What is the evidence that sound travels as a we39,l kw ed1gdave?

What is the evidence that s)/8;3 mrx2jt/wlztbjbg-f iszn 05 hf ound is a form of energy?

Children sometimes play with a homemade “telepqk.zl;:4fwyel x i5f9 hone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels e:q; l5y4lkwifz9.fxfrom one cup to the other.

When a sound wave passes from air into water, do you0wwg5sljh ;g400js wc expect the frequency or wavelength to c0whgcg;jw 0 05s4sjwlhange?

What evidence can you give that the speed of sound in air does not depend signifo .f :- s8ltir0rz;i+z trd-qaicantly on +rq oz.t8rfidi atz rl:-s;0-frequency?

The voice of a person who has inhaled helium sounds very hfe6,q6 cn rcmsoq32r8igh-pitched. Why?

How will the air temperature in a room affect the pitch7 eaf wb4:5 cprng -mf+,oanx4 of organ pipes?

Explain how a tube mi ar54 vxrn)zlklh6t-kbs,m.m 332pj 9 nexwf /ght be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car ms-ehlv3 rj4 t/ ,6l2bkar .m9nxnkpxwz 35m)fuffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer toget,hskyi jg nrh-le, -n (l/ex01i zp4u0her as you move up the fingerboard toward the bridge? s( uk4ip 1,0zllirh/e ,n-0hxegnj- y

A noisy truck approachfrg77 v)f, *r 7zlk s2* c:zt.txpbjzaes 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 7tfx*fzr pg.bazk lzt 27r:j*s c,)v7 the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interf j x:vjnaw6 *ylv;a*-4oya+s terence in space,” whereas beats can be said to be due to “interference in time.” Explain.4*yoa;j+v*jwxt-:6naa v y l s

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin)ddj6wvrz 2 9/ rr6tsots D and C (where destructive and constructive )69 d r2drvow6rs/ztj interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people wh:k mv4w1nrif+o 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 1f +nkrwvmi:4noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be1q2 frdcx c(/d thought of as a superposition of two sound waves with slightly differencf2c/dx(q 1 rdt 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 th;;vqgjq;kp .he source and observer move in the same direction, wip .gq;h qk;;vjth the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sou8 egikf(cvyx/nbr k.bzbu/84f,e5;p nd heard by a person at rest with respect to the source? Is the wavelength or velocity chan4 ; eyvu k/n xczi.e,g8kb/(frb8bfp 5ged?

Figure 12–32 shows various positions ofex;6i 4d+cp su)+usof 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 through E, will the child hear the highest s;+i d c6s)foe4puux+ frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fz; -thq)ppks.+b gu3 cp ,j5p( en+f pt2u,rafor the echo of her shout reflected by a cliff at tp p+zt+)asf guq j(2-cp h pkfn.3be u5,r,;pthe 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 just below the water71t2 q5dl .cd un2*dy-qoomr yline. 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 yd1uy7tl oo.m52 n2dr q*qc-d12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 8m.,uw( m8ok 7ex;ig)e 8:o*xz zmt.f papp is20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy darpp)b , ti09wkgqyjn0( +b,viy. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses viki9r ,g+jq,w 0y(n0 bptpb )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 striqz ) z,va70hxgf5f6e hking the water below is heard 3.5 s later0 )qvz57g6f,hfxzhea . How high is the cliff?    m

  A person, with his ear to the ground,u;5vhe 2hd,p2a (estv sees a huge stone strike the concrete pavement. A mhpv2;2 ,5sta hd (evueoment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofx8;o :ex*k ov+dw+cku distance by the “5-second rule” for estimating the distance from a lightninu dew v8k;+o +xcx:k*og strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the p.5yknpkpti4 )8 k.qn gfyh-.u ain 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 4 8wt5ea5ifd sis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce aj8yuj 5j2itz 8 sound level of 95 dB when fired simultaneously at a certain place, what will be t8t2jjy5uzj8 ihe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a c3sojb 2f- gzjzb5rt5p/) 8tz,wmkek+ertain distance from an airplane 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+j e )b-wz2rskmt5o 8 pgj5z/ kft,bz3: Add intensities, not dB’s.]    dB

