What is the evidence that soundgdo9t2 rqlq6al o29o: travels as a wave?

What is the evidence that sound is a form of energyqnb +af slfc vh24gsm1e4 5-qrcwy8.:autu0+ ?

Children sometimes play with a homemade “t m(d1)d o:,8eiwoj s3pnihnk/elephone” by attaching a string to the bottoms of d, oik :ed()nh8jwi sm/n1po3two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequencylgkzf ,:v(4 nz or wavelength4l(zkn gv, fz: to change?

What evidence can you give that the speed of sound in air s8qcq:n- z1aj+ 9oapx87l bj ( rjy9ftdoes not depend significantlo t1l z(qa b q7jy9rjpj89c+:8- asxnfy on frequency?

The voice of a person who has inhaled.(v +1mvkqxus+xvs2,gzp *yc helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipe +pev n /ns:6 ca/wr-uvfx(x/ls?

Explain how a tube might be used as a filter to reduce the ampli/rhoth 3zr)6m +pms 3jaik1(atude of sounds in various frequency ranges. ( khz mahmp3jio r() 1satr3/6+An example is a car muffler.)

Why are the frets on a guix d.gea2c:b;o tar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the brid :acdo2eb.x ;gge?

A noisy truck approaches you from behind a building. Io, .ne, 4hfbk5hq0l;va pcdfcm;py *. nitially you hear it but cannot see it. When it emerges and you do see it, itsh4kemp d ;;,*.fh, fnqcpb.y a0ov cl5 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 s7 dfcg xzw5+:wpace,” whereas beats can be said to be due to “interfer g7zf:x+ wd5cwence in time.” Explain.

In Fig. 12–16, if the frequency 2; t u9nux+twstw: 1wiof the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or close29:xw +wu stutw1i nt;r together?

Traditional methods of protecting the hearing of p fp81pi+ye nd-yu8rh2eople 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, t 8yrdp- yh2f81eni+puhen feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave ca1q) n 4pz+wanm*ij(mvn be thought of as a superposition of two soun mv+w i(*n pm41janq)zd waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mo: szqwhq( 0lk7p5d ) ow7i;uolve in the same direction, with the same zwqp( 7oq)lshk ;7d0wil5 :uo velocity? Explain.

If a wind is blowing, will this alter the frequency of thlxir9 7 clk0rp:epdhspx jl(;2 e); )oe sound heard by a person at rest w (xrhl )lsceprixpl;j9 p):2 0e odk7;ith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. w9,kk,8fhxt 6a jfegj: rj.l- 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?wj f.6ej,: l8fxg a-tkj9krh, Explain your reasoning.

  A hiker determines the length of a lake by listening for irp9 7- pug*ubthe echo of her shout reflected by a cliff at the far end of the lake. She hears the upu r7b*9-pgi echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the y0d9*czfyxu6yhinz. /k- f-kside of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. Hocxdfzi -- u/9 yn.ykyz 6hk0f*w 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at ct6nd x (a7js/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 ab q+ufuxxh*(c60 r1yy gove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses bef yq yfux +01u6xrg*h(core the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the tob yoizkii8ucq95k .0fvy6 (9lz u yqn6+hv1o0p of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the clif0iuq iy1 ufnlqi z8oy6 5 kc6vhzovy90b9(+.kf?    m

  A person, with his ear to the ground, sees a huge stone styp9grfhlh1k f p/(2; srike 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 apart. How far away did the impa/f 9f2lysrp;h1phk (g ct occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance i8csm /2d mmme). xng(by the “5-second rule” for estimating the distance from a lightnmg/dms ne)mx 8i(c 2m.ing strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? 60xa *t f ;czvv. i6nash6s/z;6ooini   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 +k4 .k 3ikvtynk-*rbywhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wo+h. kr rsh-+mo t4aj9hen fired simultaneously at a certain place, what4t-9oohmrrakh+s j .+ will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noi(p; yw; pvncxn1.w kz9sy jet engines is experiencing a sound level bordering on pain, 120 dB. Whatw(x;pz;vc 1ynpn9w.k 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 +x3ynk7 3bg4sscf a1:1;t :o o:mkjp0 ljozfdsignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device?3j7zso1j of+ kg1my:sd3 op;l0xaf: 4 tkbn:c 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from(u . 9sf25vrxx yr5szzwy7 )mt a person speaking in normal conversation. Use5w)9v(2u y xs ztfy7mr r.5szx Table 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 eardrm6ferxq;7w k wm/rdp, an1, (p4-zxhlum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier2xoh8 */i gx5+hnqjwv 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 xhhix8vqn*/ow +5 j2gconnected 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 ;7pszxm3 8n7d 5kx nmkmeter registered 130 dB when placed 2.8 m in front of a loudspeaker on the x 5mkpk;7 3xnmsz d7n8stage.
(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 6(v+fsjfd2ak gs0 dp 3difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this aags+p0k(fj ds3v2 fd6mount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a souum*j:uhzcb ( u*/s 0,. wnkdjtnd wave is tripled, (a) by what factor will the intensity increase? Itu/,kb0 m**:jjzchuu s (.dwnncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes,.n/r,+gb g(gyov 7vwg but one has twice the frequency of the other. What is the r rw.,+v gv/oy( b7ngggatio of their intensities?   

