What is the evidence tn4cjok2hbp 3 c, e/)ay7fq,+6iwapwlhat sound travels as a wave?

What is the evidence that soundzyb3f. l;kf8 f is a form of energy?

Children sometimes play with a homemade “tdqu mb2 p7z; e l(rzen3y:;i5belephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels m3zpe uibl;(:ze;dyb2nr57q from one cup to the other.

When a sound wave passeurxja nm91f6uc0o 3db:,k f 1gs from air into water, do you expect the frequency or wavelength to change?kux :r1mnfjabfdu6c90o1 3, g

What evidence can you give that th v q/1opj2 5w2y(sqj fb 6m)31bbjaqbfe speed of sound in air does not depend significantly on frequency? fqbbvmj21qybw/jp) f1b5 qj3a o(62s

The voice of a person who has inhaled helium sounds very high-pitched.( tuek)6x1 5 kp7wd.z3 zglhsonikk6. Why?

How will the air temperature in a room 9j;et8mnb.ry* y* a iiaffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun(a oy7c 6rnvjuw6cbzvw + 4xih5vj)2 1ds in various frequency ranges.bcrn z4va)wvv2 +(1h o6x7yc 5jwjui 6 (An example is a car muffler.)

Why are the frets on a gjm+ip; it t8kz5g6jl* uitar (Fig. 12–30) spaced closer together as you move up the fingerboard tok5m68tj l*git zj;p+iward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but :rqusp.fj j5g;5tu0ui 0ucx)cannot see it. When it emerges and you do see it, its sound is suddenly “brgrstju:5 u.u iqj0c5u)0xf; pighter” — 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 “interferep55-p7p:li-0-ovegue/ hw afk e;dg j nce in space,” whereas beats can be said to be due to “interfe-5/d pi0:javl-e p7ug- fegek ;p5whorence in time.” Explain.

In Fig. 12–16, if the frequency oe.)n 6ckrb+* d2b jfgjf the speakers were lowered, would the points D and C (where destructive and constructive i )rk db62bgje c*.n+fjnterference occur) move farther apart or closer together?

Traditional methods of protecting the hearil9ceo3twi:2 w, 2 8;vwxvd pjmng of people who work in areas with very high noise levels have consisted maivc3t29 2w;o:mw,ex8 l vdw jpinly 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 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 cayu09sj: glkfu q7m)ti (bf 2(ln be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compo lki(:u0(9 uqbfs jt )ymgf2l7nent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sob 5o/e 8aqdg8aurce and observer move in the same direction, with the same velocity 8a8o/a5q bgde? Explain.

If a wind is blowing,zr56.c9dn,yts 1jr q l will this alter the frequency of the sound heard by a person at rest with respectrrd1 .,9j ct6yl5sqnz to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitw5cjyq)f d,/dpp+ge2or q+fg,2/)c 5ed wyjppdis blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a ik1uyz vbu;y:z- p,c;lake by listening for the echo of her shout reflected by a cliff at the far end of k ypc:;i;vy ,z1- ubzuthe lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below p*lt:+p/qn :pw q) yaothe 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 sl:qy wp:*potp q+ /n)aeawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aiq8*xig dr69p n-reqze t1z26zr 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 s+ bqz12b 7x:gn bie-owchool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.gi2+beq bz-bo: n7 w1x0 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 o)t66w (cw8/ fd3uc3lmdhyn fzf a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff?wm6hcddfcl f/yu3)( zt63 nw 8    m

  A person, with his ear to th o8.ntn y. a)7iuew hpmn.,u3fe ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the aiuw7 i8yf,.n)m .u p at.nhn3oer and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percenm)s-8 s2im vpp+ otjo1t error made over one mile of distance by the “5-second rule” for 2v-o 1tp+)o js8mp msiestimating 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 soulzdm84 r; pj6end 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 whp 84ueda0j6m4 . l(f79:gdlkl r uojszose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when f) hz2wu ih2 s+4ykwt,wired simultaneously at a certain place, what will be th2ww)2 y4,shhw tu zk+ie sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distau8.ek.cov olte32h 8-fnw0ur 5eb* iynce from an airplane with four equally noisy jet en k*itcuue-o ef .b.n8hr5w320lyov 8egines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said 5jnvc9/svq*zpnqmnulef6nj ,a +-)0to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 9f9pzvne/va5n*ncqs,un + qj)0m- j l65 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 output of sound from a persoj.*hmc:;ir gyn speaking in normal conversation. Use Table 12–2. Assume the sound sprearm* h.icy: g;jds 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 s7jn*hmgx +q 7atrikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at dw).r m n7hul ycz3;a2250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m frz.lhw3dc7r2n)ya ;muom a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m i9kg d9:7zfuhv n front of a loudspeaker uzv 7g:9khdf 9on 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 differenc cop)0i7oac. ge in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds w)o7o 0c.gap ichose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intece,er1 r 14jjqnsitycr 1jqe, jer41 increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemeng)ad;cwd)1 .q cuj7tct amplitudes, but one has twice the frequency of the other. Whatw.)dg1qa);dj7 cctcu is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresp:yi gb7y:euc6)v (xu bonds to a dg6by:: yvxb(iuu 7) ecisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wha no*qm q tp9jfh3ob:ok97: 7ght sound level to seem as loud as a 100-Hz tone that has a 50-dB pk3gomqqh9 jh:: to779b* fnosound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear dot*o76 t/tcs eygt*:can detect when the sound level is t/*o7c tseot6*dty:g 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hugeagv0d preb2 iz5/ yg 8; aht)4*4pizst range of sound levels. What is the rati tpd*2 r4zz)yig 8hp/0g 4a;t eab5viso 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 off *odb62ft6dfg - dd.l 440 Hz. The length of the vibrating portion is 32 cm, and id*d-fg bdd6 6f.to 2lft 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 fundam2 1 t8/ev0ps61y ,dozuh tfirsental and first three audible overtones if the 2ez1yd o, st ip108/htvusfr6 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 expe vz7lud nd9;a 5ijfb,)ct from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tb59d jn,z7 fl;) iauvdube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range (i b ot0xd70asr5 +nt90 -yzy v.hsiiuof human hearing (20 Hz to 20 kHz), wha.uia+v ss75yrht(xiy d 0-bto 0iz09n t 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 d ab7s,os(c32eby 5( iwaqc+.f5b etiits third harmonic. What will be its fundamental frequency if it is fingered at asbbe7fb(35yw5ce ai ( c +2dotaq.i,s length of only 60% of its original length?   Hz

