What is the evidence that s0g y94d0le6p pdydw.l ound travels as a wave?

What is the evidence that sound is a fo+ x./n;sb*xkiz*l it xrm of energy?

Children sometimes play with a homemade “tele0) jmh +,okgvpphone” 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. 12–20+)vkph,jo m g9). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes frvyvpdk d7vx(syk.,vk3f90 k+ om air into water, do you expect the frequency or wavelength to changvspyvv0 x,kkdvd (3+k7.9fk ye?

What evidence can you give that the speed of sound in air does not depend signifx 97 gvtk5+((hgvgpmnicantly on frequev( n txgh7v9k5pgg(m+ncy?

The voice of a person who has inhaled t;de-3sprkni/*a3dx helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organw-ks *q3 jik62d rrfae o.b(o. pipes?

Explain how a tube might be used as )jhx,5e h z6pfa filter to reduce the amplitude of sounds in various frequency rangh)5 6exf,zjh pes. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacv)gfk2q 8v wj*6c+ jwsed closer together as you move up the fingerboard towardq* k6w 8f vcw+)jg2vjs the bridge?

A noisy truck approaches you from behind a buildingf 1 bqe(npln.7. 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 higf1 q.p l(nbn7eh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be l,ds jgcr8/*osaid to be due to “interference in space,” whereas beats can be said to be s/ j8*ldro gc,due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would theibvpk pa:hd+m 9h-w 54 points D and C (where destructive and constructi + bhpv -5d:9im4kawhpve interference occur) move farther apart or closer together?

Traditional methods ofeg(5a9cjuqn6 c 2va b+ protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it e 6b2nace 5(j9+q cvgaulectronically, 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 be j0t :bh h6vh9tthought of as a superp: t6h0hjbt hv9osition 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 frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in l7mfeml- z4:lmtl g,1the same direction, with the same velocml,f 1 lez-mlltm:4 7gity? Explain.

If a wind is blowing,s mdc.ba/mu,g-,a.yh.;gpf (s cui- )gr g5ku will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changm-(hgg-.)ukgc,y.p/us f s gr ;.iu,madb5aced?

Figure 12–32 shows various positions+zai :kmjl1 m9 of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Expla mlj:9kiz+1a min your reasoning.

  A hiker determines the length of a lake by listening for th-go)dipi+taq 3,d 1qde echo of her shout reflected by a cliff at the far end of the lake.aoi id q1, p+gq-dd)3t 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 jui6yf 8p(/tkd12 ; b:grw3nk i cu2wnrmst below the waterline. He hears the echo of the sound reflected frwu1g:bn32;fk tiw2( nmr /8y ir 6dckpom 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atvr2fw) zt2,t ur9mo+a 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 schotmq 525;k khmaol of tuna on a foggy day. Without warning, an engine backfire occurs on anat m hqkm52k;5other 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 msf :) cu:3 gp(n i5wrglpe. 9ruoog*w:akes when striking the water below is heui fr9:uowle( cn:)wrg gp p5.g*so3:ard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, kx + wuf)y- scmfc3.hkqw)i7; sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and thc y;3 mfuk fscx)-)ki+.q7whw e 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 6 g/ kbyxnz8*ng4v lo9made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30ky6 /nvog 9*l4b xng8z $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 128wd*or guj(1g0 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 id;)2nkafkib/kb, + dr6a 5gkls $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9c((jn osryp4z-s qn4qx7 oj++/qr gz 85 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitieo/zncz q-or snq7gr j4 +(8yxpsqj4(+s, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy xi3bd; is/6u *xtvp,ojet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would t s botp,x;6xv3/iuid* his person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is saimg1 c2p(l-ru9ldu vy cck:/s 6d to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgroun1kpu l6gm-ccsv 2cdu( l:9y/rd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakijix9 ds 5uw.a*b3eg*5.ptnl*p ( bxling in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on th(ja95pw 5nbilx ..ue bitdl*sg *x3p *e 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 ear*txze*c.k;l l wx;7aedrum 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, whi: 9 77axtmmgrtle the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn at77 9:x gmmrtto each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frontu)q0:dka7ge k3nzuqrj i/+o.j5fqs) of a loudspe7 s3j5a .:0qgnrjufqi )z e)/+oqdukkaker 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 dy i4(haak5 3:6.r,mr5 vjmf lxlzhf+ eifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels (4+x5lfhr.flzm jeaa :rm,6 yi5hk3 vdiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripledfj82chba/ o0i, (a) by what factor will the intensity increase? Increase by a factor ofo8chf0j ia/b 2    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal diy(ua02v mec4 +ritf:g splacement amplitudes, but one has twice the frequency of the other. What ismy:t 4f(u0c+2g i vare the ratio of their intensities?   

