What is the evidence tyru;ov4v3 ls-hat sound travels as a wave?

What is the evidence that sound is a form of enej;slep0g i6r.j) . qh,dy8hydrgy?

Children sometimes playjxguc- -oz 7/y with a homemade “telephone” 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 yz -/ojx-uc7g the sound wave travels from one cup to the other.

When a sound wave passes fc lkq)(l .i8emrom air into water, do you expect the frequency or wavelength to changel(. )cl8 kmiqe?

What evidence can you g lek ss,)5y(7no4yghma ;x 2ruive that the speed of sound in air does not depend significantly on 4r7nysh;s,)a(kg2 u l 5xmeoyfrequency?

The voice of a person who has inhaled helium sounds very high-pitched. i;g7*r r i jia5(xfiv k7ve63f,a1 fvq-qsj-o Why?

How will the air temperature in a room affect the pitchku .5omid78tv77 ye./p8i( 5 tdxv evj;alvth of organ pipes?

Explain how a tube might be used vdtcz/ uvdo4+l u+ 2a:as a filter to reduce the amplitude of sounds in various frequency c uv/l+ +d:2ov zuat4dranges. (An example is a car muffler.)

Why are the frets on a guitar (F *px *vkigc90t9pzfe) ig. 12–30) spaced closer together as you move up the fingerbifkc0vp)gte**z9 9xp oard toward the bridge?

A noisy truck approaches you from behind a buildiv* y8w,imxzp )7xrp(86gy-pfy:khe l ng. Initially you hear it but cannot see it. When it emerges and you do see it, its so8z6w)*:pyhlxpmx yy8e v irpg-f7( ,kund 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 “interference in space,” whereas beatf3pw4 z(n 1ssox4gp zg12.ad7 o uzqn2s can be said to be due4zupzp1 og2s2n awgnqfs7 x4z13 d. o( to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouh0*ik vc hrj93ld the points D and C (where destructive and constructive interference occur) move farther apart or closer togetherhkhv039j*ric ?

Traditional methods of przst 2 rk0i)4nwotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instentr)i4w0szk2 ad, 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.nbkb 4f-4,(wjd*h l iiz.+*prhdd*e e Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, zrp+h*d,f nlk-b(**h w4didje 4e b .ias 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 p-at k/(r r0h9roh vn8if the source and observer move in the same direction, with80p rrhtkr vnoh(/a -9 the same velocity? Explain.

If a wind is blowing, w+c;)li f. isqgill this alter the frequency of the sound heard by a person at rest with resis; .cql+g )fipect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positf+2 rf)(yjr s09bd3cn drpgm9ions of a child in motion on a swing. A monitor is blowin0p fnj9+ cd)dsbyr3mg (rfr29 g 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 lake by listening for the ec)lp 3c,z .0diwq2(dwgamk1 kd87iu ywho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting.1d0qip wmy .cg38 d u(k7d,w 2lk)izaw Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bw9f s)lm9 n-4,dmompeelow 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 pointmpm el,d ows9n9-m)4 f? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air/ 6m v/xxmbfj) k/kf 7/ry4set 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 o76m) /anm eet tn4sje (*tawv2of,k. is drifting just above a school 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 . o ( e7k4mnevntat2 aeof),j/w*mts6the 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 wwpcn 6/f:j w,ihen striking the water below is heard 3.5 s later. 6njiw:pcw ,f /How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tazwpjs7 ;3g g2 zhq(2lhe 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 1.1 s apart. How far away did the impact occur7 hawqs2zz 2pg (l3g;j? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erxc; z 2c9qreg*ror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning s9g*r xc2 ezc;qtrike 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 kgjctp89r; ho,l7j5cof 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 whoxjsh2(, )hj ajse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound l6g6tc r wuyf-8evel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hw 6g6-f8 uctyrint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wib;s:gvqtk e6- th four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pers6tqkvs-ge :;b on 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 58 dB, whereas for fa9mvxk d i60t(g pbg x7k( y-sztkg/)19mr,ra CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? rak1xgdkgmk-(0fpmzsbvxi/ t t 69(,r)gy 9758 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output;eurzcad a):: of sound from a person speaking in normal conversation. Use Table 12–2z::;a acd eu)r. 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 akd5)t m bqznsr ;3r(zjh:o *(cn 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 250 W, while the more modest amplifier ;gs*:l ykj xj+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 conj;kjslx y*+g: nected 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 in froy+a a/f 9drm6dnt of a loudspeaker on ay9 damd+/ f6rthe 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 dif e c+b k(dr1(unyqha0:ference in sound level of 2.0 dB. What is the ratio o(rca1 kuney+ d0(:b qhf the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound waxgh2 ++ws, jb pzj/ g a601lsco+6hwvfve is tripled, (a) by what factor will the intensity increase? In+2h,/sgo bc z6wj j+afvp+0l6w1 xsghcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have es n):nwo -905zodnafcqual displacement amplitudes, but one has twice the frequency of tdcn9:wna-z fs )0 no5ohe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a souq8 ao3buq :6kz :hrftfprdw+ +562ozj nd wave in air that corresponds to a displacement amplitude of vibrz 6 fwt+f :uhr3p8 obzoqr+d6:a j2qk5ating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w z: b -8xw1a( ;0lhj)csgjvoaphat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sewcp0 l g s a-jaohjz1:x(v;)8be Fig. 12–6.)    dB