  An unfingered guitarhd9klh5qmyizvz1 :,k1)hj e8zjv/6r string is 0.73 m long and is tuned to play E above middle C (33iz/1mkj l9hzqd jzk)v 6rh :1 hey,8v50 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 middle C (262 Hz) k)88wbxqj h,4h wigh *when the temperature *h8ibhx)8k hg ,wwqj4is 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 a6 ;3 4wbcthhlat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute inaa,i:p:ccfyj 0w34dv0gdid1y crc6 s(w+3bv Example 12–10 should the hole be that must be uncovered to psa: ,0gvjrav34: pcdcd( cd6c1b3 y+fy w0wiilay 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 2*.sqvnu 6)dm1 1umzyb;s +cce 64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open oc1vdqczs) .u6;1sume n b+m*yr 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 rlaa:0 wa9 zm8sesonates at two successive harmonics wzm:l8 aaas9 0of frequencies 275 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 3l; ,mxu/f ybd$^{\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 audilfdpzya*p 0ox+d:2a9 ble range for a 2.14-m-long organ pixp aa 20: yfo9zdl*pd+pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately*o s-f*;8 .cvrcn22sa g2;ovkqwdrwk 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 in the graph of a*k; 2*.;r 8fgccv2s w-qk vondrsw2o Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s(p2f juam8txvj xsfaz -/, x97 when trying to adjust two strings, one of which is sounding 440 Hz. How far suxtv x-29pj8(/fafz am7,j x off in frequency is the other string? ±    Hz

  What is the beat frequency2e fo ;-8naw0m50 )axi1so ielrt,ocb 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 operates at 23.5 kHz, while another (brand X) operates at8l p3v wphbwv8tz +k:u3vn -v+ an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating-:+zhv3pukbv88nvl w wv+t3 p frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork andqn.o v//5pinw(xmx9;nmt t;q 9 beats/s when sounded with a 355-Hz tuning fork. What n.xotx/9/v ;qm5 n(q ptn;iw mis the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freque4//sdb,o sezo6c -n b,h myp4hncy, 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 togethc6 m4nh bs/y s, boz4oh/pe-,der? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two 3.n(hamggzyw6f w 9 n4i32nhe identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the oz hf 39wnh (6eyigw.mg23 n4anther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whekdfmwj *pm; k0 /,exg0n A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency wkpmefk;x,/d 0 gj0*mis 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 apa(a du ju.rr;yb4 4doe6rt. A person stands 3.00 m from one speaker and 3.50 m from th (rr; uj6doa.db4 4uyee 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 to9f uo( j8tti /xw4g)hears threetj(/ox fito 4 uwt8)g9 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 of wavelengths 2.64 m and oj 0tz6zr*zdkbg*kwh1a -t;02.76 m in air. How many beats per second wib * z 0ra-htgj0dzt;*o61kwzk ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqo1seycf xn8,7uency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 cf7 ne18os,yxm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose x* p8 )sir64 kzcloggwi5bqi6y;tced.z 1 x+5 siren emits at 1550 Hz moves at a speed of.k 5 lgc4)sxi668wtc*rdzi; yoz5 xgpi+b1 q e 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving t,)t rm q38 l+n9yzn9uwyl5hhtoward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequlqzw uy nyr8)9+nh 9tm5ht,3lencies 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 x5k2gwfc;byyya;1 uy 7zn l85 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 5.5 Hz. What is the frequency the horns emit? Aszg2yl;5nk8f7byya ux w5y1;c sume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out e1z+6 k(h oexkultrasonic 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 receiveh(x kek1zo e+6d sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a )fpj mh 3eh/vm(f4w t)wall 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 i the)f3(4pw j )mv/mhfn the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movit79+ h29tq7w ii;c i0hl kamvnng 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.2 0 ma+ c7t;lhwiqi7kt hi99vn 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 wah d-*bi9td80*vpbk d xves 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 blo *kb8*vdhi bdtx-d9 0pod is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi7t ly vqo3zs)i8xu x:,ng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the x uhrl ipr-/6*wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at resxr -pul/*ihr6t,
(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 mov8jw yqv-si,3c;o/u3rzhqbgvdl m64 4ing 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 hjl(rjja. qe r)3077q 8i kydt:dz6tb (a) What is the angle the shock wave m7jthj dr07e(z )r .3:bjq qldaiy8t k6akes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speet85kkjx h2 *xud of sound is only x kxtk5*u82hjabout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling gi6ab i x5)-nfg dl* zc7k:/vl8500 m/s strikes the ocean. Determine the shock wave angle it5i:gi a*nc/lxb-gd6 7)k zfvl produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle izo1y/pl: t6 p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exau .* xc(a tpw.iy(y0pcgtp7c5 ctly 1.5 km above the ground flying faster than t5(gyyu c wc0p.t7*ipc.( paxthe speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. 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 so3kj 2bhivg,8lnar 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 jgi8lk v3h2b,designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the8pz12ik6lkzdxk (qi vr .-.6j 1(ciwyki6mw o human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consist3yr f )plejj).hd- 9qas of many plastic pipes oyh r9lq-)efj j)3ad .pf 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 lpy9w .x2:xp m op,fi09jrw2ta sound close to the threshold of human hearing (0 dB). What will xw woyjl0tp:p2f2xr .9m9p i ,be the sound level of 1000 such mosquitoes?    dB