  What would be the sound level (in dB) of a sou q/(rhh(7t3 hd0skr jnnd wave in air that corresponds to a displacemetr7n (0(s hr3d kjqh/hnt amplitude of vibrating air 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 u0( rjvpu2)+ovzmes+i8b k )mhas a 50-dB sound level? )evuomruv0j bp)kmz+i8 s+(2(See Fig. 12–6.)    dB

What are the lowest and highest frequeidtux 9h3os0 9gmy 17oncies that an ear can detect when the sound level is 30 9 x1uti 0sg7yhomd3 9odB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the sd8h3(bhi,;kthtxy wg; ;0ojratio of highesh0;3; db;ih(jt8 k,hxo ty gswt 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 ft( pzm0/fr - jwvo.zx9undamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 gjom 90zz /x tw-(frp.v. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three au+s 7yg(xw8yr k r.6* cv2yyfbcn2rag+ dible overtones6c yrgfcbky+*27n wr(8y+g2yvrsx .a 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 fr,t:ex);hp3fj pzj , kbom blowing across the top of an empty soda bottle hfk,b; :j3tjxpz,)p ethat 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 k,fzivdi *f :,oxb94hopen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ranxi,f zhi v*kbd:4f9,o ge 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 ha.h r448 h*zga3keoin 7s:zn igrmonic. What will be its fundamental frequency if it is fingered at a length of only 60% ofh4e4iosr:gg*z7 n8k3zi . nha its original length?   Hz

  An unfingered guitar string is 0.73 m*;qjido rc 2ub:3p 4d zmah7yzka)51x long and is tuned to play E above middle C (330 Hz).2praqh;cz :biad5y okd3*u7j z) 1m4x
(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 C7i* sel6zp vwiv/ l);+ l buxkmeg)5i4 (262 Hz) whenb))+mwl*lispugk 6v5/ 7z leexi4 ;iv the 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 aj00g8je jr (i2m *sakwn pez, zxh;ds 2;rnr84t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moutht; 527zrep0zp(npg si piece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middl (;tnz75g0 ezpiprsp2e 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, xeobz2t37 n1(xc1pdg but not at any other fretzx7 21xnd cb1op3(egquencies 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 tube 1.80 m long is open at both ends. n l i8z7-not+cIt resonates at two successive harmonics of frequenci nziln+8- cto7es 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 cy *cd xt1 cghegi:1r+v53zq( $^{\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 vlu 9 r2s6f6yu2.14-m-long organ p9yluu2f vr66s ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the out +qzl2y ad(tw16gl t5j7roq9c side 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 isq 9t5l2o1wr( j t7ydqlg6z ca+ 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 wffsgv+ dy )o y2v7l231u1gvkadjust two strings, one of which is sounding 440 Hz. How fary2u+lgvv1wf 1dg)yo7 kfs 23v off in frequency is the other string? ±    Hz

