What is the evidence that soundgpplj 5 b2y+0s travels as a wave?

What is the evidence that sound is a form olv9njx;h3*gij ;q r:of energy?

Children sometimes play with a hy56upkwi ka(2)ilye 2omemade “telephone” by attaching a string to the bottomsy lk(ay5p6iiu 2)2kew of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect th3uz1v ,kr,rcf e frequency or wavelength to1zu,c 3kvr, rf change?

What evidence can you give that the speed of sound in air doesngy.:tarcrt 0jav8+1 not depend significantly on frequenctj r .0an+y8a:r 1ctgvy?

The voice of a person,5 -;pwsfo tgiy85fmr who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the p f110vk/t bvtava,5yuo05l7loq ws4 fitch of organ pipes?

Explain how a tube might be used as a filt;geans- 6cb ltd8ai8-er to reduce the amplitude of sounds in va8asnbc6 t g--;8ieald rious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togiiyzrf1.w : m4ether as you move up tm iiwz 4ry.1f:he fingerboard toward the bridge?

A noisy truck approaches you from behind a building6s-qx5t5v;v4ap.)d.hd q yds/f izqw 0a hi4n. Initially you hear it but cannot see it. 5 i5x/ dsa6vq.f s40-zt dyn4i.vahhqqp)w; dWhen 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 diffraction.]

Standing waves can be said to be due to “injtsa a4 qzi03 (t8se0zeqer(1terference in space,” whereas beats can be said 8r 0s e1q34zaej(q as(e0tti zto be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointyja q z(55g;s5k.dmsdg1fg+) 2t kmnw s D and C (ggtnf sm5+s.5 yk5w 1g;aj d(2)dkmqzwhere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing c.j3fjg a5dypw v8(x4f.mcz u+4 o8zlof 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 electronpu o5 jgd .a8f+(mlw3 cczj.z84vf4 xyically, 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 th2lt xfn(r -9:k 4pebedought of as a superposition of two soundtpk-rdb(4l 9 x:2nefe 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 obser- i m/lidbtry,,ix7;uodw -j+ ver move in the same direction, with r-mwxdu/,+,b t7l i;-ydio jithe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bulht1 k0vkz 5 fu/pd84y a person at rest with respel8 p4f vtd/k05k1uz huct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positl*zpt18lt 3rb ions of a child in motion on a swing. A monitor is blowing arpt81l3z*lb t 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? Explain your reasoning.

  A hiker determines the length of a l(viqc2g0iccf + qi3q 8 ;rnzs*ake 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 nqsccc*( r8i 2;q ivfzi+03qgafter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just z0 im7 nn/1)qg uqaiho gi90s6below 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 1560 m/s (Table 12–1) and does not vary significantly with depth.0gumzhg)/isiaq6n n1 q 9 i70o    $ \times10^{ 3}$m

  (a) Calculate the wavelengtc 77*vtz66- fgjyzjiohs in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school. (,og foobsi, of tuna on a foggy day. Without warning, an engine backfog.(so o, ib,fire occurs on another 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 makes whe)j07 u r4hf *b+yihgzhn striking the water below is heard 3.5 s later. How 4jh z7)+ yfgr*b i0hhuhigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stri arrpd:v7 l, fpf 9zu9n5s)/joke the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1. f7upr/a5, :r9lfdzvp njo)s91 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over o nm/ bqm6g 5y5+4as*sx*tug6wgbhm1kne mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30*m5x6b*ggta/4 hsb 5wmq6k u+gsyn1m $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound jl z8i+oqssdfu2+,l a0d- d6wat 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 wi40cvyw. l -wbaiy ,,bhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sim) m8bto*uihnnd5 ke(*3w 1k lrultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, nrn mwub*kd (t*ni3h)8 lko1e5ot dB’s.]    dB