What are the lowest and highest frequencies thathic2kegz16 +b an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)kzcig6e1 bh2 +

  Your auditory system can accommodate a huge 1my gb6s .hns6range of sound levels. What is the rn6s16m.sg h ybatio 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 ow5g,ai* be .r440 Hz. The length of the vibrating portion 5o.ei*abr,w g 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 fuo 51kh:*eyow6n; -;;kai4ffokr,uz amktm + undamental and first three audible ovei w5maeufkof1 hu rt6 ; :4o;okk*y;m+z-n,kartones 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 exp / rp.bscu+g3dect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wrsb. pu3c+ gd/as a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning fw4. +y k5zt*pk nr;plthe range of human hearing (20 Hz to 20 kHz), what wouldnwkz p rpl*54k.+y;ft 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. Whk.u2 n+y80 eaff(fg4/jwmvwe8f wjv -at will be its fundamental frequency if it is fingered at a length of onl2wm e8 g.av -4f80f /ve+ynjf wukfjw(y 60% of its original length?   Hz

  An unfingered guitar string is 0 0tfgja,hkqu 72f. c9l.73 m long and is tuned to play E above middle C (3 l0q, g9k f7ucat.j2fh30 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 mq 5bvm8rkc-cs4j,n7 c iddle C (262 Hz) when the tebk5 m8cv csr qncj7-,4mperature 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 ugfk5k*7 gt7(meze 7gat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthp gponqslsw,7,,o)2( z -txr*z ky/lnaiece of the flute in Example 12–10 should the hole be that must be uncov grl )l,ss2 ,, xqwtn(poy kn/za*o7z-ered 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 resoaf45i q2bne2vkm(n( znate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betweenm ((qzikn na2ev45b f2. (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 long is open at both ends. It resonates at twowp8 4v ,cee5ac;lfy4y successive harmonics of frequencivae4cp8, cfwle4y ;5yes 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 ug4q/es *.pcp $^{\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 au f01 /1g8mpeuio*ii dldible range for a 2.14-m-long organ pipe i eo pig8*1lui/0d f1mat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxl2sk bulz 60pbue4,z,imately 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 c u,b,2 6z k4pb0ulzlseanal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s k :lgd0hd.:rryo5 h q5when trying to adjust two strings, one of which is sounding 440 Hz. How far off in fredq5rh. l:r:g 5k0hy doquency is the other string? ±    Hz

  What is the beat frequou ck-f mzj oc ,/az05(t:fyi:ency 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 (b1v/kjo24 ep lrrand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequ 2krj14ev /ploency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string producesx8ybh tnsp, n+q3p(9/f 0xhmz 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when soundh fhy8zxpp3( sb,+xtnn0/9 qmed with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned toe* )z kpvh)6cl5xrox ul5d 8i* the same frequency, 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)zurh 5vd)6xke8ll*o xp*5 ic–13.]    Hz

  How many beats will be heard if two i.wn:,ub0oc yk; 3zhd adentical flutes each try to play middle C (262 Hz), but one is:zach 03,bn k.yowd ;u at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44bh :,4cd y: wo8-ctkqm1 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. W k tcm4c:b dwh-o,8:yqhen B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and 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 spe9z mbhix1y/) jujmexvr6+4 4-c,f o1kk f9 vqeaker and 3.50 m from tq -9m fx4j/rfzhoe9 1 x4+kiyuvb16c ,kvj )mehe 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 sup :t.7hx)-pmnv am.1b qh jx8qoposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a)h81.mhq) boq:-jxnma7 p t. vx 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 g o8hvf(-6l:ql)5zfptpb n,km and 2.76 m in air. How many beats per secovzl:lf()pop5q8n,kh6- f bgt nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of 9t75zi/hy 6m +8o 9dqo4.s xfgqk buoya certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/yq i tzq.o5omkyu+f7/dgxh 6 b8 o99s4s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a f/wsogyrd57tl .f 9se)jv, q /sire engine whose siren emits at 1550 Hz moves at a speed of ./je so d9wy)/srtf,vs5q gl7 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 toward you at ; a+2b0eeubnb 8r,lqm15 m/s versus you moving toward it at 15 m/s Are the two frequencies exa+beq 8reb bmn0;2la,u ctly 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 on-). igvvxy+a p, qrvk*,bq8same single frequency horn. When one is at rest and the other is moving tv8o vayxik)rbqnvq p, , +-.*goward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50nx5 :tgj+a.aazml 8.qn, 7 :ljylwm1t.0 kHz and receives them return mtaxl 8yt q.lajwz+ g:,jmal157n: .ned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall ag 15kjvdpji 4;;lhw(d d9;erat a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequenkjpj h l9ad;r 5ei1gv4 ;;dd(wcy 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 playa;q6,w*mfg/ ew 2sgdled on a moving flat train car at a frequency of 75 Hz, anw6fg/*dqw2 leam s,;gd a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses g(kk7,mr n4ft f2ruq0f .l i6vultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in lff7 umkn k0.6rtv2l,gq4fr (iarge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of vl-fs; u)fr pfpn.i2( 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 . ioe86w 5cvgnthe wind velocity is 12 m/s from the north, what frequency will5e86 .iog vcnw 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 moving oqj j41ecv;qw0n 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 xhh6 +brl d0ds,z( wa+Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle w ahs6+xz, drlhb(+d 0the shock wave makes 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 speed of soun2,c4dk 08qstu4 .qc daex ;gspd is o x,; dt42sk da8uccq0.4eqgps nly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determ+9v cc 2rli hmvoh34b5ine the shock wave angle it producmrlv+cc3h 2 59ovh b4ies
(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 b5: y uavzzzg 0g(od-7$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly yon1rk+ vj(*e3 jpp5pw.. pwr 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 kmw rj ep5kj1*3.rw.p+ (oypnpv. 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 qbbj kfyuu1n:0.x+d.sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it ix1fd: +q..jyb ukbun 0s designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there qigd7ba, fxd-k-tk-*in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony:(gowa reu0ezpi qn2m -mb(:a 2g9ra-. It consists of many plastic pipes of various lengths, which are open on both ends. o u g-wagei-a(r:q r:az29nm2( p0em b
(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 persu oq f/kyiy(am:;i.94om py* non makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 10 q .m:ufn4i ;kam /oypyy(*i9o00 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB st5oxu191ls)0 q qic,l/tkzdi ound are heard simultaneouslyisq tk u)50tx z,lc9idoq/11l ?    dB

