What is the evidence that 2 bqi iyqp/n;w-t1 sk2sound travels as a wave?

What is the evidence that sound is a form of enu-qjgi 2 vu*qx6 u+sz;ergy?

Children sometimes play with a homemade “telephone” by attaching ao4jbj 5vl7rq( wns ,cl122czb string to the bottoms of two paper cups. Wh7(z b wcj2v,ns1 bqjol2 5cr4len the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes 3hwl*g0rz kz7 from air into water, do you expect the frequency or wavelengw0*z3g z7 krhlth to change?

What evidence can you give that the speed of sound in air does not depend signitm rn yzxc08- drig,58ficantly or z,tx-0nm8cd 8yrg5i n frequency?

The voice of a person who ,frgw /hpc0-7 l i7h/ku*rvtj has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipe n)czhlr+utb2)/ wq a8s?

Explain how a tube might be used as a filter to redg*m8m ztiu uu kr0nkc,4 gn6)(uce the amplitude of sounds in various frequeng,)6iu n k (r un*k4gm8z0muctcy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up-bho6w.db)ci p(gt ) j the fingerboard toward the brjo p(.wh) b-g6b cdi)tidge?

A noisy truck approachema5vy,v*(v mb d.ep/ks you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: /(mbe vk.y 5,vadp*vmSee Section 11–15 on diffraction.]

Standing waves can be said to be dued x)5pl9t6 bpl to “interference in space,” whereas beats can be said to be due to “interfe9p6tlldb x5) prence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,0ctj,0p 7ewzm)j zty)kpbb.. would the points D and C (where destructive and constructive interference occur) move farther apart or c.z.zb0tm))jp kj7 wey c pb,0tloser together?

Traditional methods of protecting the hearing of people who work in arlgth4x7 (b:;ox(eq yueas with very high noise levels have consi ye :bthxgo;qx7(ul(4 sted 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 sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wavym ) pxr65*,s0agecqd e can 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 component f ,6x5 mcdyp)q*gr sa0erequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thekxt8ma 18jk,w same direction, with the same 1 kw8,kajt8mxvelocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard b. ub:rdf,w m0by a person at rest with respdb r.,0wmbfu:ect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a s;mttr6snb9.)ysz9 , szfsw c2wing. A monitor is blowing a w ;b. , cs629z)mzsnfsys9ttr 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 obxuf 8 o:zn86ftl7 *unrg n32lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of trfn n oufn tuo8*g8z6l2b 73:xhe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the etp ebe*dtl 6x.n5 d:gw)8 d.bycho of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume thnlt b ee.d:5t8*w)p 6gdy bdx.e 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*x0 4*:r vbige g*qs4on qqr/v air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just n 5pd4u de jm44uumz*5above 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 elap5m 4uduu4*ezj5 m4d npses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped f tvkz ;n5+ysz:rom the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the c 5ytn;vz:ks+zliff?    m

  A person, with his ear to the ground, s b lfs,;xal13yees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s,f1ll 3 xbsy;a apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent e:(hs;b2vu;h .u fy-cg by j1rrrror made over one mile of distance by the “5-second ruleb srh-hfguy; :v (c ;1rub.y2j” for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound as7f grdc3 n 6dpr:qk+v7- h)alt 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 kmq8 k *tv6 p2n,*whhxwhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously( hdoy4:kg.ib at a certain place, what will be the sound level if obg4o(k :di yh.nly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a kc7ec mn(+v)w zke s-9certain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Wh()czmk kc-e ns+7w9veat sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 a8; d)lcnsgkont4l 31dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each dcnn8o1 4g;t3l )akls device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norm+fctpb1p e6:i,3-xp *t:xjz hp8gdv eal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly overg-:pif,dvx6 pec tp jz 3hx+e*p81tb: a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum+r,zcgwj6*j 9by8ie ny 8i+ sofx,i5d 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,0w,2jyecb 7e3c f :tbc while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in dyw c3 e:ec ,c0bft2j7becibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered g *rl06k8y casteyh: y 5tn:q0130 dB when placed 2.8 m in front of a loudspeaker o:tn yyr05:s*8 h0 kytglc6qa en 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 o.a0din6a0c :lvxzd a+f 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount:ndlxa aac. zi600v+d? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) fjnerire5 3wi r:z) hwn* jv9+ r*v3qhcw/q(0by what factor will the intensity increase? I h/ (e*9zrw3j w nn0qw f:3*ivh) rv5qrrj+ecincrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaoa2svb;r8-vm 6.mq i acement amplitudes, but one has twice the frequency of the other. What is to a; 8vmqar -im.2bsv6he ratio of their intensities?   

