What is the evidence tho8v3+ djvcvl;at sound travels as a wave?

What is the evidence thatq3j2ycbjdv:0xk53b mo q z gf(z d*.x0 sound is a form of energy?

Children sometimes plpt6 ,q+6 pr ag,fink-lay with a homemade “telephone” 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). Expg qk6nrl,p- af+i p6t,lain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from a.ginq;ezjog y .mti2 7r7eg8f k, 5f;r 2i9jxlir into water, do you expect the frequency or waveleng .qji7fo 5;r,8nzfykx.7jmirigg tel 9;e2 2gth to change?

What evidence can you give that the speed of sound in air does not depeh/,umz6j09x2:rakwu+7 dc m ;es eaddsz.s +r nd significantly on frequency?.dmj2 c+ z69rddws;zx:esushaear/u +k,07m

The voice of a person who has inhaled helium sounds very high-pitched. Why?u9w tn5cwd91subg6bs b :0,ad;.eoqf

How will the air temperature in a room a5f2hq5 yg lrh2e1-y hwffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ampli-9x yi gb*q:ixhgiz)j9-t- n ntude of sounds in various fxh9 z)nign-btj x-iqi9 y-*:grequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fhcn o1s44:ez sig. 12–30) spaced closer together as you move up t1h44:nsco s ezhe fingerboard toward the bridge?

A noisy truck approa(xo /c.(lh zpgches 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../xlhz( cp (og Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferencecj0v fqmy24j0 in space,” whereas beats can be said to be due to “inte f4jymqvj c002rference in time.” Explain.

In Fig. 12–16, if the frequency of th73d;e:qyj ky tei7oq5e speakers were lowered, would the points D and C (where destructive and constructive interfere735yke7eq qotd; i:yjnce occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoplegw n1a*nb eg2/ig o xjm/4:3ky who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is 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 gi n43gkx w/my:o2 n1/ *beagjthe sound levels reaching the ears?

Consider the two waves npt,b2b aeqa2ms8;9 qr* mxv5 shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies82epbma,rqn sb;*a2mxtq9 v5 farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directionehps-av( ey84td dlo-h 1j9- y, with the same velocity? Explljsy(op th v49-ed -a1y8e-h dain.

If a wind is blowing, will this alter the frequency of the sound v x8zjg*/ j6nd8;d kb/yb3zvyheard by a person at rest with respect to the sourcej6nz3x yk dbz 8y*v;jd /gvb8/? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swq0noql6.qh4bq l96.gxz8 c rf ing. A monitor is blowing a whistle in front of the child on the ground. At which x9orq .c l4fl 6.nqgzhbq0q8 6position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length ofw mf;r)1euv 5y 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. Esmy15;uev) fwr timate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belo,gbcvq66ur/fw*m qh bl9v8 +sw 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 this point? Assume the speed of sound in se/h 6gbw,crb m69vlqsvu8q f +*awater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelesuo2 a+ k21 :q sxkw9wcfvg/3ungths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of v8zgv8v 8lr rds8 bxjxo5)a5/ tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12– rjrv88sozgl8b) 8vx5 /vadx533). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strma88d :qb7zoil ux m:2iking the water below is heard 3.5 s later. How high is the cli8xmm:il2 aouq: dz 8b7ff?    m