  What would be the sound level (in dB) of a s nol8-47n wogfjv+/ vq+n6k waound wave in air that corresponds to a displacement amplitude of n8q+a- f n v jv/o+gol7n6wwk4vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as le;./pgkrv4vn/kv) lpe9ty: no *vdu 3oud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 124 *pv)gtvk:9le. / dounvkr/npe vy3 ;–6.)    dB

What are the lowest an e4 ruaql jh gf1p;7vh,c9*7:t -azcued highest frequencies that an ear can detect when the sound level is 30 dB? (S* qce-z719lg fhthu;ecr:uj7a4 a,pvee Fig. 12–6.)

  Your auditory system can accommodat u0 8pmognnp)dh;+sb :e a huge range of sound levels. What is the ratio of highest t8ghu b:+;0npmp )osdn o lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a viohe6p 6 qj1bkd1/or og2lin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what g dehp6 qj/bk o2611rotension must the string be placed?    N

  An organ pipe is 112 c24 hu3 au,e 5;ihp(5gevfq winm long. What are the fundamental and first three audible overtones if the pipea(35v4e wiu2ph ghef,n; iuq5 is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from )d sludlvtp w(9+r 54zblowing across the top of an empt5l(v+ t)up4ldrswd 9zy 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 pipee;va-7ep r+4)*1mhf y dk trcf 7u7kmws spanning the range of human hearing (20 Hz to 20 kHz), what would be the rm*pk -7y7ef1huedram7 v;r4 + wf k)tcange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string lt+vf 3am9oqjev5l 74has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it qvet+j5 9am4l7 ov3lf is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pzqlj,y d-r* 2vlay E above middle C (330 Hz). vd,q-y2jrl* z
(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 tj;4(ytenofs m: hmj8 1hat emits middle C (262 Hz) when the temperatut8o ( m;:1fj j4hsenymre 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 3f)rf,h+7dbh lyb( t bat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in e1fejl:j d1 w+Example 12–10 should the hole be that must be uncwfed+jj1 1:le overed 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, andh1hy4jx *mrcl-ozcdv-* 6(op 616 Hz, but not at any other frequencies in between. (a) Show why this is an ope14mj d*z hr vo*xlhc( op-c6y-n 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 ,g+drhh/rc 58da0 hhyy5 ,ql fve-q/nlong is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is /h/g5lnc8yr 5a, d-0h q d,vh+feqhyr
(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 5fedxafdwc;:0,w ty2 ud0d/k$^{\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 m;c6h sveum 9u30- oo7nc1lgpa 6 3zjtopm ,2zwithin the audible range for a 2.14-m-long organ pipe c-zp3oz03 t79h2c;o1a v6m muou6 g pmje,l snat 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 outg;;rj 2so g8ec6pp8(b 7hhu lzside and is closed at the other end by the eardrum. Estimate the frequencies (in the7h po p;j;g82gh8rc bzlu(s6e 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.y.buhx:. h w j.ur,ja40 s when trying to adjust