What is the evidence that sound t 8 e:am fkdbe,)yl74qmravels as a wave?

What is the evidence that zhr: jl8rli 9 .jw;h5lsound is a form of energy?

Children sometimes play with a homemade f1xf:v)+ *zj gamj /i8sxjn*x “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into jz+1jgjf 8*s:xfmiv x/x) an*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 yx *nq33fy q /aqksr*il+6 k:coou expect the frequency or wavelengtsf+3q3iqk or l */cx6 n*yaqk:h to change?

What evidence can you give that the speed of sound in air does not depen ;xm0rz q3 /fswoq,u4cy0j p.i1; dqhrd significantly on frequency 13xq.fq 040cy,ozr;dmsphu wj i;r/q?

The voice of a person who has inhaled helium sounds very high-pj2y h4 /..k prrcefr2bitched. Why?

How will the air temperature in a room affecty9wt ,.d7aqpa 7x tg4g the pitch of organ pipes?

Explain how a tube might b4)luer pwd 0iq2i8ff 8e used as a filter to reduce the amplitude of sounds in various frequency u lre 0w)f84i ipq28fdranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethermz/ nn + egz:0ytlv74h as you move up the fingerboard toward the l y4e+vg:n07n/mhztz bridge?

A noisy truck approaches you from behind a building. Initially you hear it b8d./mwchuk,.6ksjklbhbb y2 :8r u7 out cannot see it. When it emerges and you do see it, its sku/ldwhh2 6o:c8 8bs.umb jkb,7 . yrkound 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 b ;d a:jt3euf 0g3qz5k8in 4gahua /dg6eats can be said to be due to “interference in zg58 3du3a 6tu ; e fq/4kah:gingjad0time.” Explain.

In Fig. 12–16, if the frequency of the sp8z,7u tf:x d+f 4xbgzxqmr 9i(,ov,exeakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart oqbz9rf8(xux f,:ozg7+ x, idx v4t e,mr closer together?

Traditional methods of protecting the he*4dp4- -vw7 t8b vm mq -ixiyeltmhe.2aring of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sounm vi2 vmbe-- xp4t mdlq.7t*i-8w ye4hd levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eachf/2:)hjvu6cj;ft xqy;wo taej 57 s(y wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fi:2;s 5 t7fj(y)tcve;wquahjfj o/6yxg. 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 shin).sn/ dt hgce 8;jc,de+ns17i -x8l6qmcdaq ft if the source and observer move in the same direction, with the sq/q;m1n eh )-ans+ ,c. st 78cjnixdgec 68lddame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hearda)qczam4vsny-d78 7e m-n4g-lu +odh by a pers4sandq)8mzd-74-chauo ylg7me+v-n on at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a sw sell(rrp 4u2zd ;u)4kl 3(howing. A monitor is 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 reaso(l;rs euz(4 owlp4 hl ukr)2d3ning.

  A hiker determines the length of a lake by li btmlk6d3;ro ki-jy0 0stening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estik0loy kbdi0r6 j3; t-mmate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side oo. baus2cldr 4uxfw)03.l4s l f his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depthoscrw .4a.us3fxb024 d lllu).    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air 4j1 3)bdhkg1zkn1yk w 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 of tunagx+r 3jm:xq8+)mxrwi on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elaps: xmw8jrgrqi+m3 +xx) es before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliffjvtm,+n(sqh;i 92 rcgcx+ zdv*r f*v8. The splash it makes when striking the water below is he cf*c *2xmrv;zdh+tsrvgi( q v9n,j+8ard 3.5 s later. How high is the cliff?    m

  A person, with his ear txcxccj(j rm3s xn) xln1)) uwfa23)6wo the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and rjlc2)a)su wx()j x3 61mn3wxnxc) fcthe 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 percent error made over one mile of distan17s .9s kfxeavce by the “5-second rule” for estimating the distance from a lightning stx9va.7k sfse1 rike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s3cqz d9 +pzh: 1vfwqb,ound 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 naj9i mbzfh)9* 1a))tm -flat sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelz3 aio( sp )ewei58b6q of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dbw8(63z 5s eaqp)oiieB’s.]    dB