  A person, with his ear to the ground, sees a huge stone strikewg ) d.5l l0;ek p1okee3brrs5 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 trk0dl5 3)swgep.oe 5e; 1b krlhe impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mec, u3fx7cn37e p(gc wile of distance by the “5-second rule” for estimating the distance from a lightning strik 3(en3,fcxep77 uwgcc e if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a yx,l;uoba , k/xnj g7 7rp6m0ksound 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 inteuf v 8yrx9nk04nsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level 1brckwkazrcjd f9/19d +9 bk5of 95 dB when fired simultaneously at a akwdd 11krc9j rk5b9bc+f9z / certain place, what 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 a8h /u(o 7avfjuirplane 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 u/h u8vo7fja(down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rati8twex(ofb,tqb;+ . yco of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of ;, ct+q8t xeby.fo w(bthe signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounuzll4p83epgz3-nch9 v m(i9sp u b9b9d from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unif9i- hsl4vnbzc ep 9bu93(pzl3p9 8um gormly 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 e 2zw2.mdbbnto 1 a9-6fqnw x8aardrum 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 ampljk p q0wq,k-8tru4dl( ifier 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 kkq4,wr(u t- lq0pd8jin 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 rclrd54ocw-)8ma p(c when placed 2.8 m in front of a loudspeaker on the48wr crl(accd5m-) p o 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 in sound level of 2.0 y qql7db 7r4jfduqqlm)btof5v/.7.4 dB. What is the ratio of the amplitudes of two soundsolb7uq77 f) 4.md54jtbqy/ .ql qdf vr whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave ivh . khjo9c8,qs tripled, (a) by what factor will the intensity increase.9k 8qhojvh c,? 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 has twice the3+sx;lz r z5trg+dn ocv6 vn94 frequency of the otherv++rld zcv;x 6go stz4n59 3rn. What is the ratio of their intensities?   

  What would be the sound level (in dB 0o5df; c:txfm) of a sound wave in air that corresponds to a displacement amplifc o5;x:d0 fmttude 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 a1dm,nbotluhbm (9+pss,k6 0gdp bk 36s a 100-Hz tone that has a 50-dB s u,pk6s lht0+mb9k ,dm 3b(gpndb61 osound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect emd0 .z 379gbr.k(4 2hwy ovlhnxxw:e when the sound level is 30 dhm ynxh3.z07d24be( gowvrx.: 9kwe lB? (See Fig. 12–6.)

  Your auditory system chlw8f; ) 9gynlan accommodate a huge range of sound levels. What is the ratio of highest to lowest inlgnlfy); 8hw 9tensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of thm+3;p2-3o*fv jdda** c:xv 3d c8ju pc jktsrpe vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must theccrt: vfjdocad; pv-j23 +px*sdk3jm 8pu3 * * string be placed?    N

