What is the evidence that sound travels as a waver2 t x+ gnlz45)rdo5k+hi pw2p?

What is the evidence that sound is a for3 ch2uny1w 511w-dcvu3ybp0dn8 kpfrm of energy?

Children sometimes play with a homemadcha q ./vfs.rgb,2ut;e “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched an ga b.qu/h2;cfsvt.r, d a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freqv0 oeq4s v/pc7k2jci 4uency or wavelength to vieo4q cs4jc 2p/ 7k0vchange?

What evidence can you give that the speed of sound in air don)bh 8.5h ovnu2ktfs9 xg5 ap*l 0,xebes not depend significantly on frequencyp*ehtv5f)l, s ona. b b89x02xhgku5 n?

The voice of a person who has inhaled helium so4lz1/ artnju ddl ku. h5+74gkunds very high-pitched. Why?

How will the air temperature inqh5yghzt */-)ik5uzj a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sp epxe/*/i ic6ounds in vxec6*pipi/ e /arious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move ua5n/pc p gd6;lt t*axu.q97q lp the fi*l/lp a a d g69xn.qq5p7ct;utngerboard toward the bridge?

A noisy truck approachej 9umn)dq)1ysa ,m* fls you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddey,a1 mf dju* q)l)9nmsnly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beai.r bwk8h6oy*ts can be sai.8o *yhkb6wi rd to be due to “interference in time.” Explain.

In Fig. 12–16, if the hdt9. 1zy8 ayevx2p )dfrequency of the speakers were lowered, would the points D and C (where dest8adxy tzpdy.) ev129h ructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who workls,,ye ) , nweqj5- tod7xqt/b 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 elec, qxt-, yso7) /jwqbe,tdle5ntronically, 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 supxp9w qj57 8+qmaxucv 0erposition 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 8jmwc+a 0xq7vp5 q ux9farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourx3b0/iga deqg ;aitpy-n6gx5 x6z 0; qce and observer move in the same direction, with the sa0gegzaiyd bx;anxi5pt-3q ;/6 g0 xq6me velocity? Explain.

If a wind is blowing, will this alter the f:ux7y- c;xuh frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or veu-7 yxhc;fx:u locity changed?

Figure 12–32 shows various positions of a child ;drdvti), 7b-arxr8gin motion on a swing. A monitor is blowing a whistle in front of the child onig t rv rdx8,;7a-dbr) the ground. 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 length of a lake by listening foyywd7hw5 :a, llxd) 6bp+l z4lr 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. Estid7 lhwpxwly+l4l :bza6y5d,)mate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his, ix6e4a qjn4d ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1ndi6xea44q, j 560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthskt-ov:ih6z 6p-*j h* s +vvlbg in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a nn8glzfvzy1s;6u -a hh(5 pv+a )br 0uschool 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 backfire isug 6s-yb5nrzu +(ahnva 8z0l f1)p;h v heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliffqz0z0 q-j eyl.. The splash it makes when striking the water below is jq-y00 lq zze.heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concw1x1;nu0 :yfcdwtt f 0y 7snj,rete pavement. A moment later two sounds are heard from the impact: one travels in the air and the o;nct7fn10t0jyxwf,:su 1 yw dther 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 disykh/dc:rp .6nv -ey5 scckm 0,tance by the “5-second rule” for esti5 p.,ys/c0r v:d kme-kcy6 hncmating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1204m*2: t0pg spg wtg,gh dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levtchu95a9ju0 h5jmp 7m15f8turs y h+g el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produc4bt4;iq p v kyyu3i6)pe a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only onpvq;k4iuy3 y)6tb pi 4e is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance f0fp 8gr 1*azr phln/)fe et5y:rom an airplane with four equally noisy jet engines is experiencing y5 :gr f) pznepa1f/lh *r0te8a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-/h( xgb mkf 7.pwa,diyd wi96)noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratioh )y(6gm.fa dw/7 9w,ikidb xp of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person7gi 1 g fgjb7 t7(ph,asbd1/qm speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly 7jb(7ip t17hg dfb, s 1qg/maguniformly 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 aref :rd;3 kvf:uw+i0a7gsppme .a is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifie1ie mo,x-0y(x0mdrj cr B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a mdex1 yrm,0 -xcj0(oi 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 mq+by2tt 2ja9m k+iv 2aeter registered 130 dB when placed 2.8 m in front of a loudspeaker oi ta kta2b+m2+y2q9vj 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 differb.cc e +..n hc;woyg,uence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amouo.,cghc+. nue;wc .yb nt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)d -r,pao 7,tsw8yole, by what factor will the intensity increase? Increase by a factor pl o oatw-y,r eds7,,8of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, ,t+ef 3tld6 yuat,s3vvfu f6 4but one has twice the frequency of the other. What is the ratio+,l t, feu366fsf4avvd3tuyt of their intensities?   