  A cassette player is said to h.xd;hvztx+z ,txs w- +ave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rt hs.ztz wxd-+xvx +;,atio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output ur/rg:-lo,daof sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mou, g/d:-rlru oath. $\approx$    $ \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 area iss9 -,iycp8rz z,55uwx1-tdxh uyivb ( $5 \times10^{ -5} m^2$ (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 ade gsy:t6emlxwv atpa/e-5m (3le* 0y n d(92mmplifier B is rate y 9em-d:lte nmy ga3((xeld 5tea0w /mvp*6s2d at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to 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 when5xj 4 h.- cmcsyjpk:nk04(d hb placed 2.8 m in front of a loudspeaker o (jjbh.5nkys0-4h p 4dk cmcx:n 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 in sound level w7xx mq,x1ub- of 2.0 dB. What is the ratio of the amplitudes of two suxb1x,mq-xw 7 ounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave inb*vyu7 /(gij0; haqas tripled, (a) by what factor will the intensity increase? Increase by a factor of i;*j g0ynqabv (/7uah   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement;p4zfwzbof)f (uan:2 amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities?():pou ; ffzn f42wazb   

  What would be the sound levfryv 1*xsr 38zel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules xrsy 1f*rz8v3of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hav02m+wjmt8 ba/7 dw0p iwtg3qqe what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–tg0 wdatw2wb73qimqj8 m 0p+/ 6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sou5kcvt ox/w0*x.y1vpw6 z1ocsnd level 51wcc.*pky0x o/vwt1 z6xs vo is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wz7a0t dlko6,ona. : +j.jkmedhat is the ratio of highest to lowest intensity jo ,.ztk:kaeo.d+la07 jn dm6 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 freque m d*n,x;f;z5oy ;ui wmwt(e9incy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must ;9txd wy;uef(,nmiowz5* ;m i the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible o-: . .tqcyvv6b)axx5+5n daiqte12qez/wba o vertones if the pipe is1aw tb5ybxtq2zo.n-65/dqive v+ce xa .q :)a
(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 fr4verd fs a++z*yd id6v l98m)bkb k68oom blowing across the top of an empty soda bottle that is 18 cm deep, if you as6 elsdfbd *d9mbv)4 +z8v y+kk8a r6oisumed 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 spanne 3 eew+tilxjtbvf1a/ v9mpap:s,, 00ing the range of human hearing (20 Hz to 20 kHz), what w aipae0be :tvj+sm, lt0391xp/ e, vfwould be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string ha6rw:s6b/wkwy qk teb .u9i5p*s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of onl:w e* k6yiup9wt5 /skb6r bwq.y 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play Ec m cfzn*m444tvz ,4oa above middle C (330 Hz)omfn 4zc *4,va44z tmc.
(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 middle C (262 H:1o-kd 6y 5ie8dt;cf/fvu qanz) when the t/ a 1 :ny6of5icfd-eqtv;dk8u emperature 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 vs jh98vp p,*v/qde4l$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exalzmwu0 z 1+70 unwdsq ,/ukor*mple 12–10 should the hole be that must be uncovered to play D above middle C at 21wn 0ku uz 7qz/l0+ rs,mw*dou94 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 notcayju0;)*:a jd c 5pub at any other frequenbc ay)5u;0aj u*d:pj ccies 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 opv1 3 b:n 3;o ;g:whtvusnaq4yden at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is ;shvn3wd:au; 41q 3otgv: ynb
(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 h- 0 bvbfe2+fg:wq4j a$^{\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 k rk 8,(tu96 b-ddxsluthe audible range for a 2.14-m-long organ pipe a(r6ddlu,u-bt9 k8 k sxt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. acfvztr:9m*s4 6)hqn 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 c4c*:r6nza s)9ft mhvq anal. 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 dfz2up f9ce/9b5jj sod w+ -p+one beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz-+jzded 9s+2 upcbf jp95/ owf. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 3 c)wb0flp mmeht9u :x8h;ji8Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, w ket csoq9x.w/71o2 tds6xr8pg ( fls,hile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are playp/(.fc 1r t kswtdl 78o,o6esgsx9x2q ed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork an/sj tcasun 4p)my9 *r3( fdhy1d 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reas3s ys9u( )tj/r 4 mayfchpd1n*oning.    Hz