  A person standing a certain distance oqyii:kuf7-g9v z *vc2/c v3wfrom an airplane with four equally noisy jet engines is experiencing a sound level bordering oy2 gk: cu iz/-vvo3fw i*v7c9qn 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-noise ratio of h:egh r8uj9b3 ctg;ijo9 ) v3z.xcwp7 jp-o e+58 dB, whereas for a CD player it is 95 dB. What is thjo:ghzp .hwgo e3 73 )+j9pe8vcbi 9turcj x;-e ratio 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 person spej2 iin .(: ewu3ky:pxgaking in normal conversation. Use Ta2::ew3jiu.kp i( ynxgble 12–2. Assume the sound spreads roughly 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 area-+ztfz ia-ld7 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 mode* s( +bn8aceeq t)xwy2st 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 tob)wy8*2s tcae(en +qx 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 xmtg4fv:iop9), f8h owhen placed 2.8 m in front of a loud:4 )fp9fgvmh8 oo ,xitspeaker 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 i .8 ertcq v3ks8 zt638p:afdudifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two souns6 88:ezr.8vpu3c ftidq 3aktds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by7w,yqh;r-ivy .om sd7,, yqdf what factor will the intensity increase? Increase by a . dyyriqsy q df,;h,,m7-7wovfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplit.ln5yv0 v-ul pudes, but one has twice the frequency of the other. What is the ra - vlnyl5v.u0ptio of their intensities?   

  What would be the sounfavmw1 3 q k k9v9q/pgwor(85,scb/d td level (in dB) of a sound wave in air that corresponds to a displacement 9cgkf,tqwa d(8 k9vm/ pqvbr3s5w/o1 amplitude 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 10nuus ,pl*ql 100-Hz tone that has a 50-dBq un0ul, *sp1l sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soun/xxdwj lpnobi i;b ;:)mp 42p0d )wpx4/ 02b:m ;lixj pbi;podnlevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can actdfvjc fe ;//2commodate a huge range of sound levels. What is the ratio of high j/fc;vfd/2e test 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 440 Hz. Tht 68ydn9 rhhcwu6 1vv2eblv. 4/zms5k 7 xn4cce length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tenvcx9v7 l1k eu hn64zdw/8.vm5bhsr2 cyn64 tcsion must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental ane tr4-t s d-0xne*wkr2d first three audible ov-*wrst4ed0 - etkrn2xertones if 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 blowing across the top of y -sb 5p1h+71m1zem ojx+:p +yvtbpsuan empty soda bottle that is 18 cm deep, if you assumedbp7- p1 m5o1bzj1ehuypm : sx+ s+yv+t 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 phzl;ah),rq9:w:p-/pnmfq z qri4j. aipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be r-w: jfl)i qhz: rqaq/4ph9a,. znm;pthe range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a f(a f9 qeezx,k(requency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its kx,efz9q a( e(original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle C(l4nm l qti8:f (330 Hz). m tqf8n l(4i:l
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (*e6e+ 5gupih-u3z;li w-gpzlc5 ve ut vg/ o,6262 Hz) when /i-vv gpu5 g, u +ie*wlog;hce p6u-3zte6 zl5the 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 nv 8x -mmvi0r;at 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 should the hole be92vjd v+2 tmds that must be uncovered2v tdv9jdm 2+s 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 u 3x b1zolt/q,resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed u/l,z xob 3qt1pipe. ----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. f ,z :4bb0 ij zj;zkhlli)1t8dIt resonates at two successive harmonics of frequencies 27l8b0zfi:1hld;,i4)jk bt zzj 5 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 4wd)ifit pin 3rv++ ii+na8.. e q;yrb$^{\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-lonhq. -z71 rgfuug organ pipe fzruq1.uh7 g -at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal iselgmkqdnob -* yg,8k f1n8)8a approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information nk8bd-,q 8a)kyfo8*1 mg le ngin 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 wuz u+gk9ix8jxcmv6ah u ,a;jgcznxf4/ )1: )phen trying to adjust two strings, one of which is sohz+f p/ ,uxx1 )vjazca; u8ck)n: gmj9ugi4x6unding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) ando* 5 5bvvl0senz4me;pfr2: xc $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whilr3z49d th p wpa+ yhg+:n i-py05g1rlre 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 s rg n3 grhhty:r4pa-1d05zp9+pwy+liimultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tun03 xlrt+pe kk txi+:1ting fork and 9 beats/s when sounded 30 epxt+k:+ 1i tktrlxwith 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 freq+bpz;it45 auje6ar( e uency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.] e+it 4(;auz p56e barj   Hz