  A person standing a certain distance from an airplane with four equal ds,t 2++xb35 uejnvbv)m3by qly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person expxnsbt3qmjd bv ,u+23ye)bv5+ erience 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 raty s3kesh 01( z eqi,ix:4wu0ghio of 58 dB, whereas for a CD play,e3 g 4 iqh0xhuz(kisw1e:0sy er it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perqy4ci h*mome:o+/x rg1m/ .li son speaking in normal conversation. Use Table 12–2. Asx:ch lrm/yoom 1i mi4eg+.*q/sume 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 earhe8brd(eb tw c-l5m x .nwmosx-;-16hdrum 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 f my.l a8o2-m(i8eomj vn2b: brated at 250 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 from a loudspeaker connected in turn to eachvjm of8bl22ye8.m (obm -ain: 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 dow ,bkr53vk kmb581b: ,xpjiq4 h-kxsB when placed 2.8 m in front of a l5v x: b,1kj4q,-x35bph ko8wkir sbmkoudspeaker 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 difference in sound level of 2.0 dB. What ism.o n7rzy0a4 c thenrc4. a 0y7omz ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a fs:yrfg y,shc 3zm8*+sound wave is tripled, (a) by what factor will the intensity increase? Increase y *gh,c8 s: zf+3fmrsyby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hasa ,ss::ja5uxd twice the frequency of the other. What is the xsaj,:asd: 5u ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air t(dta,s(/qpb o/3m. m5s g)bc ;kh feklhat corresponds to a displacement amplitude of vibrating airm ( bf.)o/ah gdkc3/;e5lsbpm kq(,ts molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that rm oa-6mbt/(w 9mf)rghas a 50-dB sound level? (See Fgo rtbm/m6 wr -)m(f9aig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whek(5lm4d,z p d:iklab4 n the sound level is 30 dB? (Seela ,kd5 dizmk4 4p(bl: Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thyoj9rz/g +s 13i6ksmce ratio of highest to lowest intensi1/isk 6o g cz3jrms+y9ty 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 v52az14vo g q5s9d hbtfundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Undehv5 g2vs59o 1qtbad4z r what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible o(ifmwsxki9:8o1k s( tvertones if the pipeskik8ftx9os m( i( :1w 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 abf o3z raw)6(*udrp, ecross the top of an e)a6 w, rbfdru3*ezpo (mpty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes 9 (vwft-cf8 (to8wmvgspanning the range of human h 8w9 (8tg-cmw(vfotfv earing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz ac zn.mius *d/aq2,ea;s its third harmonic. What will be its fundamental frequency if it is fingered at a length of onlca/2u zan mi, .esq*d;y 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is td*u a4v0tuh0 /pwa z/kuned to play E above middle C z/vt au0kwahp 40/du*(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whend+3 )0zmz v 9nw)rclmv the temperature z+l3vc9 z ))m0nwvmd ris 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 aqgfol8 a 8k3)dz e4zg+t 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 h9hp 4p ki8oes9ole be that mu99h p4s piok8est be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, anzfm qqunzj8cj1r7)l9y/t mt(wt 4 15pd 616 Hz, but not at any other fmw9 qq8mltu1z5j /4 )fpntyr1 z cj7(trequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tub4i )- ooys/ salr-98gn y// yodbu-ly ihpp*m4e 1.80 m long is open at both ends. It resonates at two successive harmoni-y 8doysyl y9 )*o-l4p-au/hmrp ni/iog/ s4b cs of 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 p: t gsjips41p364uax $^{\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.erc8 ap9 /.xoc14-m-long organ pipe at 2r.pcc oax/e8 90 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. le (7 (oqzmqn(.gbayg7sy9q3 It is open to the outside and is closed at the other end by the eardrum. Estimatebzag77q(( myeq3ysg . 9n(oql 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 Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying *fp;im 6968tpvhoaex to adjust two strings, one of which is soumav8tpf i*p;ox 669hending 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262d .jj alfsm /5d f.ee+1hdox+( 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 12o svuc/ w. j2zlqffnyc//7aX) 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 simultaneously, estimat.7al 2/f2zc j vw usn1coyf//qe the operating frequency of brand X.    kHz

