d zf 6gt rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estic tgft(wsd3 5 9zo-6nimate 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 j4vvmp6lo w8kl9 kj wr3b5i+) 130 dB when placed 2.8 m in front of a loudspewjw5l )4vr9 b+ikl8 63jvpmokaker 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 difference zss nc-0x o20q+;tntr in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectio+q rot0nn0s2z;xc t-sn 11–9.]$\approx$   

  If the amplitude of a. qm:kba.ep4k,n) ddd sound wave is tripled, (a) by what factor will the intensi)qd. ap. ,dd4ekb nkm:ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one o7jlb-v3gfa)g.v1gs z- 3bwr has twice the frequency of the other. What is the ratio of thei ob. - v7fg3vb a1l)3rgjzwsg-r intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspjkq*sw+i nfv-f2rygy(iacqy6f*( p;:8 vg6bonds to a displavjb ffp6ynv - kf 2ga(qry*(6*+s cyi:8 qi;gwcement 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 as a */ f;odlo(.x*fdsw k8 nof8dj100-Hz tone that has a 50-dB sound level? (See Figf xn do/of.kj*d;s8wo(d* 8f l. 12–6.)    dB

What are the lowest and highest frequencies that an ear can ftj ru4cf6ngbd /g+3j1(3h xcdetect when the sound level is 30 dB? (See Fig. 1231 3n6g/+cf jfcdgbt(xj u 4hr–6.)

  Your auditory system can accommodate a ho. tsz5, t1ohcuge range of sound levels. What is the ratio of highest to lowest intensity at 1zth., ots5c o
(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. ds r q4d6bm/v+The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stri+d 6dsvqm4br/ ng be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audisacd7tp3y,ubu7cz (cs7 vz/9u 7w/yg ble overtones if the pipe z yy/7,bstws 77cc/g u7( uv dz9upca3is
(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 fr c,upp.rv jd cywb3ad6;.*(ei om blowing across the top of an e,.cd wb6.adjp *ic;u y(pe3rv mpty 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 the range2n p ezuxo ;:bha;iplt-;/ay; of human hearing (20 Hz to 20 kHz), what would be the range of the lengths o;path;lz2o ax/ bpy;u:; - nief pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hx9rc obfpda,0 t5b q1(as a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60,p1fb r9c ( xoqbta5d0% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to ply: f4.y5habl-b7a.p yyv1 mh jay E above middle C (330 Hybyj .p754b1.fm:hva h-yy l az).
(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 midhi 2v3 xn,ulgw/8v(pyom 8f.udle C (262 Hz) when the t fum(v.i,y/88 xn3o h2wlgpu vemperature 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 gri4k28aj0f)tn tip 5 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examplev 79r2uks n;lt 12–10 should the hole be that must be uncovered to plalt2v;9k r7suny 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 p:0ohqqvqlbir9 s+hg+e.i 7r ml.5pn ;-ln b 0Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why l:7r5 mq. vngi;pnob+lr00b.s q+ qpi -el9hhthis 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 1.80yl4 lg): 1 urt78kfkz-baq +ve m long is open at both ends. It resonates at two successive harmonics of frequencies 27tqlr 8y: v-f4e 1u)bzl+ga kk75 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 wb u09qimdktgqb1abn t9778/$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-lo4 f39yc 0x, fvecrn4hfng organ pipe at 20 en9c4cf4 f,3rhxy0v f$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. Ig, 5c) gl)t ahen/d*lnt 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 relatio*)t 5anc) l,e/ghg nldnship 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 /2tq9j sb; s,uxg*un/na q9oe tpk-n *beat every 2.0 s when trying to adjust two strings, one of which ia ntsx;ekqnb pq2*u n /9*o-u9sg,jt/ s sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hwemz3 1nz:y 4kz) 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,bnfl)htcq(g 7r+4 km 23.5 kHz, while another (brand X) operates at an unknown frequency. If nen+)7t lcbh( mfg4 r,kqither 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 X.    kHz