  How many beats will be heard if two identical flutes each try to plateafxaggsc ew.y 9 v4wt 9mooz+:49(29) dupuy middle C (262+9to9vcd )4 2gxfa9g(upte.9mzewswa 4:y ou Hz), 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 / d*h;62cat6 se6 d /bxolbxipB has 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 ths;p 6d cxoe/x662dl/tbi abh* e 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 speaker an t1kel3rvp*e8 d 3.50 m from the otp lt3e18*krve her.
(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 toh ae /,udk2r-e be 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 at 132 Hz, what must be the frequency of thedeka-e2u /h,r 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 mn*v i1;l go4ns.k(jxt in air. How many beats per second will be heard? (Assumnki1j(*lo. x4gvs;n te T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whennsb2xno 8 sh91e0a q:b at rest. What frequency do you sa8bbx9 2n0hq:1e osn 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 a fire eng40 ewf dcqy**.*f jnzpine whose siren emits at 1550 Hz moves at a speed of 32 m/sncz q*0p yw *fe.f4dj*
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movingtja1com -1g7v 8 ocaq* toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cotg j187v- ccaqa*m1olose? $f'_{source\,movine}$    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 4g2d07zfg-gj; s aoqq4la uc:with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.57:-qfq g4cg u4 aajd2o;gl 0sz Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50e/h(voe3lgd)m-4w g z xj0l6bew/k 5t.0 kHz and receives them returned from an object movin5tk gem 0e l63hxdob(/lg- wzjw e4)v/g directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w:8j,shyi,pa0x 7u 0o;f6dw 2i t1ce9bqnmu dvall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freq0fjd1b 6iy9,pxuqu2c0 ia m;edhsnt,8vw:7ouency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dcah;s9 z,; qt49hvokz oppler experiments, a tuba 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 railway station. What beat frequency was heard if the train car approached the statiokzsz c4 9v h,q9ta;h;on at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedy0xf v-zkig;6eyz-s ;ab0x1ss. Suppose the device emits sounxe;v sk;sb f--1 0y6zixgaz0yd at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrason)/vu 3iln0 oftt7smy 09nl+2lo 5ctlyic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound ,pj7xt+ 8qpqm+- 2-ia9mae xrj s0cysof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will8qp9q-ymcj+- i,pax2 a sjtx+m s7e 0r observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object mdaeu,it.dir0ar:- -mi9 tg b 3oving 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/s (a) What is ,u,d yo 9-96g5sadi-ejj dfsgthe angle the shock wave makes with the direction of the airplane’s motjds9,i-6 de5 s-ggo,uajydf 9ion?    $^{\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 planetr ,x2l5t vu.vfh,cwo 3 where the speed of sound is onlytv.,5 f ,cw2oux lrv3h 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 traveling5pxzo /fx/lspe,y s(- vro;3q 8500 m/s strikes the ocean. Determine the shock wave angle it produce p o,;-lqy/o3vf(x r/e5spzxss
(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 fd1o9oq06un8gl yp4.jm cn1c$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and se5a )w-+l 4 a o8cftwmli(lm)r4tlxj4be 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 distance of 2.0 km. See Fig.m rx4ill4 la+8 c t))-ow(f 5lmabt4jw 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 p9:ws6dct+nh device that sends 20,000-Hz sound pulses downward from 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 the minimum time hwts9p: 6cd+nbetween pulses (in fresh water)?    s