  Two violin strings are tunedn.i 2eyk7f5 cw0pxfr,uift17 to the same frequency, 294 Hz. The tension in one string is then decreased by 2.ie2 x7f ,wpcrf1k y0.fi5 un7t0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idenih oj9h u+gr+8cd ;. 3guqosd(tical flutes each try to play middle C (262 Hz), but one is a9;qi.hc ug u(3rs+h+j o godd8t 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 w4h.g0,jl*m-pwbck a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 H jhk.0gw*4bacwpl-,m z is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 my- tjy5gtqhfn c i;)1v/4ht.h apart. A person stands 3.00 m from one speaker and 3.50 m froy hc/ftyjh5tgintq v4;)1 h .-m 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 aqje93s+o un3yyasj) 4 piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 s ysoa9ej343 )u+nqyjHz, 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 air. How many beats p( p f r6wp-jeaah(k37ger second will be hef r(wpkh -aj6( 7pag3eard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque;8 .6j aoy* vfib(sam7no5tnency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency oi5 a8jbmn. e fn* ;vsoa(y67tdo 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. :o-6/l/cfo ue iakl 7wWhat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves a/6eocla ufw -7ik/: olt a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towar+6wg+ikrw/m 5t1u7 x.lol kq ajp4vs)z ,v;zy d you at 15 m/s versus you moving toward it at 15 m/s Are the two frequylgx ++ mp;76qawz 4vkuv1.r/jzwtls ,i ko)5encies 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 frequency hornk( mor8( i5f-j sbbl9u. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest heamif u(bjl8 os9r(k- 5brs 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 wavef2wugrkp )00es at 50.0 kHz and receives them returned from an object moving directly away fro)r0 gef u0p2kwm it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it (h,u4uw ls8*w jc 7.ae0zjkbqug(8ii flies, the bat emits an ultrasonic sound wave with frequency 30.0 wcie4bau8zu 0su gw *ihjl(j ,87(.qkkHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played o33pzkm :nef2 o7z sfw2n 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 the3f2wszn zm :k 2eo37fp train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloozhww /fg19i ezoh 5/j9d-flow speeds. Suppose the de h5zewgj / 99wfz/h1oivice 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 arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrmfn;z n*7.j rid cx:pu36mm6basonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency qy/7ztjv f-+ m570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers m-zjqf7t+vy /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 spe8xqjn 8nbv(0/ z)vfeu ed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where t mu .:k4*jzmkecvj 9w-he speed of sound is 310 m/s (a) What is the angle the shock wa em 4c* 9.:vjmkzjwk-uve 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 xbdo o.siq3,1thin atmosphere of a planet where the speed of sound is ox3.s,q id1bo only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock cvng7px3e;m qs)g,9e wave angle it pre3sqm ,; n7cgep9 )xgvoduces
(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 /d8a , .4ia6 b du(h,hm1gm nvrxna9mu$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above 6bu,/7o;p 6rr(p,j d8)dkmmqxayg ah 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. 12–34. Deterruk,q odxa ;8my p/db76h rjm(g6a,) pmine
(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 sona9myvka6zn cit2)-:lv- m*f sfj7 x-vvr device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then d*i 6)msyxnf7vzkc2vvl-tjf:-9-v m aetects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in l 0:r:6ctpgjsz xws-0 the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of ma04+d huqxk 0mwny plastic pipes of various lengthsqw00 k+u xh4md, 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 fromq:q v9 *q9kq7gi8gq4cgnvv7 g a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 14* qq8g9viv 9g g7qq7g:c vqnk000 such mosquitoes?    dB

