What is the evidence that soun3ne.vx9 mdid.l fl5 p2d travels as a wave?

What is the evidence that sound is a form of enej, vzu9e +27sc.n 2 vwg9hpwxurgy?

Children sometimes play with a homemade “teg+7 wmrxir k; p pmys47r5n)(ilephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the pkn rgix)+rswi;7m( p y47rm 5sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wasx r,s-8j l/cqe; y3uwvelength sj,l rxs/e3 yqw-c8;u to change?

What evidence can you give ;d v*v7 ap (je ,vvy4gv9ek7fgthat the speed of sound in air does not depend significantly on freq9e;7fygvje7v( *kd,v vgav4puency?

The voice of a person who has inhaled helium sounds very high-pitchr*gb1l072ei tydi p, ;,yfsvxed. Why?

How will the air temperature i /c0/ a;htmcgcn a room affect the pitch of organ pipes?

Explain how a tube might be usuw1 m30q t) y (jvuwoowa 7yue ei-ye+v)s.*w.ed as a filter to reduce the amplitude of sounds inu7 ij aw3eo 0 y t+uom()eue1.-)qywwy. *wvsv various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closx lg2gk19 mx/qya i7q *g6n mf/t1t-dter together as you move up the2t1 dy q-k6917mfatg/gqlgm /t xi*nx fingerboard toward the bridge?

A noisy truck approaches you from behind a buildi pj;*mj8 id zvok6mn w066abs+ng. Initially you hear it but cannot see it. When it emerges and youd0zmwo+*jbs;66mpv6 njk8 i a do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whdpcfizs7 ,zm*5 yil-:ereas beats can be said to z*dzi 5p7:sm, i lfc-ybe due to “interference in time.” Explain.

In Fig. 12–16, if the frequ 7jhczcci8mmq 164xf7cqt3t- ency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farthechi- ftjqmmx3c8c zq1 4c7t76r apart or closer together?

Traditional methods of protecting the hearing of people who work in areas weuaump+vh (qnkh4+ k4.(qbd+ith 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 whinmkaqphv ((duu4 .+eh +4+qkb ch 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 wavesd h ncdduw;lz7bb9 -,0 shown in Fig. 12–31. Each wave 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 frequencies farbcunbl ,;wdz9 d7d-0hther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in them)x0i; y1enizd aaa-9 same direction, with the same vn)aiyai;0 az9d-xem 1elocity? Explain.

If a wind is blowing, will this alter mvtg sx ch ,g9yc1c-u m(9t/;pthe frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or v;hgg(v t/ 9cs19ym-, xpcmc utelocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moni,z bg oh/kgi x;o60rmj*fp.) wtor is blowing a whistle in front of the child on the ground. At which6.r*i/ ) xogkbm g0 zo,jpwfh; position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengn* :a1zqw3q z u6qojk (3xm+q ufxa:t)th of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.maq63*1)uqznq(z tfxjo3u k+qw a ::x0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the34tlhv +/oz5mai e0vix .7ulo 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 seawat37ovue5+io zvmhtai .x4l 0l/er is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2yw9h0kd/ x shgc)i-0n 0 $^{\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 tuna on a l3f om*2g atu/n(jnm7 foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses beforelj(go7m n /mut* 32anf the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikia0 p:fwkgh1u, ng the water below is heard 3.5 s later. Houw,p0 a k1:gfhw high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cog8 k kq7fp ds70l8c5 vds4c.djncrete 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 apavs87 0sqgfkldc5cpj.47 d d8krt. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percenrye ;lh-.q 48cee )iy8en1dxst error made over one mile of distance by the “5-second rule” for estimating the dd-e l ysxyr8)q48;in cee1e. histance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a somdgn 7r4k66e eund 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 levelre..)* mor cpi of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 g .k(xu z *hjonqdbk5 ,e9b(6xdB when fired simultaneously at a certain place, what will be the sound level if on(9njk 6qzo*hubb.xk,(xge5 d ly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally frwpx0gw qa/3u j211web .e5vnoisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intep1qxw2u fa10j5ger.vw w b3/ ensities, not dB’s.]    dB