  What would be the sound level (in dB) of a sound wave z kz/lbyk ke4cgy/r1-( a*td(in air that corresponds to a displacement amplitude of vi / y 1(l/ka-(4b kzrdzctkyge*brating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what om0e;j3o(grksound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12m3 0(j ook;gre–6.)    dB

What are the lowest and highest froxu-7wuo.p; wx miesf./1dv-equencies that an ear can detect when the sound level is 3/mo-iwxu.7.;osxp- df1w u ve0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What iss0chm x++hpqw+ z+ mqe5xn82 i the ratioxhmeq i zmn qsp2+ 5c+h+08wx+ of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of j34;cuw1fl0*uh wui gg(g nw6 440 Hz. The length of the vibrating 6f(hu 4j1;u*3ig0c g nl wguwwportion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three auphl8/v+y 2r mvrhlxf 2 :;h;ytdible overtones plyy+h8h/f;;:2 m2lvr rh vxtif the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blosqr6 l 2o (j ;36b1dypo6kjwlowing across the top of an empty soda bottle that is djl w6l q26sb3oo y(6po1;krj18 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 pipgjxg j39r3s *bal)hx, e organ with open-tube pipes spanning the range of human hearing (gs 3rh)l*x9jx g3a,bj20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wha ggm:cm2b/0hsm ap3 9ut will be its fundamental frequency if it is finb2 ug gm03p9asmmhc:/ gered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 07:zh 3 wpffw;u ;0tfaw.73 m long and is tuned to play E above middle C hw7w;wpuft3f;0f : az(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits kn(*0o 5ww yr mii39/ljnz* iamiddle C (262 Hz) when the temperature isi rn/5j(w0ikw9lo3nya *mzi* 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;bxg1d -wgqfzpy(qy 7k*+:km $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ook -q+m*w *od )lgjeq(ygf ;a,f the flute in Example 12–10 should the hole be that must be uncovered to play D above middgq;, wd*ky -+)e (l qgfmojo*ale C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and ca6/q1hsutg k*ja4qr: u 3,os616 Hz, but not at any ot usuk 1,*/g :tqro64a3shc aqjher frequencies 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( yj. xi7gocwt cr)/r2 long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and )jx tcwr/o(r.g2yi7c 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 pyris-)nakn +r8yg-0 ;3-cdv wj3e wa$^{\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 foczech84pltj . j05f :xr a 2.14-m-long organ pipe at 20 0pfzcte 845jc jlh:.x $^{\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 tov gdy.6dng; 0ghm gt78 the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationdnhgyd7t 6g80mg g;v.ship 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 tryin1y* k5yg o5i7eh-fvzhg to adjust two strings, one of wh5 yie-h oy75h vz1g*fkich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequef au*tj e+345h vvi1:5lrevng ncy if middle 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 operms8;ef+jy-hbv0gx g+ates at 23.5 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 frequencbgj ;-vf0gs ex8my+h+y 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35+,b8;s d ccchf0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain y8+csh ,f b;cdcour reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29h.;twxbo(r3 cc77bv n4 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the w7vc(.x bt 7o3n;hrbc two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tryuis:: sgj;d 6z to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 digz: u6:js; s$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hq)a r-pepu8h7z; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C qu rh -8)epap7are 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 3.00 m from one speads /w,4;vb wr6rey5m nker and 34/6es d bn5wr;rmwv,y .50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hh e,yjvmfd74v0;k v b:ears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must7e:v;vyjhv bdm4 0 kf, 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 5gt,5 i+brt ggmany beats per second will g, iggr+5ttb5be 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 wheboox1d4vfp m0fb8 e0)n at rest. What fv)x8 p0 ofob0fdb 4e1mrequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if t utjs77r,-u *nhkgn6a fire engine whose siren emits at 1550 Hz moves at a speeu h6nntjgu7-t sr,k* 7d of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifd s5pi6z74ebew;xdp q7x 1t/n2jb2:e/iiextt in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequennei tx/12i7 pxd6q ; eexdib4 57t2jpb:wsez/cies 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 horn. When one is atr cxe,p:9 m)ns rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is th)rse p9mx:nc,e frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultj7 t.hbo2;mm arasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received soh mmtbjo. 72;aund frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 mm6 gu)s)i7wio /s As it flies, the bat emits an ultrasonic sound wam7g )siiw6u )ove with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was br 3eshsu :gh;-3fur;played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone whr 3 ur-h b:;ug;3sefhsile 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 speeds. Supposeu2n.g,p,bvj n xx(h) n the device emits sound at 3.5 MHz, and the speed of sound in humanp,x u),g bj(2h vxnnn. tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr/q 1 q.mzrpr5cequency $2.25 \times10^{ 6}$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 emi-v.4npcgh xkn / e*lybu:w,a:ts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are laxc: *y/:u h-n,4. wgknblpveocated, 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 spr77a;-g tl xzteed 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 vs;w ms;8xy0y*b b3bv0u(6rpwnlfi- speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of t3l b6 mry s(w*-ubw80vvfnyp;s;i b0xhe airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where ;5lw4f s fuuk,the speed of sound is only about 3ff; 4wslk,u u55 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 wav)0c mm+fa*u7b qgun) ee angle it pugm* b) a0ufc)+ meq7nroduces
(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 cchhy:.5dg- zfs*tm($/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see il50r*t dy;sw8xsbkb q .fq/+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 d/ ys +.b5w r8b0fl qxkdi;tq*sistance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward frn5:tj +h4cb mw s/2mg:ribotw6u) d1s om the bottom of the boat, and then detwh):+b5b cmg mtnws2td i /or4j16 :suects 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 3rl2t m63 p9xuovglu- audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a +ukqnkg( omt)98n ba*zmq k)/display called a sewer pipe symphony. It consists of many plastic pipesm nt)/ ukbk(mag+kn q89)oq *z of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close tv4h ut0x5rc.kr2owu1 +vdg j+o the threshold of human hearing (0 dB). What will be the sound level of 1000 suc5uwoc 0uvr tvhkx 4+.j +gr21dh mosquitoes?    dB