  What is the resultant sound vik9 ;v8s/ oillevel when an 82-dB sound and an 87-dB sound are heard simultaolsiv8v k/;i 9neously?    dB

  The sound level 12.0 m from a 0l; pyyokd2 qa,m;w4jloudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates eqp0w;,j2mykd;a l oyq4 ually in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dro/hj-3qkd/zh o ,2yaklps by 10 dB at 15 kHz. What is the power output in watts hk ao, z2/3 h/kq-jldyat 15 kHz?    dB

  Workers around jet aircraft typically wea. lefnpkc))qihkh;g4 ni3.l -r protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted b p.h3ih;n )kn4flqc-.g)ek liy an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemsln f k1dc5w-hq+ r:wq(, 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 vio7;m s:sm w:o( vm ijn*:uyigl;lin 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 long between fim mp5pdw15 ;qgxed points with a fundamental frequency of 440 Hz and a mass per unit lengthq5w5g 1mppd;m 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 j:w* ky*gub8y vibration above a vertical open tube filled with water (Fig. 12–35*ygj*uk:yb w 8). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of me pd 5m2i(*/8+cyuw3o rdsh el(ybsh7 ass 2.10 g is near 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 third harmonie8rd +m(32d/wibou (y5s * hyhcse7lp c in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loopu7 rbgd37jd*chbg majf 2e9,)fs 8pa( ($\frac{1}{2}\lambda$) 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 rana*qtsn yxf9plq ic9n 3v -::u;ge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the pe:sn 9qiql-pf3v u*xnty;ca9:rson 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 y19s 3yjd k,jdconductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movid yy3d1j,ksj9ng train?   m/s

  The frequency of a steam train whistle as it approaches youyr*)gvmn q *7q is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving qnr g* m7vy*q)(assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars j4zja.( .hhn bbbicvtf/km/) 4ust 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 straightaway. ( 4tbn4zcbf /v)k bj.mhhai/ .How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a bea92 tn7swet)p7x6rqcv t frequency of 11 Hz. The shorter one is 2.40 m long. How loq)pvr7x ts2we7cn 9t6ng is the other?    m

Two loudspeakers are at o1;tro pe wu;r7pposite 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,rtr;; uw1e7 po in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0./ 4nx56b, nvsi 7dpjd2ozb5 ki32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directe,b4562j5vxn obsdink izp/ d7d 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 6hcrkj hi0)4+bu,rg g* .5 m/s while the moth is flying toward the bat ah cg,jr+0 u*h4igkr)bt 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 pulsers5hr 1fma .(ms as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away c5(hrsmfm.1 aran 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 h vc1zp. suo4o 97gy4*mbeh5u 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 oveuo 5ebs*u9cgohz m41p.v y74hrtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be45 chluluy(c/w j aiu-85:buq7bh )a r compromised by the presence of standing waves, which can cause acoustic “dea/-ju h)clurb(ayu:4 ba875i q u5wlhcd 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, slenderdhr)xg* wf) ywj,o-.:yd qc48 cpy 3xf aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practirwj q,c y-x:c3gwd p)yxh4 8oyd*)ff.ce, 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 the human ear at a frequzdhc /bb/42x-r3fb meency of abo 3cbb/-ed42z fh/b xmrut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the gr8 3l. lagpx.r+5 axh-a4e4lnpmpbx1found hears the sonic boom 1.5 min after the br lx.glxp4 -3hn x 1m+f5l.aa48ep paplane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatk 36fzi zvsx(( 3aoy;wrw2,wj is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h