What is the evidence that so4h/:saqs q: ha19crop und travels as a wave?

What is the evidence that sound is a form of enewmcn c23fx(+py a/x/w(y/q w 1+xoq ksrgy?

Children sometimes play with a homemade “telephone” by attaching a strin5 -qyi3n i*v*qki*co1 (q ujylg 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 sounii *q vyo cjq1 ylqn(35k*i-*ud wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frao6.+bso: txw2oth5v )/waby equency or wavelength to )o5 t:hwab6. 2bsa+oytvx/w ochange?

What evidence can you give that the speed of souqpa09qs08 vb end in air does not depend significantly on frequenc qa8b0p9s ve0qy?

The voice of a person who has inhaled helium sounds very high-pitchtk0 ytiat+lyc29j,45 opbq9p ed. Why?

How will the air temperature in a room affect*8gy i-i5klh e the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude oxp0- ,6krafw lf sounds in various frequela 6-f rkwxp,0ncy ranges. (An example is a car muffler.)

Why are the frets on a guitar2z l3vyka q+;j (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge? ;aklqzv2jy+ 3

A noisy truck approa6i uic n+t7ls:ches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diff i6ui7cn+: ltsraction.]

Standing waves can be said to be due to “interference in space,” whereas bea.ejz3/ j)- l )h,7 8nhy:zwss jninskats cshiwn7ny-hjj, l3:8jz)ass )/zkn.e an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speak8sx7h8 * h; .cmeihnjm( i(d sxgogw5/99wjuiers were lowered, would the points D and C (where destructive and constructive in(897h oim8 ; gws ei5s(uc d/ xignjh9m*xhw.jterference occur) move farther apart or closer together?

Traditional methods of protecti(s:blvwlspstt6/ 61k ng 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 thes sl/t(16ltvk: b 6wsp noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a fe s -0gk0jdk/rl;mg7superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the ;ejmg0gld -k/ks rf7 0waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift i*a c+rz; 25ct* 97pohr+,bdhsl1ji muw9 ftdif the source and observer move in the same direction, with tht9lwit7rz cso+;h+rm1bd *f,p*h 5du 9i2j ace same velocity? Explain.

If a wind is blowing, will this alter the fr; 6u h n.axk7fttns*)dd5gfg3 equency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity ch67x35fndngu;ahktdf t s*.) ganged?

Figure 12–32 shows various positions of a chzt-f* 71mpzvfj3qhgx h0 -,vtild in motion on a swing. A monitor is blowing a whistle in front of the child on the groundjzf0 --vfvhpmzgh*t 1qx7 3,t. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the (y4b f g 6ydxjz.i yb2h1pi)6jlength of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. 4 j jy6xi2 (6g1 hzyfbdbpi.)y$\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship justk cfu z.-n5b5.y 0ixce28lwpo below the waterline. He hears the echo ok.fz8.yxwiluc5e0noc -2b p5 f the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in 4,4plxa6ad1 oo voej1 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 schp/kj4(uwk xzri /e-xe 1/fo6 wool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the baxp46 kfu/rjz-/ (xiw1/k weoe ckfire 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 stn32 m83ucyjp)f1+anqslly a ,riking the water below is heard 3.5 s later. How sl3)1pa n3nmfy8 cajqu+y,l2 high is the cliff?    m

  A person, with his ear to the grounddc.v7 qmtu7c; , sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the othdc7u.;7tq m vcer in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the73z0o mrlk *ud “5-second rule” for estimating the distance from a lightnin z3uldk o07r*mg strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soufd5 1:*ux 8uccgcihe. )zyel0nd 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 intensituujl:+:qr( n e464)e 8fwnylwdj f xp-y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce akt, nc t68xt6i sound level of 95 dB when fired simultaneously at a certain place, what will be the souxtik8t6 nc6t,nd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy je,/n we6,ykyy yt engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the capty kywye6 n,,/yain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise +23n8e+fo.*jjzmx qe;y m;vchwcf)yratio of 58 dB, whereas for a. wzf+v8;yfjq chem2 ox y;e+)3nm*cj CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outputvhqdp0dmc-ix6(,a2t ;o9cg 7d 1 cvsy of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rouggytd o;2079vsima cx -,d6qvphd c(1chly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose areaibs ty4-gw( .e 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,mq pieu2j/ 6imv0(dui+ k 13sw while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point em+3sm1( u6v/ip ij2qduk w0i3.5 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 m* pv ucu 7;xv4bjnpe( :dp+3g(t qvr2jeter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage.(puq bp+vd e* c j:r47v2(npxjvut3; g
(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 diffec(s*-/ s xmwusrence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section*(-u ssxswmc / 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor w:f ,ywmxes/lzr d8: /pill the intensity increase? Increase by a factor of ,z d8wp:es/ fr /:mylx   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, buai1,/ u m et )jrwnlk1*j7std.4w ;jwht one has twice the frequency of the otherj etn ;, mirls7w.kh*u w)1 1wjdta4/j. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave imyn ,c wm6t 476cjhrb+ijtq:3n air that corresponds to a displacement amplb6,m6 my3h:jq4tc7jcn tw i r+itude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-y wh*51bp dds/s 0eg2eHz tone that has a 50-dB sound level? (Sep /se5db *d1sew0hy2ge Fig. 12–6.)    dB