  What would be the sound lecj3s 4 m c1fr06dncq2mvel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0ncdcr6m 4f0m3jq 21cs.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100pdq54e;s lg7kr8fjr.*3 lm zy-Hz tone that has a 50-dB sound level? (See Fir*qde l7.l8m4;gyr5 jps f zk3g. 12–6.)    dB

What are the lowest and highest freq1 ry:prnj5aa, 5ukz8rt:2t ncuencies that an ear can detect when the soundkr25ru pn81 t:cnzay5j:, at r level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound leviy; uw m i,2ka)o odpgmea+)md jk:9yb+s .)3uels. What is the ratio of highest to lowest inte+jkm3,i d)))+ ogim puu.o;swa9 mb a:kd ye2ynsity 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 funxk. u5khlk78rax ;u u,damental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pxu87a5 x;hl ukkr .uk,laced?    N

  An organ pipe is 112 cm long. What are the fundujshd 208aeqljlbmr; * .a8 s:amental and first three audible overtones if the bs8re:8sld*a.uqljj2 0ha;m 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 woul+w d:.psh( yop/wql k7d you expect from blowing across the top of an empty soda bottle that is 18 cm deepwd lsk. 7opwqhp(+ :/y, 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 2 l c1qi87bykrpipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ran7182byl qr ikcge 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. What wiylsbis*m .bt;j md a;8,vx/u,au2nq7n - utk 5ll be its fundamental frequency if it85imxls- tkvt7b, y/,ja*ns bm.qu;2u nd au; is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long an*wdhxb : y0gh 8gr+yj(d is tuned to play E above middle C (330 xb8:gdygh + wy*0rh(j 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 Ce /retnu3o3.q 6cb0laqb72i c (262 Hz) when b3/a2 ueq.nec 6 3btloi0cqr7the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune atwbm5e fgzi ar8t 4b;4.bpcn* - 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fr ek8,ud6el .)m61nry2xrld flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 r ,kelrfd62 8xlm1reuy.d)6 nHz?    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 pj) ti/osb)l ,xipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betw j)/ oxs,lt)ibeen. (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. wgc.3vaqj+h wt i8r98It resonates at two successive har.ac8r8hg 3+ iwtvwj9 qmonics 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 8naa4ec,b6k9c 7 ludr$^{\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 2.14nyn 3 :5ctss/h-m-long organ pipe at hntcys: 3n/5 s20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2. f.f;6s uf8zds akdr305 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 ansk ;z3fsf0.su 6rfad8 dwer 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 bem,z6)0 k; qnthqg.ewhen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the 0zek b ,h;gq emn6)t.qother string? ±    Hz

  What is the beat frequency if mid:wfgq b;wqmg(3o rz 35dle 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 (bra9u5m;*emd5/ mybmp d cnd X) operates at an unknown frequency. If neither whistle can be heard by humans when played separateeb9*m5duc d;/ p 5mmymly, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beatsk eh7a2d0bm3 grby c 7xn1,kr0/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hzxbg b ,7m10ed3k0nha27ryrkc tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the9/ yequ9cy fl0p)pa,d same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard whenf0pyad9yuplc9e/) q , the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will 2 pl7d-z ho)x*nkfeo h+9wj.qbe heard if two identical flutes each try to play middle C (262 Hz), but one is at -ne.of9 h2*zkj)wopqdh l 7+x5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, ;2;uoj,3 7t+qes i uokvmop1qb-c3d)vy bf/h 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 is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are souq)mcq tjk-+s2;;ue1b/uhdov7ofv3o 3 ,pyi b nded 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 persomqq 6x2z2 rn,ln stands 3.00 m from one speaker and 3.50 m from the 2 qnmrzxql2 ,6other.
(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 pepkn8 x9( s2 i,81ddazzaz + 1avascq2iano tuner hears three beats every 2.0 s when they are played together. (a) Ifa(+s8vi2,8ed d 9 qa1p1nazzxc2a zs k 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+qm(1l l;q *ps n:pnfj of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Aq +q;mn 1 sfjn*l(p:lpssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sj tv8 fr/g4t;..6 ch/ ilqpwl12ba yskiren is 1550 Hz when at rest. What freq 8c2j6/l;r ap.bi1t4 ghsqt w/f.lyk vuency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect i 9tj-wj0ya2n.j7f6oteqf- xxf a fire engine whose siren emits at 1550 Hz moves aj9ft -xoxnj f7te2qy6-.j 0awt a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift ioh zps u:yg0hrnv38 /9n frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving towarhgs9/hz0yo3v: r n8 upd it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one i; 8/1+epbew+om ftwmk s 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 tp;+wm km o+e1fbw8et/ he frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them rethur3o0 8q6 ofeurned from an object moving directly away from it at 25 m/s What is the receir38h u0eoq6ofved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the171qkhaxmi5 0 k8fxp a bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected 01hxik8q a57kmx1 pfawave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mo* fgd* aaz/9enq4nv-s*fr k.jving flat train car at a frequency of 75 Hz, and a second iden9 a-/vnk4rs**n daef*f .j qzgtical 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 ultrasound wvj yqo 8/thwiru-7 5 r7cs6d5ncox u:-aves 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 r/quixt -d u87o-r7yjw :n6s5 o5hv cc1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr a2b9htsw-bx3equency $2.25 \times10^{ 6}$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 em oogrh) gt9c2 oy,4e,iits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at resoe rt iyog,,cho42g)9 t,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at z57(b + tngvpjgi(a/ j20 $^{\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 ofnp8pd8xd1(r;or a5 e m sound is 310 m/s (a) What is the angle the shock wavne15;8 d(xrmardp8op e 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 hx. 9xk t dfz4fke/zr+fj.:5cgqj 3x/atmosphere of a planet where the speed of sound is only ab g.f9q+ xfkxrf z .3tjcj kx/:hz4d/e5out 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 s.dz2 wlt1au 5utrikes the ocean. Determine the shock wave angle it pr2uw5t zu da.1loduces
(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 hyttb (+bk( w(-1vdrl5h nty 6e ;urw2$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a planej jppcp+x gii4( u+3u/ exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the pi xuip 3ug+ /jc+pj(4plane 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 sends 20;3e08(:ob) f*d sb nyg jjfwdz,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it id)yojeb*sf0gd( z:jbn;wf83 s designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible -b tem()8qbe8poay 1ju b.zs;range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calle nsjjtwkad2l +/ic+ujs/* 0;od a sewer pipe symphony. It consists of many plastic pipes of various lengths, which ar/i2/;okwn j j0 *ajscu tdsl++e open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of hgz zp1)35x usjuman hearingp 3zzus5g xj)1 (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound a-ed tmqizfg7+y0l-l vb f4 90are heard simydg i f -l-ze0f9v4+07tabmlqultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. nctu0 krfod*gq) 7(q 28p.c m5 pxgbt*What is the acoustic power output (W) of the speakeq fm)0* k.5g bp rcgxd(cn2ou78pttq*r, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output d6g9rtj)igj s ;69;iu celnw3i rops by 10 dB at 15 kHz. What is the power output9gujl;i9 rjcw6sn ;t)igei 36 in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices overq2*5c hbpirg,brg5*kdh(c08xs w2 ib 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 power intercepted by an unprotected ear at a distance of 30 m from a jet airplane eic dx5kbgwr28p*2(0qsi *5bgr chhb,ngine?    W