  A cassette player is said to have a signal-wda: ek,o0;jad 6 r8/u+ wmehqto-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratiouaawd 0ko,;w+:6h ejmred/q8 of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person syo4t7fxbk a 48peaking in normal conversation. Use 48yf 47xboktaTable 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is drgd g1xk+7, ai0-cbx $5 \times10^{ -5} m^2$ (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 mol n0: cfj4a7rrre 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 in7 :rrfja4c0 ln 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 1305 poz1 ncfzel8 6:(rku dB when placed 2.8 m in front of a loudspeaker on thf :lz6(n8op5e cr uk1ze 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 leve0lw,uddtj9fy 5(c ;vul of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: 9, udld;ty( jcvfw5u 0See Section 11–9.]$\approx$   

  If the amplitude of a sound wave ie74:;oztpn/ gsna ;tts tripled, (a) by what factor will the intensity increase/;:sng7 zeot tp4nat; ? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice t3 )/ir6g:e icjuw( wczozllfv*k 422rhe frequency of the other. What is the ratio of thei2z cr w6lrf i*l:kejzu2igo3wvc /()4 r intensities?   

  What would be the sokpgt1-8fq zq( und level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibratingq81z t(f-qkgp air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lg x 66sj,: :d7h+i s+iawuuymievel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig.j7:+i hx6sywa+id:gi, 6mu us 12–6.)    dB

What are the lowest and highest frequencies that an ear c0yk :2et6y ok,wcvs8ia,hf,5lvx uo( an detect when the sound level is 30 dB? (Seekf ( s8,ik:uyo,02 vatev6c l,xowh5y Fig. 12–6.)

  Your auditory system can accommq/ q. aj +ypa.ri26jqdodate a huge range of sound levels. What is the ratioja .2r6q/+qadqiyp .j 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 lv*- vg/1 pptgj0wss9 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 j9p tw-vp/s g*lg01svstring be placed?    N

  An organ pipe is 112 cm longhut1ei qsx6jk 2 r(7ze r.**oz. What are the fundamental and first three audible ojoi x 1*tk7uq zrreh(s 2*6z.evertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from bl0 atygpsxr7,07j+x s i5mc(b qowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube?p s+0ct7(qb0x a57 sigxrjy,m    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pmma3tj0o4co g(, wgae/2myf6ap ,t(k ipe organ with open-tube pipes spanning the range of human hearing (20 Hz to egf6 wacap m0oo3/a,gkytm,2j( m4(t20 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 as itssq , ):m5:bdi i.veyax third harmonic. What will be its fundamental frequency if it is f :edaq : iy)ixm,s5.vbingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle Cn0d7 v(fy lh w ci+nd4y3,mn9w (330 Hdh3i (n, ynlvnm04 wdcw 9fy+7z).
(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 org;37y iydag5 vntkqu;:7ymvk :an pipe that emits middle C (262 Hz) when the temperature ng vu7aqvdyyy7kmi; :;t5k :3is 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 at 20tvlvuuyrz86wc(5z6c r k:9d ietq8(e4/4jtq $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of ytm;e4+rh+t h the flute in Example 12–10 should the hole be that must be uncovered to play D above middt t++4e;m rhhyle 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, and 616 Hz, bu:pt *:lntx8vxt not at any other frequencies in between. (a) Show *tx: t:vxn l8pwhy 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 two/2 lobupn 4+z*ltkw/w successive harmonics of frequ2zbo+lp4 n/u*wlkwt /encies 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 ze7u69 fh55 w dst6u:brc)khu$^{\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 +ycmse 2;u)nm.y5w x:f jdzsomj1s 7*within the audible range for a 2.14-m-long organ pipe at5ju7*;x:s omscf 2y)y mnsemjw1d.z+ 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It,h9px0 tg ,paitio5 b9/- zgny is open to the outside and is closed at the other end by the ear5 t 9,iapgpyg09i bxo/tn,h z-drum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, on.(z-l olk own.i5q2l a5bzd/ie of which 5 o l2-5zol( i.n bl./awkizdqis sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C m-2mp cdz-7ztsrrniv* u 4a1 .(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 operat );8hl53 ;po-jh ;cr/lc dzszwmw15dcxlx k3ees at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 H s 8l3d 1 ;z5k 3wclem5oxc/jcl-rdxz);;phhwz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded withyld ,vy3a2y d96 r8ufn a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning. vlay, y2 3dfdur986yn    Hz