  What is the resultant sound level when an 82-dB souj8 r;hxytea3j3.(st w nd and an 87-dB sound are heard simultaneously?r (a. ts3 t3ejhx;8jyw    dB

  The sound level 12.0 m from a loudspeaker,84ti( y ppj.bn placed in the open, is 105 dB. What is the acoustic power output (W) of the spea4jnpi.y tp8b(ker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outp*- h z2vgz zyvztl.f,*ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wha*zt-z yhvlzz 2.*,fvgt is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicall3byu8em,e2i r- s d*c10b7mx x -pfgroy wear 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 effectb7x s3- mr8y m0bfdi p- c1xoeg*er2u,ive radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, ogh09nr :+gsbthe 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 viobmw .tfin.8 . cah1z/ qm1po6ltc4awdt u+ 2-olin 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 fixed points with h)l oouddgfrf5l s0(zv4d,2 1a fundamental frequency of 440 Hz and a mas5r0 ()dv ud41zdfo2lgshf ,los 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 abovou 3egm 7dvlmb,-2bo/e a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube ab7 o-mg2ubo mdl/vbe3 ,ove 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 4j;u d ugr)k c+0dcqj-string of mass 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 mod +cdrjgu-;dq j0k c)u4e) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to (hydf7 8 rq:lfresonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming ja.n t0pp.t qbb:;wlu6 g: 3iv /wi3ozfrom two sources. The sound is loudest at points equidistant from the two 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 iag3w.:l zibv/ t3pw;n: 0pbt 6uiq.jos the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Onyb27msd85 2mw wi,k6 vhetyf 2e train is stationary. The conductor on the stationary train yvks7ih w2,58f2m2ytbw 6 dem hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam traipk veh3(z s,a9n whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocit(vashz3 ,kpe9y)?    m/s

  At a race track, you can estimate the speed o (2tzsi eh6v-ffb +)hjf cars 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 octave (frequency halved) a6-jfhzt b+)evsi(2fhs it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding tow0wd :. pbmf95d,tlnv gether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Hovww. d lfm,dnt9: 0bp5w long is the other?    m

Two loudspeakers are at opposite ends of a railroad carq1uu v 9orxx;zgizkyx-0 xkb*f *)- w5 as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequo*v--ru 1u yiqf bg*x)9wz ;kxx05xkzencies 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 bf 7ke j*qavj(c5s gb/4lood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blo5jge qvaj47 f*bc/k s(od 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(9fr nz3l7x ir rm57(wyz0j- hass0yo 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 the frequency of the wave detected by the bat after that wave reflects off the molsfjihs5rrz 0rwx9y 0a o73(-y7nz m( th?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a(vh om*/*jd1hl 5b sk xjyb(sdgo6c.- moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the mvl(.j m*hdx/shj dkoy6cg -*b s1 ob5(oth 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 ot k7g c1bbl.j9nce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only gbltk 7 bj.c91one 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 listening can be y dq+/sfg.6j bcompromised 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 j/+qg dbyf.s6m 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, slenc6mevee --(am5 ;wyz a31ldjrder 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 clear, loud, ringing sound.d vejmyc5a3m-16 za ;- lewr(e 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 thresholdtl x*)5o hda)pohjp52v2b8i a of hearing for the human ear at a frequency of about 2l82p pxb5a)*5itoajvoh d )h1000 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 bo8tihqc)u9(ls0 3 /ou ojkt,at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhesk oojbu)8h t tio, 93(l/0qucad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat02 / j9gvldx q)stwg. .sr0ldb 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