  What is the resultant go6 8fyh2ege+ sound level when an 82-dB sound and an 87-dB sound are heard simulta+o2gh 8e6egf yneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What x096m14ev d26hb tcv5 waxq bxis the acoustic power output (W) of the speaker, assuming it radiates equally in all q9xdh 2 b twea4x05xb6m1 cvv6directions?    W

  A stereo amplifier is rated at 150 W out9:rbefln s;pm7 ms1; i t5i1zvput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output vn b7;ssflr1:mz9tm1i;5i pe in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over xj8l ho(xl9 i7i2a1we their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that t2eiih x wl7(1j98xolahe 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 communic lbarvhgd6 aw-(+2rxsn7e9rn5qx 5o. ations 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 fre jc;p0 qijhd0iatr8;/quency 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 vionms -r1o..esn i5t3ovlin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and3s5mn tsvr1 -.in.o eo 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 vertical oay e d.th)i)q6vm g/a3pen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly.a )a y) m3qthie.dv6/g As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one*s:no.a wmzx )+zbiml+f *.dl+ bcr.c end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in itf b ml:bccd.w*izrox nmzs+.+. *al+)s fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as oneuhx wq35z7q* mu-1f (aqnwm,t 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 1zuwg-i8, q p28hzsfz range coming from two sources. The fqh8iuz,zz2s 8-pgw1sound 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 is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One tr)oo ch0 rjd/wuha574z d i--nvl ,vb5tain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approac n4rdh7-il,waov5t/d)hv ub -j5o0zches. What is the speed of the moving train?   m/s

  The frequency of a steam tra, bql(n(x pisr:++ephin whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was l+exsq:(+n rhp(b,ip the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening tob+e cw-k:;gun .td,gn the diffe;dt-c.:g+nbwe ng ,ku rence in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Th8/owgl1 /szhe dbh 5q7e shorter one is 2.40 m long. How long is the othsl e/hgwzohbd1 / 5q87er?    m

Two loudspeakers are at ozbj c/ p ;nqs wsp)xi88ix17f7pposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens fromfw;zxqb7/1sj p )8iinsx78 p c 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 i +.(7yz 2svcf7xwwu6;f otadk6fa; dk gs 4u8xn 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 blood c(ows77s x.y+dafakuw2uczt4; gv6f; 8 k6dx fells? 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 w em9rc.actyw 1k81 oq-hile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of acey .to8r kc19- w1qm51.35 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 soy q 2)nrg6u*w/vxk z-mund pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, 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? vkuyw6q*n/x -z2 gm)r   m

The “alpenhorn” (Figdj8 4b(*vldb sor :.xz. 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptsb. xljrd: b(zd8 4ov*ible 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 listening can be compromised by the presence of standavkyi.h+ g;+ eing 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. Calcueh+y .;+agv kilate 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,” involv0h5y1 yxrv8v4 n pri:xes a long, slender aluminum rod held in the hand near h5 r 4xrv8:npvy10xyithe 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-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 freq/q,jzr;8hkz2/ zzi ty mla sd)* 67ytluency of about 1000 Hz izl *a2)l/i zm yy,sk6zt7d ;z8rqh/ tjs $I_0$ = $1 \times10^{12 } W / m^2$ 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 hears the sonic boo wpms0t1 ra4khku 7yq- 11(hxhi-:itlm 1.5 min after the plane p m1 i-l4ai ts tur1w0h7 py(x:khqkh1-asses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1 9yla35jlttmm-k 1 5qr5 $^{\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