two strings, one of wh hr.juj,xyh.. bu:a4wich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mi7w myd), kdx:gddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 2p;:.tkh td,u)id )yff7fj4po3.5 kHz, while 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 played simultaneously, estimate the operating frequency of :tjt 7 i pfk.fp,4)o;ddhuf y)brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning forme rb6, sd*o9b6hqg4f k and 9 beats/mhbef g*6q4r ,9b6dos s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one nj uz t 2t, /1+yrd;/t2fmtufystring is then dec+,ff/1 /y;2uztt rn mtdut jy2reased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will behgltg ()0wf 5o heard if two identical flutes each try to play middle C (262 Hz), wgh)(f5 ltog0 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 0twuhh3w0- +pry: yvshas a 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 beat frequencies are possible when A and C0pyt+rw-hs03uv hy :w 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. 63-5b*x uf;a /nb+ t- qq*edsr odaivsfw-*zpA person stands 3.00 m from one speaker and 3.50 m from the other. oxn6f-a *-; iq+sub p5-3ev*drq sbz* /wafdt
(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 b kaw6s9wrsi+o6 g38+n5xnnq zs qp+.ze vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating a6nsa .+9gqn5qk+zsn3ozp6+ sx iwwr 8t 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 sounddt+z)d uhbm4w1 jr 4i+ of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be+r)ibt1dz 4u 4 hdmjw+ heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when atpj(bot68b3wc8;,cll 3j 7o hzcd4ok b rest. What frequency do you detect if you move with a speed of 30 86(wj7pdo3;l z o4 cb 38lb j,hocbctkm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wh 9f4:im-xrh8vp 5kv hcat frequency do you detect if a fire engine whose siren emits a9 kh8h5i:fc4vp rmv- xt 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towardfpt8bqz0 7gu t21s3js you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the3s82 1ubfzjqtp s0tg7 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 freque 2,:h7ba/ hnlkw3hnzzncy horn. When one is at rest and the other is moving toward the fir,hlz /7az:w23khhnb nst at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sou8m+sbpufny3. lx6f3 le ;2 xkand waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/fy b8u.mxp nk2xl3; 6l+se3afs What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits anmwa(m)u ; ubb1 ultrasonic sound waubm(; a1wum )bve with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopple txnk ne*v9p ,ub4h+q/(x5io lr experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, b(nitnulk pq e+x/h49vx, 5*o 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 approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow s skhxo*w:v6m/b-*yd7p: t. al*tm * jaf3h orapeeds. 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 arteries at 2 cm/s directly away from m yft * oolr*t3/-pmwvhx:hs.d :aa*7ajbk*6 the sound source?   Hz