  Two violin strings are tuned to the same frequen0r0vgoj296aqk pn+ e c9n, ekscy, 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: Rn6kqc+s9o,0jv 92gnpak0e erecall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each ;.-y4pcux trib1 4s ormxc-o een34/btry to play middle C (262 Hz), but one is at 5.0°Co4 -xrucc;x4.pb-oby 3 1 n4emet/irs 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 44agvo*ikc e3 l4g9 1m4z1 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 kaeovz9m ligcg *31 44possible 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 sxwjyj:gkinwx: f n fotj4 *19ibm lo8*9u3/:s tands 3.00 m from one speaker and 3.oijk*4wu b*jxf :yn 8/ 3lfj:nwis tg1o9x :9m50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano toky 5oa5 ;o.vwz8x9gc uner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of t.ga 8;zy kwoo9 cv5x5ohe 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 wavelen( ri (fnswbz(vdg:+1i47zz eo gths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume7+wez4drgvz(b1(if:o z(is n T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaifbs 7k7sqe6 7tn fire engine’s siren is 1550 Hz when at restsb7q7e f 6k7st. What frequency 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 if a fire enginep)reqb / ec * /qgin,xw3cz6*x whose siren emits at 1550 xri)cw z63qnb q, p*e/x*c /egHz moves at a speed of 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 6yeqfg kp.b .b:d; rg-n3 *:)svljaz ydfx-8y at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are t- .r63g azk ; -fdsfy)bx.8*nelbpy:vydj :q ghey 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 wa u(fe6 c4cog*gle 3e.ith the same single frequency horn. When one is at rest and the other is me 3 cg6(coga4e*l e.ufoving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out uyak;y b8* nvm4-*dry hltrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sounyady4bvm8 kh;*n *ry-d frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/sh1qyyuzw8 *0c As it flies, the bat emits an ultrasonic sound wave yhc* z uqyw801with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp8z .i)cz2mtat ler experiments, a tuba was played on a moving flat train car at a frequency ofzt)2tz m ac8i. 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ult vy7ara:xkvd: . nnc1.rasound waves to measure blood-flow speeds. Suppose the device emc n:7avn1y.:dxvrka . its 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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofke/j 7ch+s ga1, gfi6y0 8dird 8i)qhx frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wi1 3q*1g lqsybfnd velocity is 12 m/s from the north, what frequency will observers hear who are located, at rey1 s3lq1gfq *bst,
(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 movinto2s:d;3cfgt*s q i,s g on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the skljb 6k1i7/ncpeed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplan bnlc1k6 /7jike’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 pilfltzw;*6 ,/ w8p zu3zuvzk3fv9 j1dlanet where the speed of sound is only about 3kzzufzwl/ ,t;wvf6 8*i913zp v jd3 lu5 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 o e)nkbq/ e.4u( kqj;xhcean. Determine the shock wave angle it producesn b e quq(;e/k.x4)hkj
(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 d/hwa;(xig/ jl (z:s y$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead anda8u mf5(ja3 5ssi4np , sgyzoq56eq2x see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the t8i54 smajxg5 eao2quq(f 5pyss6nz3 ,ime 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 sends 20,000-3f69ig i o hsr)ihd0j7Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 20 o3hfhi0rjs6i)d7 i9g 0 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many ocudpd 7 8-g odtg(1h2)i k2wcfxtaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Itz:7fepog33,4hyc0 5v z zkltqf kt)q) consists of many plastic pipes of various h0 :7 l 3g,zfy)fezptkz4 qkco)qv3t5lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes c+hk/ -u axif+a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoefx++/hc ua -kis?    dB