  The sound level 12.0 exrtxbe g ;;84m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output ;xx8gteb re4; (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outs;;yury 81bonf3v9 wcput at 1000 Hz. The power output drops by 10 dB f ;nr;wo1v by8 yscu39at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weaouszk ;1 /nbs8r 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 effective radius of 2.0 cm. What would be the ponoszus8 b;1k/wer intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the0jmqbokz 4; (yn gp:(v 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 tozk( +ai;l 8ssg 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 be8hgird. 3(sk76j 885 mjnv0uyv it, jww:fltntween fixed points with a fundamental frequency of 440 Hz hi8j:6wvj(0f nvtk, .538t uigmd r j8 ws7lnyand 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 open tube loa, 5 axv1d-ma;2y nlfilled 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 a,dy;a om a l2xv-1nl50.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string ofc v.rsxa/q9gri-d (u* mass 2.10 g is near a tube that is open at one end and also 75 cm long. How(-cuix / *srq v9adgr. much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obser,b,e ut87hef hn1 7skqved 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 500–1000-Hz range coming from two sources. T; ,fbp1nc6 . s6rzhu (7xzvtyghe 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 nztr sz7fyb(1 u;hx66.cgv,pother. What is the frequency of the sound?   Hz

  Two trains emit 424-Hzwx ny:td ,bk,b+6udhz (bj6p8 whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other traxy (6pub+d bbh: t,,jn8zk 6dwin approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it f k/1zv6 gfhg6approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velofk z h6v/ggf16city)?    m/s

  At a race track, you can estimate the speed of cars9/ j2avfk80es;r mund5f upfs+xd 1f4 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 (frequencfv4a0f1f s/rm8 dxdue+ p;usk2f5 j9 ny halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipeslw c/ka5i6.wx :y5uve, sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other w6k wcl5.v:ay/5i exu?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past i *l7 eggbhv5*o4a9h4gmuxx: 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 from the position A, in front of the g9h: u**x7g4xbo5hmivgl4ea 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 (r4mp kag .yem,6bnqwf:8 hi1about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and r6 :,ym aq fw8 .n(mprikhb4ge1eflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth .3lrzijtfp:4k 6 jz /wat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The 4j:wzr6lp.tfj/ z k 3ibat 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 moth?    kHz

  A bat emits a series of high1nj.,w:gxcu-a3 cgx y frequency sound 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,a1g -c:x yc.wjung3x chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to s,qjh/bq 7km f*jqhv, :end 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 play,,b7j/fqvm : qkjq *hhed 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 bib8l,ttlkd:6 6va c+ ce compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roomctall it:k6d v6c8 ,+b.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrationdne*pa 1 9aen9 s:0yhd, 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-long rndp1da :enh90se* y a9od,
(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 ,ui. alpow)*)t-z ltuwqm :.pus a9/ xthreshold of hearing for the human ear at a frequency of about 1000 Hz is s:qupm z)/u9 .iw*l-u .wo )pa,atxt l$I_0$ = $1 \times10^{12 } W / m^2$ 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 atpkxh0h -k:,cc76x ymv Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s h h:60,cm7vxpyk- xkcaltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15hlv*91w :7le 9x-,, yqqg nvfmg dkyj5 $^{\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