  A guitar string produces 4 bmauyf 0gp1 ,/qeats/s when sounded with a 350-Hz tuning fork and 9 bep m g/y0q,uaf1ats/s when sounded with 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 frequency, 294 Hz. The tension in aiob:; 5n8*em :t2ar qp4w gnjone string is then decreased by 2.0%. What will beoar*:g j 2nbni4ptqm5 e;a: w8 the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fc7drd0-;kf6 b 69 fz ka/mrohz- pw(frlutes each try to play middle C (262 Hz/zhwp;a rr7 d96 0r(fcffkd --b m6kzo), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin:1 +.uqbv aew0k3htzc g forks, A, B, and C. Fork B 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 is3+c:we0q uvzkt. bha1 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 areyyowpb nq8; +8 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the ot pywyobn+ ;q88her.
(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 supr qh3c1 -xp*6tga, ebvnn6h+nposed to 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 vibratin* x+ v3hp a ceqn,b1-6t6hgnnrg 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 2.76 m in air. How manh7 zp mn9hzmlj3y541ky beats per secohpnkl1 h54y3 jmm zz97nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of 1lc;h, pcsw7t6 4mwzza certain fire engine’s siren is 1550 Hz when at rest. What frequency do you7w,;s6 tc1p c4z hlzwm 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. Whatt-iqyk j8xmzl-mv jtyi* (6,( frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 mjiiqxm*l6z k8y(vt,jm(t- - y/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sou8 )vm3ymeejg 3oq *4zorce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are theyg 3q8) m3j*vme4oo zey 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 freb l.cr p(gng :f,rl7(q1 uy9rjpix . 3se6bps+quency horn. When one is at rest and the other is moving toward the fir il+by 9s:pgpl (up.ngsrxb6 3qr7f r.(,c 1ejst 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 wavwi;j 8idsiui4 0eg cp 6l9.cp2es at 50.0 kHz and receives them returned from an object msc ;idcl9i e2u8i.4p pi0gwj6 oving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at ,h uo(psr8ew2 a speed of 5 m/s As it flies, the bat emits an ultrr p2 (,owe8suhasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experfn/nhkt5tic - ) * jtrg8z3;dhiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the sam)*3-5h8hi cjntrtdtgfzn / ;k e 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 ultrasound waves to measurq delmj(rn 896/faa jw -fv(/be blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s qn6(w- (f jmbl9/aj dea/ 8fvrdirectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency 0v v*g)/s a/nqd4gkv c e)2usw $2.25 \times10^{ 6}$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. y*x/ m,tvc 2c- p8b ,xk1h ./ekapei(low2dllWhen the wind velocity is 12 m/s from the north, what frequency will obser e- xbo(ykd,,x./ellav/ 2pc81i2p tc*l kwmhvers 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 on- f87sjxp tpf- ;pwl*v 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 iu:6lxp13d.khc qvu/+ty5fh js the angle the shock wave makes wikfy vq5j +1utc dl h/hu36:px.th 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 whe)zdy zpmpuc:3;6i/ aj re the speed of sound is only about 35 m/sppz :c3yzaij) 6dmu;/
(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. Det1 knx j5s,nahtk*c9 kft/folfr (d,:: ermine the shock wave angle rkc hf :a91 jkn,/, sl tkf:of(x5d*ntit 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 :xo-3j x 2sdfv$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a planekn s 3r1 oi9fza.m.qp.4vfb,t exactly 1.5 km above the ground flying faster than the speedz ,3 f..fbms a vpkt4onq.r91i 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 sonar device that 6 le/1rv*k 1mfi;,r kup he:tisends 20,000-Hz sound pulses downward from the bottomk*6i1mr i:/lvu,hf1re ;te kp 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 between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huuuo9x c 4p7cn4xl7zd:k 3 exh5man audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It c0zroq6y cwte;6j )o+ konsists of many plastic pipes of various lengths, which are open 6 wjy)keo z; 06troc+qon 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 clnl;(tfdqg nkt;84)yqose to the threshold of human hearing (0 dB). What will be the sound level of ;fl d8q (yk;nttnq4)g1000 such mosquitoes?    dB