What are the lowest and highest frequencies that an*2yz.-xblb e q77httj ear can detect when the sound le 7jh-7ytqt* zx2.belbvel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range ofy/ esyhg-/z:p8h (azl8k 7fzb sound levels. What is the ratio of highest to lowest intensity atga-l(z/8 z e8zshy/ :kb 7pfyh
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has c8.txn4bs: c ja fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it bt4c.j n xcs:8has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 *4hfq (n4gfsaai k8c gh-/j2r cm long. What are the fundamental and first three audible overtones if the pirs /*4gciq f(nh8h2k gja- 4afpe 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 ys dmkqe 18 wt d8qazzjp26;rw);l*wq8ou expect from blowing across the top of an empty soda *spzdwa; 8wdek1mrq8 zt;2 6qwq )j8 lbottle 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-8 (k: p8 gi2cvuyb3*(le e:ekr*fl aultube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would urpybge:e:(ekuc8il *all*fk(8v 3 2 be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string ha5hm ak:pi,km ,s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only m,a:kik5p h,m 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p(ie:7t8 qpnxn2d)l umlay E above middle C (330 Hz)( 7nt)u:liqnm xpe8d 2.
(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 auru3 uw.2n4 proh ),, +1nxomoy wru*open organ pipe that emits middle C (262 Hz) when thw21nroo4rorhm3 x *+u,uwu)any.u p,e 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 c2jm.8x + ky2axso6lzat 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 Example 12–10 shouhtth: uca:2s bm +p.m8by1(vcikg( *qld the hole be that t*8hq(1t:.ycg:vih a sm+b u2p bckm(must be 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 Hon gekz(2ljs+cv70jzkms:2-z, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this i -slk0n:z7j+o(jvekcs2 2g mz s an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonbjebk n6gv*a0g45t rf2b8 qo:ates at two successive harmonics of frequencies 275 Hz ar b82n0t*5: 4jv boq agg6ebfknd 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 0jy5 4pw(hgdx $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long organ+s ewkh v,d-;y pipe av,wsd- ykeh+;t 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 tqdsw(:/.x3n ku j1 wfeo the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible 3w/ewk.n 1fxud q:js( 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 when trying to :26xqwsn*7glipktcg1f0 3)tvg ho/x adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? pxhtt)*:c/2fsogq xil61 7wgk 3v 0ng±    Hz