  A guitar string produces 4 b4vbi qybr8s10j( ardvs/ (vr8eats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sorjyv/4v isbvr(88(rq bsa 10 dunded 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 frequency, p:5n oo,av8sl 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 pol5 , :n8avsoplayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if t, wnve/ 1 d 0 qbx3me6,d/np4o*lziizswo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other i zw */s30e41/iqld zed,x v,mnbpo6 nat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has ap, io+6f83cezte e1 iz frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beatct8eiep1+ef 3,oizz6 frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker aw0-vvmq1r r0v: 9dr qwnd 3.50 q r001r:w9vmw v-dqvr m from 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 1*c gzc cdv- hn2fsh*e5e2rp :832 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 bds *5ncehrf: -ghc2v *c28peze the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats d6co4-k1 onw ; c8km p, *t9v7hleplxvper se;vd pmcx*nop,to98 kew h 1vk4-6 cll7cond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certa.gxa21,xpp7 y)y ay lqin fire engine’s siren is 1550 Hz when at rest. Whatpyy2aa) 7lg1x qypx., frequency do you detect 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 dxq8y2 kj/dfmy)us 1b td+.j5ketect if a fire engine whose siren emits at 1550 Hz md.+2j /q tm8 jybxk sdu5kfy1)oves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency x*j((yfi*ivflg+*v pif a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 1+jfx(fp lv*(g*yi iv*5 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 samtocp 64sr/ bf5e single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency 6p4tob c5fs/rof 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic shgoq e*(x2uf j pgx8 g0i-:,vqound waves at 50.0 kHz and receives them returned from an object moving directly away frovqxx- i2qpgu:e*0,8og jhg(f m it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall att3v4tse; 3j x p4bw;kb a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency doek;v xwj4ttbe 3;b 3sp4s the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fk.xttcb8 t78f 7b)eollat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the 8t)eb .b7kf7t8xt col train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses pgq0wm*ow s9:6zp7py ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arqo* 9gpyp p706m:wwzsteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ocq 2j758imlw s5ahl b8f 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 lb8sax s-jv-v( oj28 l570 Hz. When the wind velocity is 12 m/s from the north, what frequency w 88jalljbs(s o -v-vx2ill 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 speed at 20cv p cs:t1 7kvrex2o)1 $^{\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 spvyp 7hjat 6+xq kp 7,5oreh*;reed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction t 577e rv*6ah r ,jypkho;xp+qof 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(v:qzg rx -c ae9cixb+v8ygb9w;h/2o of a planet where the speed of sound is only about c/9-y;hrox9(i: z8bv qawb2c vge xg +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 /l)idiu dpa3 nc -:-t d 3dk-o2tus6mdstrikes the ocean. Determine the shock wave angle it 2ti -soiu da3m n:pklc6 -ddu-t/3 )ddproduces
(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 uki 7(n2s.m *9r tkrzb$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pl-kdko 1dk(6 7ptmxdu6ane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 1mxp(kd k7dou-66 t dk12–34. 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 downward r x b9ybdy k/,c./,dj+ktt v:zfrom the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to workz9y./b d,+,:kbtdkjv tr/ yxc is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humanperb o)poz83 3zp rv/ba0u 3yzs 8:.ccy-mab7 audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It considfw fy if+ylj1m;v935 sts of many plastic pipes of various ledf f19m iy 5j3;y+fwlvngths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makesi y7n 0ntpje-080y6vfw :hzmf a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mpz7h6ij0 t8f y:nm ewn0vy0f-osquitoes?    dB

  What is the resultant sound level when an 82-dB sound a affo/;8am9;ed: *d ziaqai;wnd an 87-dB sound are heard simultaneousl:ed;i q*a/ afz daia;;w fm8o9y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whijdkgr/( o98py,e/km at is the acoustic power output (W) of the speaker, a,g/(kimj 8koep r y/d9ssuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpueqh (sq(howhpz4*7a oh.; 1 uwt at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whe7qo* wh(qh 1;a p.hu(ows4hzat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theg-6cnvaty gr-v4z+f +ir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotegnt+vc+-ra 6-f4yz vgcted ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy zmqo132fhif ,stems, 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 tu8ob 4bk t2/u(dulpu3hned 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 wi1c,fmzl(3gruell1p, th a fundamental frequency of 440,r3 pe, l1lumgl(1fcz Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration aboqq o:ubl;y.k.x cf/+t ve a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning 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 fc/.l: +yxt qukbfo; q.requency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near zevsp:.k;zd1gxznp)k5 oo 5/ a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thir5oneoz/ ;p1zz v gk)5 dp.s:xkd harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obserlmhk65u fk.tc w b0auh:8zd/ )ved to 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 ui5 sd6iw59qw. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and fidwqw559 is i6unds 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 trai*q+8mvv p dru4n is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appro rum*vd 48pvq+aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approach/8ed v q)r 6tk(qw)ezses you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinge)vd6(q s eq)/8wzktr (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by liste:,zw6lgpgdel m)x4 w0 tga3)pning to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car d) gz:glg ma l, p3e6wdpxw0)4trops 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 frequency ofjpy:c3q 7 avct:-r 06k/e h(t shtdu8o 11 Hz. The shorter one is pr c-yu6ct e30do:v j:8h/h s(t7 tqka2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastkntzsya+ 84rw:ugkbk 2(v2i0 a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identi4iw0 g2kayrz kbv2k:8(t us +ncal 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, at C?

  If the velocity of b1cj+r*4,tv ujm j1(x wfdqw z.5jttf8 lood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect it,ujv* wf8 (jq15 d1mjt+fx.w4rtzcj f 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s)llnvewd.r /9 stm-/d while the moth is flying toward the bat atsl/ vdwd-/l. te)9nr m 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 after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound jm8vb plx00)nt b o3n1pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. Howt30xnb8bl10nm po j)v 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) wa0i, gwq6dt,sx6q xa2my0jzq*s once used to send 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 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 open06xw y z qqg, tjdx0qi2,s*m6a tube.

  Room acoustics for stereo listening can be compromisedz-03u 3wsu 1 0w6 0bsjhhmfx3ebvys b) by the presence of standing waves, which can cause acoustic “dead3s hv sbf00j-ubub3smx3h 0 6eyw zw1) 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 aq*p,u** qaamxcjmf 21 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 am2cj xum*,**p q1qaaf 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 threko rkf(clo7o e(,//*qs:wn8h i( ek toshold of hearing for the human ear at a frequency of about 1000 Hz is8 koe/ser (o* fkq7hi/n (,tlw(:c ook $I_0$ = $1 \times10^{12 } W / m^2$ 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 soniyx*i1j arem5 ,c boom 1.5 min after the plane,5x mj1r*iye a passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i 66dk4tg7xat:uv r w,xs 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