  An organ pipe is 112 cm long.)7th+vt x -h4(ncbwt x What are the fundamental and first three audible overtones iftt 4x)v(+7 hwn btx-ch the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect frj89 lmir*-*q e4; m+abrt i2kvszla5aom blowing across the top of an empty soda bot4era a2;-+k95 lbizq*mjaml 8 t* virstle 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 range 32 c7fgg 5hnnrxh8e6e of human hearing (20 Hz to 20 kHz), whn7 ehfrn g83cxg5h62 eat would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a rij p,le,2)rshtl vcxpy85a2i3;x 6p frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lepy6ihjvp r )ec8tl25 3;l ra,xs,ip 2xngth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned ih tf/edf j0aq*tb038(c;rjk 1ih-mvto play E above middle C b ;-ajfhm8t iq 0k1c/hd3tf0*ie( jrv(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emp f4mml3 8+dyhtox-n)vmu:n+ its middle C (262 Hz) when vn)3lp4+mm8utfd+x o :ny-mhthe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20(jqizq 1; xat0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should thetwyl4 vo amo mo)/*.q9o j6p9e hole be that must j9m.l/waq*o49t opoom v y6)ebe uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at09qdx9ns7 n 6; uabgbr any other frequencies in between. (a) Show why this is an open or a closed ux0qs7n ngr9 da;9b6b 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 resonates a9qg rku3 y,y-tt two successive harmonics of frequeyt,-yrq 3 k9guncies 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 c z8 dulkb0h9.$^{\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 rangeq4k f8qsnv7z5 for a 2.14-m-long organ pqn sf 7v8zq45kipe 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 open to the qmvz- .+hzzzji d6kgw69b3w *outside and is closed at the other end by the eardrum. Estimate the frequencies (-k qh96gbzw63+zd*zz miv.w jin the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s z1ji g1e5nx*yyhf8c+ 6lyf( bfc uz:3when trying to adjust two strings, one of which is sounding 440 Hz. How far o jzgn:(*ze5y1 f6ycf3+yuflbhic 1 x8ff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (ep ux m7d(oo i;nox/)*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*5:js1q)ns/blz tpm q kHz, while another (brand X) operates at an unknown frequency. If neither whistle cantql:s/s1 n5 pq) *bzjm 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 beats/s875 kqayf9vjn when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with y 789qv5jank fa 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, 294 Hzpo(5 .nvxwh3.4smvl f. The tension in one string is then decreased by 2.0%.4l5s3f hv.xmvw(.nop What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will bw-bo w+wd garap+t,,p vv5yc/( f9p *ne heard if two identical flutes each try to play middle C (262 Hz), p*r,/( av5w9ty nfwb, wgv-opc+pd+a but one 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 frequency of 441 Hytrym-v. /h5 rz; 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 ofh-.5tmv yr/ yr A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stand1h8eicxs j m ytfixbyq+;73; 4s 3.00 m from one speaker and 3.5mciy 1y3qf8+7h b;;se xtx 4ij0 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 132 Hz, but a piano tuner he:x .wyph)yr 5kars three beats every 2.0 s when they are played together. (:ky p.xy 5)whra) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in ai9(da1 ub k ijam6ujm0)0xeif 7r. How many beats per second will be heard? (Assume6ua)0jmb9u 1 jf xdiim k(a07e T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is l e82tt qfm*sn)pu3b .1550 Hz when at rest. What frequ*3)pqn tfus.el8t2 bm ency 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 detect if tp*;;rroaq) pt bix4) a fire engine whose siren emits at 1550 Hz moves at a speed of traopxi*;t)p ; 4q)br32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift2dtq cnslw: q85 o5.ml in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are t5m.dq s8lwq2oc ln: t5he 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 mc9rdeh (++ qofrequency 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 frequer9de+h( cqom+ ncy of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out urs.3czug;0a/ d j d33 +hzjlrmltrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivesd.;h lazc d 3j 0rg+/uzj3rm3d sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a nay pr.:z+.m n d-ise4wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the+ap-i. z y:.4snedm rn bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba p5sh,y)akd;0bxr + 3(h nobt xwas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approachedh3;xb5 kn+dabhxt )syo,r 0(p the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasouh kh:(t( e9q(u-k5cioq7a jovnd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MH-e9k5vu7iock:qot( q hj (h(a z, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency kflh9tyk 71uopiu/) o -y1f5p $2.25 \times10^{ 6}$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 emih3m jeu,rs)jm huk ;27ts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who a;jue km7 3h)hmru s,j2re 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 *j f47qtqoq2 rodd0u( d 3f+nrspeed 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 whequ 5+1l jyozqyb- v:l3re the speed of sound is 310 m/s (a) What is the angle the shock wave makes wyob zvl-+jq1:yq 5l3uith 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 where the speed ) w:y5/+ ndy2egv) vo(fi7 ehlforz i3of sound is only about 35 v75 f(+d v oz2neifgohlir: )/ 3ye)ywm/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 thfe.k k f2piv; th65m dz;85dsge ocean. Determine the shock wave angle it produ.5mdsz5tf;; k dh8 6fp 2gkvieces
(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 nz ex .c2+mzwa.mk4 2*iq 21bnkxkcz6$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan1: vbg-q1tn xvq2n7 ove exactly 1.5 km above the ground flying faster than the speed of sound. By the time you nv :v bn2xt711og -qvqhear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound puchu9fu3lt 2 0z:*ktoylses downward from the bottom of the boat, and then detects echoeo t390tcf*hk:u yuz2l s. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octave)ew2t d5o 7e(we+oy o /edbg1-uowg 8us are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dis* w 3ze en4 :vs;p()/zf7 ,amzovbmaraplay called a sewer pipe symphony. It consists of many plastic pipesvzfz :/ aabwpnm(e)v7ma3 ;z4e* ,r os of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the t nr *kd0n i-kx3kn gylo5yl(5 :s4q;x:n1 hpephreshold of human hearing (0 dB). What will be the sound level of 1000 such (sd:i*4nlpkxypyqkx5orl0 hn:kg 3n;n e15 -mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an )fs1 1ssf ir*xg:kr3vn4p2if 87-dB sound are heard simultgn r)x*k114 ii:pfrffs2s 3 svaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105pwd0jy/*v a,k dB. What is the acoustic power output (W) of the speaker, assuming it radiav/ay,p0 *wkj dtes equally in all directions?    W