  What is the beat frequency if middle C (262 Hz) andh+ mqi kz/wd.3 $C^＃$ (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 kHz9 :6a tqhjlj aby;vck,)2i l(o, 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 pla;jl2ac 9yqi khl bvo,a:(j6)tyed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and a);z y,1vdg; vdug;wm9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string;, 1w;d yauvgv )dg;mz? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freqekipd 02rqjp1d1q:,a 3p)8zfz 0pycev.q 5 rauency, 294 Hz. The tension in one string is then decreaskpded8zz p:,aa0vqfrpyeqj 1ic 2)01 5qp .r3ed 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 be heard7c1t5 idu :/2uvrdzzl if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at7ir2utvu1 5ld/dc :zz 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzw z;10g+kdvg p; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B g1;+0gpzd k vwand 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 m apart. A person stands rj20r-g(puou7 rbzg+ 3.00 m from one speaker and 3.50 m from the other. jur rb2zg r(g7-0puo+
(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 subp7 n 97x xt (,:lpqgkww/lxz6pposed to be vibrating at 132 Hz, but a piano tuner hears thrlp/76blqx9 gkwt, (n:pxz wx7ee beats every 2.0 s when they are played together. (a) 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 cl /g a7;y,tzeof wavelengths 2.64 m and 2.76 m in air. How many beats per second will be healcz/;g yt7a, erd? (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 at k3*xygry 9vb4. k:gwdrest. What fr9kgyg:*w bdv 4. xyk3requency 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 frequexg95p/p1p pa2*taosdp7m.ag iteg ,1ncy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3ept /g m 1.a *tgp ip5pogxd9paa71s2,2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towa0-o a ife-ahl,aim6t9 dkx371y. xooard you at 15 m/s versus you 71oaykxa -atei3dlmiho,x 0 f.o6-a9 moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with pzv6.0y,ofy p2 i r8()czvn mathe same single frequency horn. When one is at rest and the other is moving towarv60i,n2yozc.8yrzfa (pv mp )d the first 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 ouf:) y dqyd0;vht ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directd; f h:vyy0d)qly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wa3 g61(xuq )yntaf+ii;t 6vnr zll 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 bat hear in the reflen+)zqgvi(itt 66f3 xn1ayur;cted wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba smk*ofiby+ je, *ze0)was 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 raiem 0yi)*fke,bs+jo z* lway 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 wxy hi d0;w9yz7aves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large lezi;hdyxw0y79 g arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequefuv b 3rdw kvwwf7)4+295mgpjncy $2.25 \times10^{ 6}$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 570 Hz. When the wind velocity gk0- (yy 3gv2c 6tzzbeis 12 m/s from the north, what frequency will observers hear 0yctz6 k z3(2-b yggvewho are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at vgnn+0zhpt /5-2s yvu 94xmap 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 sound8rvrll a:cy6w2m6/ r.3u ejdq is 310 m/s (a) What is the angle the shock wave makes with : rr r/d e8aqym j.3wc2l66uvlthe 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;w9nt;ke8 9xj*m nnlv of a planet where the speed of sound is only about 35 mx8nlve*9n; w;kt 9jnm/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 shoc5gh mpjdw3w28u .s.glk wave angle it produce s8.gjgmp.u2w l5 wdh3s
(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 sup4v( s/a3pk$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overuipn46+jeyd. (2t vqzjd3i, nhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal n6q.un(iz42dp,y+v3t jjeiddistance 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 sonaky76vx *m y;sar device that sends 20,000-Hz sound pulses downward from the bottom oa ;s7k6y*vmxyf the boat, and then detects 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 the human audible rangk8ivc3nzai9qg 8ve3( e? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It conso: svi+8j/flrxv )l )uists of many plastic pipes of various lengths, wuvlx)8)+ s/:ofjr iv lhich 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 ti oy5c .6n2sqnye 5,vohreshold of human hearing (0 dB). What will yon5n y ,i s65.ocqev2be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82yd2k+z0.k bxl su x:,l8 l4ydw-dB sound and an 87-dB sound are heard simultan.:sdbx0k dzl ,ku2 ywll4xy8+eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, isaey.m4 xx/3b d+g7 jrm 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally inrd/xm. y xga+me47j3b all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ou1jr*iv. ( 3f9zyqw vvwtput drops by 10 dB at 15 kHz. What is the power output in.rvy qjv1* iw(93 zfwv watts at 15 kHz?    dB

  Workers around jet aircraft typically wear pddtl;l2: ; py*wm)v hwrotective 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 avev) lpth2w ;: *wmdl;ydrage 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 communii1 0n ,z)1rn(zer0ee t+tfllz9kvf ),7xjivpcations 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 frk;7q,zcwa 5t mequency 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 /6in(il jg fh2z78 co.e esjx1a fundamental frequency of 440 Hz a(2io c seij.8 n1ge7/6lfhzxjnd a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vn i dc)*)3 cyu:c.pdvfertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it didc *f 3p.):yvducc) noes 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 mass 2.10 g is near4rw 4 ohf47 rw *o1*nljm2fvwn 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 harmonic in ohrljrw nf*nf 2wvo4 *w4 7m14the tube?    $ \times10^{ 2}$ N

A highway overpass was obsemybk +s2hm;a:8sb )fw rved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone inp8mym+aa,ag+*t4kj u;yn nv) the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the taj,m8)k;p unagmy y +v*na4t+wo sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles6,io6z rpi8qzi8ta )k. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appro 8oz8ri6zaqii6 ptk ),aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. A-nff6pk;5r k. p-jwa yfter it passes you, its frequency is measured as 486 Hz. Hoa jwy; k k5n-ffpr.p-6w fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jusyhcl rxr4o*e1- nu8e/ t 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 halve*hrrn4cl o-eey u /81xd) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, )orv3te8 mb 5 8sjxzn4produce a beat frequency of 11 Hz. The shorter one is 2.40 m lon5jm z8 e43xn8sr)vo btg. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stat;gb*fv3y y:wnionary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is t:yb*f; wv3yn ghe 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 aorta is normally aboutwebu6(cmgw.f98-p ac//vt n:w i/ihp 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed alongc:wgm-uiwc ph a i(/v/wpte 8 /f.9bn6 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 while the mot+s t8flm qo7w:h is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat aft7 fl ms:+8owqter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. op.x,6*fsur d The pulses are approximately 70.0 ms sxp r*6f, uo.dapart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signaln sf q6iy6*nbo/mt86e s from one Alpine village to another. Since lower frequency sounds ar8ms onnit*6e b6f qy6/e 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 listenin,f d4xu6iv*mqg can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate th iu*m,f qxdv64e fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, call15nzr b4l1t q s7od+xged “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 practice, the r415+lqzgrb dxt1n o7sod 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 frequency of a 3tpd*ehvtaog0 k2 ),pbo t0t,g*eh) 3vd2apopkut 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 ground h (fo;tos2er/u ears the sonic boom 1.5 min after the plane passes directly overheado(2o ;u/rte fs. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatfcz)9yt7e)cf/ ch+kn;ey 7 xx 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