  In audio and communications sysflfyda 0z d(1g,2i hzhu7mf u /l.3,odtems, 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 tun;ni- mnfrz, 4u ctmmj, 5)(rnped 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 f9 /1jh/z6v3ca i9 atg2w2qe -rh saxmiundamental frequency9cq91t vaxi3/mhr/6j-ie2 gsha wz2a of 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 vertical5-:q k:womumo,dm4ji open tube filled with water (Fig. 12–35). The water level is allowed to drop sl5w-u mkom:,: jimod4qowly. 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 v7ik7 f6yizi2g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with th7f ik7ivy2z6i e third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full er 78b7ir5h:f yk6gubloop ($\frac{1}{2}\lambda$) 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 8fz87l5gf)( egj o /fygu*bj d500–1000-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 g/7edfl8ygo)8j (g b fuf5* zjis the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the iat9sc v9- :up;z+w hmstationary train hears a 3.0-Hz beat frequency when the other train approachesih pu9wv +ct sz-am:9;. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afjzag59ox*wiax33 r2g ter it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?zi33 oa* 2x9xjar5 ggw    m/s

  At a race track, you can estimate the speed of cars just by listelhiof ea 4cvu50t64h ;ning to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by oeal5t6i 4v;4ch h 0ufon the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce .9 m)+t79v j 5sdqwtuqvdan)zekyj6*a beat frequency of 11 Hz. The shorter one is 2.40 m long. How longy76t 5 k+ 9 mtjaeq)nwsdv)v*z9uq.jd is the other?    m

Two loudspeakers are at opposite ends of a raio9vwibnk p52. lroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37vpi nowk5.29b . 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 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 norma0+ *zxj 6n(rqjy2l ccxphnf;,lly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along thezh2j (j0x* c nqrnf+yp cl,6;x 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 spee0+;xt j s9dtzo5 0 yni-a:qwpnvb68 emd 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits apai0web85 y- q+ 6nvxm0dt;t:zjos9n sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulgpo5knn h;n:q bn/;.ag0pj 3eses 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:;q; nh0 pg/ gakp5.ebn3 onjn moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig1-t8f yydg8wiqq c1+ue c)eg2. 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only 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 fundamenta+gq u)wy gt88cqyf e11di- 2ecl 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 3+xq3 o aja.;tx3u m w.k-qouocompromised 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 wi3u.o u.ax+ 3owtkjam o-qq;3 xde, 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 demonstra + i z68dxi)jn/smjby2tion, 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 soundsxy8)2b/inj6zjim+ d . 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 hksyp90ay2 2ry earing for the human ear at a frequency of aboutr2py0 y 9kyas2 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An pcgh 2b27u c (6 0akftxp8j/cczty ;0uobserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s 0pc /ccub7 gfkt028z yj2;6u c(paht xaltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 a5v(y gj o+4cz$^{\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