  A stereo amplifier is rated at 150 W1/ :eevugef9uo -3ru+vb - zck output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpu k:1b+f9e-c/ rvzouu eeuvg- 3t in watts at 15 kHz?    dB

  Workers around jet aircraft typicallyyk(bak f oo i(wg-2+hir/e0s 0j:(kib wear protective devices over their ears. Assume that the sound level g(0wb eji:(ak(fko-i+ s/rb2ih kyo0of 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 unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, *qxvopkzo 8 n a9ayz3qz6:,n2emdq )6the 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 viol x7cdh0n(fq)/yvh4;x j gp)yoin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm l.zx4a4du ry6 aong between fixed points with a fundamental frequency of 440 Hz and a mass per u46r . 4uaxyazdnit 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 t4 atr;vh v84fdube 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 levefvh a4;tr8v4 dl 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 string of mass 2.10 g is near a tube tm9kf(kfu: tb8p2 :sgdhat is open at one end and also 75 cm 2bksm 9kp(: uff:gd8t 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 full .xq1ekd cqxivf ugj6 -wvo: - ,g172xgloop ($\frac{1}{2}\lambda$) 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 two3o mw7hcf 3 w1r1/bstq7 vo9g *bri-ud sources. The sound is loudest at points equidistant from the two sources. To determine exactly 3r*brw9/3ohfw1qc7io mb d-17v gut swhat the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conduw96s)g;u )z;0 u ejnym.isq fwpx: 0zuctor on the stationary train hears a 3.0-Hz beat frequency when the other train aeg0;um)s;y: n6)u fwp j uiw09q zz.xspproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approa4 f(hoe (k5 gza2rvtr.rve) k(ches you is 538 Hz. After it passes you, its frequency is aro(h2(eevvkf54. z krrg)(tmeasured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate t6u 6a 1imzboz*he speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certaiuz*66 az1bi omn 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 freq9u (iz-s wqcf3uency of 11 Hz. The shorter one is 2.40 m long. Hcq3(-fiw uz s9ow long is the other?    m

Two loudspeakers are at opposite endsjh j)7hro+.n z 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 is between the speakers, at B, and (c) he hears the speakers after they have p+hj)7 h.zrno jassed him, at C?

  If the velocity of blood flow in the aorta is normally about mu bz5er2hm-qel/d- 30.32 m/s what beat frequenc q-rzm3uh/-b edle2m5y would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s w. wbq:q,x2nidtck6u 7hile 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 wawxtn.k7q cq u2d,i6:bve detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approcacoh.xz jh, *j6 9se3v42hfg aches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the ecjjcz,o *gsaheh2f . c xv963h4ho from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. xgs-as2.9bcq20x b:y5)fkwm-/ nho tv hb g8b12–38) was once used to send signals from one Alpine village to another. Since lower frb0x 22-vo ybshwbq5:x. btgn8/as -fk9c g)mhequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo liq .x0 o o/en +w:./irdgyeik:ostening can be compromised by the presence of standing waves, which can cause acoustic “dead spots owr+keo:idn.i gxo0e :/y/. q” 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, calle:q61y/n bxnmmd “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 prnn6mx b:1q/ myactice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for th gck;3a e.n1;oa lsz)b )z5 :px/hthon -etyu+e human ear at a frequency of about 1000 H3 u na.b5en zhalkg)e);p+;chxsot-toy :z / 1z 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 ty h62kk4fp8dt3(o cb the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What ihd2ycp 6 fb(ot3 kk84ts the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15+5h 1n-k9m zcpnmni *xmx4r9e $^{\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