  The Doppler effect using ultrasonic waves of frwrk bc puz+30 n(n7sz/m,y dk)equency $2.25 \times10^{ 6}$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 freq40;sb dkdt ieb6y2ql 0uency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hearl6i0sy b 0tqd k2e4b;d 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 movfjbwnn+ ))t.; pc vfc.ing on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/t -9rn 0o aa, b;q+sy,d6hgunts (a) What is the angle the shock wave makes with the direaot9t, - ;, buyrsnah ndq60g+ction 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 thinm3th4 7; 18iq uy8ijwo2j axjz atmosphere of a planet where the speed of sound isjm3waz 7ijoyh418 ux2 ;iqj 8t 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/cjj81,m3jixg l,0vynl( ap,p s strikes the ocean. Determine the shock wave angle icjigj,ll38 0m p,(p x,n1ayvjt produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ,7,qac n sw19 5enfbiv$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the g-hhid4-w )xt tv3i ld4round flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of hl3xth-4 wti4-dv)id 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 pulses downward fr wqx-aoa 2/cb*om the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is -/qa 2abocxw*the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humajorr +oiim.li mc(8vj6b3 0;/8irg hsn audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy:;urnbsvx( 4:c pg*ev mphony. It consists of many plastic pipes of various lengths, which are open on both en (:vsexu4rg nv* c;p:bds.
(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 fromk +e 25mjdutnui wpavy.889b. a person makes a sound close to the threshold of human hearing (0 dB). Wvutp2 8 mauk8b ejd.y9+5niw.hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-d3bpa b*;mgzhj m/;db+ B sound and an 87-dB sound are heard m;3a mpgb h +;bbdj*z/simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the pqzkec 8fnn5n fc, 9m- uef+1 qp1o8o5open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming npoff,1c5o5 -+f8 kqz nc1pemne u8q9it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000monq j9b- r6 ruh4(yxgjvpa44z8 td-8 Hz. The power output drops by 10 dB at 15 kHz. What is the power oun4v9-pqrhaujt 8(b o4g 4xz6rj-m8 y dtput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicesmifqs/oeyuf7/5;3xu*64lo wvlw p+a over their ears. Assume that the sound level of a jet airplane engine, at a distance of 37fly/4qvww3o5s+/elpuafx mu6 ; i *o0 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 communicaticux 71w-ys0 c rf.)wnqons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a qzhhx1bdkstbd4v2;:ym;x 3 . frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a funatr /gf of0qbf :p k7).o(i;ahdamental frequency of 440 Hz and a mass fgfqoa7r o( :.btip h/f0;ka) 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 above a vertical open tube rijo+qxc yz )77bqq+ );rzy,yfilled 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 frequency of the tro;zj x+qcz)yb77)y i+q qy,runing fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at o8n-oc hijpkz8 vkscm8x8w,, g bqo 4n53nyk;.ne end and also 75 cm long. How much tension shou -8sw;n8hv3zk yjq xi knp nob,komc85,g.4c8ld 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 lo fjyxngyx erjw).n7m );;cy q-zk,9d9op ($\frac{1}{2}\lambda$) 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 z2oenn zal;5hg; hz 68in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determineo2 ; n6an85zzglh;z he exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-H,8 o+aaiepfu /z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speeu/iaaeo +f8, pd of the moving train?   m/s

  The frequency of a steam train whih:rq h qz4*; lpg)iu9istle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (u9qqhri p4l):g i*z h;assume constant velocity)?    m/s

  At a race track, you can estimate the speed of car/rbn i* kf1 m).qx6crps just 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 octavefirmb *k)xq 61c/ n.pr (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 of 11 Hz ys9,p:kb.m u+rbjfb-, cgedza6f:e 6 . The :,jf+r,e.bkup-z9 msegfcy:6b a 6bd shorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a r+c lj9/ikjp g;x ok)o-ailroad car as it moves past a stationary observer at o- )9;cli+xj/ pjkkgo10 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 passed him, at C?

  If the velocity of blood flow in the +hn+pkel, vr6 aorta is normally about 0.32 m/s what beat 6vh,re ++pnklfrequency 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 spec v)-jsh+0zr qed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is th c) jr+0hqs-vze frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency s* r53vozvnuk lew 344t;r kje6ound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms euk54t z v* v63n;orerl4j k3wlong. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38s 1eim;5ym90nuz;h8 xl;i a fnzo7a g0) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensityzy;mi9h ;nsmi ;ef5 ga 1alxu8o7 n0z0 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 liste+*(p5kwnixh0+xejq l ozz2ht+ ,e w4nning can be compromised by the presence of standing waves, which can cause acoustic “dead spot x4el0 qh hnx2z+jiz*p,+wkwo(5 +nets” 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;1ajsr-t7ja cwz8tl:oo :6k(pv b8df, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a c8 p: z :18a -jjt7 rdwcobtl6(asf;ovklear, 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 theifs3xa pq:c 1( human ear at a frequency of about 10fa spx3(ci:q 100 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 obsc- kn7ul,t7dp erver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planpk ,7dntul-7 ce’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 w0qz:cb qd(pxx4k 0q8yj /y9a $^{\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