  What is the resultant sound level when an 8b v elz q)oe/+*iovbivn0 6;z-2-dB sound and an 87-dB sound are heard simultaneously? b)lo b izoe-vq6 ;v*+/e vz0ni   dB

  The sound level 12.0 m frpdutut6 xy3v2k b5f,4om a loudspeaker, placed in the open, is 105 dB. What is the acoustic powb t2vtup fku4 6yxd5,3er output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outp. fbs:ije r fv;+r9wf:*mz 3bf.9lgmcut at 1000 Hz. The power output drops by 10 dB at 159s .rglime;*jvr+fzbfb9. :ffmc w :3 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically++ r3uz/2wnagzfk r) f wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the averagegk ++zfrwn/af u3 )2rz 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 sy4yyxdr kc.v4 yg z0*v0stems, 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 violi7(mg*q/0h tmm4yu 0rye wzk4imwr35cn is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundad :t.s8tig t:q o;bjf/mental frequency ojtf8t;/ d:ogisq: .btf 440 Hz and 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 filled bj at-wgew;/f 94a5 nbwith waterb;afw-ab5jt9e4g w n/ (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 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 q*x nr+oh ( mo,1ssp3wopen at one end and also 75 cm long. How much tension s wom,rxq *sp os3+(hn1hould 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 wv z(-s1wqyk w4(2t*q; :vbvs1f xnefx as observed 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 i;6lfz q6 5gdvtgh94wen the 500–1000-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 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 frequency946lt gwz56vghdf ;qe of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The i (bqa7h 3z*jnconductor on the stationary train hears a 3.0-Hz beat frequency when t3anh(q *7b izjhe other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whl3ubtgpb v6: 0istle as it approaches you is 538 Hz. After it passes you, its frequency is measured a6: ubl30 tbgvps 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed ofr -28fgc+p1r 0sacde zx5;oac cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halvedoze+ -g8par 20cdr; cf51scxa ) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat f f0dr z2)yuzg9dlgnh q40 ut/.wm,n( z ,fsqm(requency of 11 Hz. The shor wu (tszz2,)m,f0 g/9z(f.ndh qlm4 u0ng dyqrter one is 2.40 m long. How long is the other?    m

Two loudspeakers are ati ,rd61z;g 4c t mr3zwda3g:jw opposite 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 Hz1g6i twzczm3d:g ,3r;d4 wajr , 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 the0q5yd dxr+x ,k aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along t5,xkd+x0rqyd he flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towax1/ rnr-hqhwc3, 0sk qrd the bat at speed 5 m/s The bat emits a h/ sw, kqc-r 1n30xhqrsound 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 sound pulses asvtj fqo, vs/*7k6 .wpb 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 detepw6o s.k7vj b fv/*,qtcted 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 one Alpine vio- 8ej(mzax4y/x0rdc.scj1x lye (l-9 v (jnxllage to another. Since lower frequency sounds are less susceptdexxo.-y(jayxcm scnell-401j8 x / zrj(v( 9ible 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 ofngxp9 5i7/n zmw5uf 3u standing waves, which can cause acoustic “dead spots” at the lp fz/37xunwu 5 5gnim9ocations 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender aluz lg-myte*bh/f8f:b 1 onp-mm:p4s7l minum 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 el74/sh1t* -nm:zgpely 8p:- obbmmffmit 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 the65xnnvc( h*wl threshold of hearing for the human ear at a frequency of about 1000 Hz is v5w n6(xh lnc*$I_0$ = $1 \times10^{12 } W / m^2$ 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 then)4qf* bymr2mg9* ynf sonic boom ybfmmg2*q yn 9f *n)4r1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 t v)3 bd7 f 12hftmgnxvql*f(b8y;0jf$^{\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