  What is the resultant sound level whek mu9 e(od-8rcn an 82-dB sound and an 87-dB sound are heard simu( orme-8c9dk ultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the 3bc 1 hxyiux89wim); iopen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiatesbcx1x)wi u;y83i mih9 equally in all directions?    W

  A stereo amplifier is rated at 150 W outputk+1* ( y+2r5wz 4n tyfixswzux at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 xiywz4 zk2u*ynrxf1 5w+( t+s kHz?    dB

  Workers around jet aircraft typically wear protective devicesjeei x op2e;yrowr vd6 syg2:7 (ik06- 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 aver0go6ejx;yi rskry2dw-e (6i pv7e 2 :oage 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 syx-obzb1u )b w3stems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequ:6x4 6si4l y ukc1taggr9eqq;ency 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 lon j:)bpgf(w) jsp:,yzg5 qb rgnwy-a)8 g between fixed points with a fundamental frequency of 440 Hz and a mass per unit lengt- jw)::j( )a b bqpg)gyws,f8ypzg5r nh 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 with wa ( :ikk+0cz jzv6iwo,zter (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 tube0zi6c+ ovw, :i(kz kjz 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 ofme 1m*,bzdq 8q ( .ln,gz7y9 yhkxwd1j mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension shoujm hq9bmkwd18,,ne1 7z*yyz .d(gq xlld 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 observed to resonate a21:sygl6*tp 3e fbqs es 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 tonervi0dttpv5 3. in the 500–1000-Hz range coming from two sources. The t5vdvi p 0.t3rsound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor /7w/xh5i2gyw;lkl qvon the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spell 7gx;y qivw //52kwhed of the moving train?   m/s

  The frequency of a steam train whistle as q0qw *-ha pyr)it approaches you is 538 Hz. After it passes youwqar*yq )hp-0 , its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of0xhah9 7wm avc986-j5tbjnj zq9 vk-v 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 halved) as it goes by on the straightaway. vv-jj0 x9-an7w 9t8 hahmqjbkz 9c56vHow fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11-9,j tm7wbc vz Hz. The shorter one is 2.40 m lcb-zmtv w79, jong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past ha8 *-i*b pu45z5ywm1jvn 52 wysdqlca 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 car, (b) he is between the speakers, at n58p*z yvyu*2-hc5jw iqas m5bd1 lw4B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in .lc 6kvgjjt*2the aorta is normally about 0.32 m/s what beat frequency would you expect ikjgc v.j *l6t2f 5.50-MHz ultrasound waves were directed along the 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 spe*asy2v *5nia6px: n sued 6.5 m/s while the moth is flying toward the bat at speea:n56 2iyv*nssax *pud 5 m/s The bat 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 high frequency sound pulses as it approaches sxh t /kn;q0 ah725gy5l gxiq.a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth ys2;/g55q0kn xhi7a l t .qxhgbe detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpinh xk:lz.sf/mydx m;7,e 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 music lmmz ;:k xdy,fx/hs.7al 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 liqff foj:9;fz2t4 -wd nstening can be compromised by the presence of standing waves, which can cause acoustin-;z4fj tfwf2:d 9q foc “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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing r1eb /xil n45c5::rwt ma4ojpaods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked w axc: ope t:4l 5miar/14bj5nwith the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hear0c7n6rgff70*wcy qt cv* 9 nuwing for the human ear at a frequency of about t0 crcc nf*9*uvn w7w6g fq7y01000 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 observer on the ground hears the sonickj *ji d*jwv 5j:kjie fw,3.i* boom 1.55jvw*d j:kwi *3iij.je fkj* , min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is o*8f4frl i hp415 $^{\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