  Approximately how many octavee-x16h *fq. fl++vhb z -bndn3dkr8ig s are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipeszf(u4p o12i e symphony. It consists of many plastic pipes of various lengths, which are open on 1u4o e(zp2fis 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 t(tv/+yal:hudyj 3p p;4 v axe,he threshold of human hearing (0 dB). What will be the sound level of 1000 v;u,:jay4hp3+lev/ x d tp(a ysuch mosquitoes?    dB

  What is the resultant sound level whee9hgbxj8u) h7v ouny824m l3an an 82-dB sound and an 87-dB sound are heard si) u3e7y9hv8l xu8 nohbmja42gmultaneously?    dB

  The sound level 12.0 m from a loudspe,o 0ww xowmm1t 6d/i2n,cwkk2to9d)k aker, placed in the open, is 105 dB. What is the acoustic power 9 k 0tmdx1mco,w/tw2kw6 woo d )k2,nioutput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier isstq g(6 3 h(tz+ .;nujg1xbw* j8rk myob)pwr6 rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power orx;tg(j3 hu)8 bjgz( *ws k +opmw.yrn 6qb6t1utput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear+.h xh3/ sg0hk9onhks0q-cy b protective devices over their ears. Assume tha.h +xhk -n03 h /h0ckgyo9sqbst the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy w pe9tw9)fbzjs-ag-) stems, 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 rzg/ 37rbcg:jjh s/-fa 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 fundamqzqho :gi/9)ayagh2 ;a0tes- ental frequency of 440 Hz and a mass ;sghq9q z) oa0 -a:i/tae g2yhper 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 tub3fxii8d4 qlga r5z0h/wq- lgdj9e)d0e filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water 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 i d0j8darixlz9q5 dg-0/wi h gqfl4)e 3s the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mqe/j8:a9v b ecass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the vq9eb8a:e jc/tube?    $ \times10^{ 2}$ N

A highway overpass was o,fvq,w)lc, ,bptl il.bserved 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 in the bw*,kof lz/poa+ : *je500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the :lza,/j+o*wpe kbf o* person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the :cf.0t92 ohhb34zlf z/y lpzrstationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traz2cyhblp l: tzh0oz/34f fr.9 in?   m/s

  The frequency of a steam train whistz zink4vh; 5tlcu+21mle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assz+knicmz2l tuvh 451;ume constant velocity)?    m/s

  At a race track, you can estimate the speed of cav zy*x(8 .htjdobbq25rs 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) as it goes by on2*bybxd5hjq t.(8ov z the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produ/z:oy och 7+cuce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long h+o/ ccuz7:yois the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves u tl:0 x:w6jxlj*/ gdu)t mh3kpast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speak xx )g tjk:m6wllju/t3 duh*:0ers 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 aorta is normally about 0.32 m/s what bea(0 2ew fty4ctwt frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blc0e ytwf24(wtood 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 thk7 zqzddmprz7v-/+5xtqw 30 g e moth is flying toward the bat at speed 5 m/s The bat em 7q5w 3+mx trz-kvpzdzg/d70 qits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sgcw/2c glw ,dnwcx( 73ound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, a clgd,x(3c/2g wwnw c7nd 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 signals from on+ 8r, i(r lj:etkxdv4jky4h/z e Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones ihvk:8y4 j,te /4irr xklj(d +zs 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 cf+db :cj.vcd6rsk; y .8a-p rdan be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider dk: da.sb yc 6+cr;.-j8vdpfra 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, lgmo.++l wqy( qdor.h -ldd+,:hezh, called “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 rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm++r +dghh. mdyeolqlo .(-:, lhzqw,d-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 huma-q 3r,xobwjz:n ear at a frequency of about 1-ro x3q ,w:bjz000 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 obser2t xr bd8gp:4sver on the ground hears the sonic boom 1.5 min after the platbgrxs:dp842 ne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatiejzna8y5 dof-a4bmc ,(. 8fk 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