  What is the beat frequexe k53omi* ps)ncy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anoth x1ot ,r912h+xkip d quy0o7dner (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when p+9 d0xi 7n ud1kxth1oyq o2,rplayed separately, 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 beats/s when so pfap v:l 70;-k1gzrtwunded with 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? p k:;10gf-wvp at7zlrExplain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hzjr(uv: 7 g; zidxrv+3w. The tension in one string is th 7 +i;urz(dxjvvr3:g wen decreased by 2.0%. What will be 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 djx/1+ q vf)ktn**lo 5)rxau uidentical flutes each try to play middle C (262 Hz), but one is at 5.0°au )xufk 5)o*dqxn+ 1/jlt*rvC and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequd2mh u k-xywhrm .qeg )3/dq82ency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togd-dxg qyru382qhmew.hm /k2)ether, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m fr(rqof2q dl7 a1om one speaker and 3.50 m from the ol21qado(rfq7 ther.
(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 beup-7 ll; iu bbrt,b)u8jjud;( vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequenp;(b- 8biudlu)ujr,t7; uj lb cy 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 manh o iu55,+nj hz-,kpl rg,iff3y beats per second will be heard? (Assnf u r,lpg5 5,ofj3zhh- iik+,ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a 4o b 84 wzkh9tu.5kqu-gy.p4fv5 zhsscertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 mws98-45gh.ozsup bk fth4vyk.z4q u5 /s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequencyz ps:9z;-b7vgv 0 j y+qxy,jff do you detect if a fire engine whose siren emits yj :x0zp;zj+9sf,vv-q b yf g7at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencyu +k )g6vw+: bh7dbn ;pamfkni )d,6ne if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenn)g6fd7ake h nd 6nmbp vw k,;i++ub:)cies 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 is at 8m7xaqu +b ;4eqms0mw rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency e0 q7xqm +m;sa4bumw8of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic 9 zw,r7w*r6(mynfmlj sound waves at 50.0 kHz and receives them returned from an object moving directly away from 7*9j lyfnm6m r,w zw(rit at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ultr,t9v42tft rvw asonic sound wave with fw4tvt vr,f t29requency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler,*gb.rlk: iq k experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical ti*gkqb l r:,.kuba 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 waves to measure blood-flyil*y ;7kzb1 * oot1hpow 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 directly 1;yl pook* *1yb 7itzhaway from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequenc(uqvyuefes8e t d02wx f; 8/7ty $2.25 \times10^{ 6}$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 x;qi tthi: r, uj8ra6;of frequency 570 Hz. When the wind velocity is 12 m/s from the north, wat6;r; :,8iqjux hrt ihat frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving y o pp/t*3j(k v76rc+ hcgv9oson 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 0(lnkopr , w5 7,ipvgnfu.mo0 310 m/s (a) What is the angle the shock wave makes withml.o7wn, v, o0u0rn5gfp(pki 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 :i+p+ph x pno. s9gub8planet where the speed of sound is only abhp ioxn u :gpp++9b.8sout 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 stri( j 0pn6fl uza5+mby+z7jad(tkes the ocean. Determine the shock wave angle it producnmaf((j 6z b0p yu z+5dat+lj7es
(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 .7i k)9tdei qm$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a rlminiu(p.;4e )7 l kjplane exactly 1.5 km above the ground flying faster than the speed of sound. By the time y(i 7uel.nk4)ri mjlp ;ou 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 20,00t, u wy 7bsfh.c3,pnvae97c*c0-Hz sound pulses downward from thpsc*9hn ,v.3 y7ectbf c7u aw,e bottom 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 human a,,q1 / crk7hhl 5e+ymmq1gcql udible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of many kob9stfz ), cq,tand ;;z2+jw plastic pipes of various lengthsta kws,2tn9 +;b,zoj df)zcq; , 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 ws80da4xnip* makes a sound close to the threshold of human hearing (0 dB). Wh i0awdsx 8*4npat 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 are he0 uzo;1mn yeca yc6r/4ard simultay6/n40mru; cz e1y coaneously?    dB

  The sound level 12.0 m from a hbeg(o)h)y :g loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of they(h)ghoe g:)b speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output3 ;fs6q4ty ,6mmxjgv-5u ojst at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whatjmt s;f s6ovtx46,m j yq-u3g5 is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weard g;rk-qysu;.p v3mdpmg3rsd9k 3g;- protective devices over their ears. Assume td 39mr ryps -3gp3sqd; k.kg-u;md v;ghat 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 engine?    W

  In audio and communicatiw95gc7c:wh zyk q* 0exons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned t00md08anm1+p/bsj a vu2b kf yo 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 b24 cv.b gj im4bd53v*7dejepx gk 5ha.etween fixed points with a fundamental frequency of 440 Hz and a mass per unit length of 3bmgvce.x5v g42 h54 db pj.jaid7e k*$6.1 \times10^{-4 }$ 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 abobxq z6wc.rlr :a t/c2)ve a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning lt6cx/ zr)c2rq:aw.bfork 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 stwu 9ku)xiq +zw5v9q vrz :bw0+o8y2x oring of mass 2.10 g is near a tube that is open at one end an u8 )x 9q+zkvrv90biw5uwz2o woyx :+qd also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lo1pv hfvk/ n843)wc,xil a *kkiop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range comin9pfi.av8nxp 8a h/sacx9n q3)dwh 6k5g 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 ah pa65wp nx9q3vfs9 hx88/dn ak.ci)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 on9 umqr47hytrzge 8 4;r the stationary train hears a 3.0-Hz beat frequency when the other train approa94 qm 7g4;zhrue8tyr rches. What is the speed of the moving train?   m/s

  The frequency of a steas8-nc . ts9 5 0.mfmzi6prgta- myzrx3m train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured asa389siz gy fc.nzpm-rxtm. tr -m0s5 6 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the d+aig i:pq68g :9vzq; mlq ztm-ifference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a: 6:89zqivglzi- g a m;qt+pqm certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, so);a 3wy.-pq y:grcuzbyxz o1bwe. 08ounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lo g.3)8w1y:oarbqey .yuc;o b pzx 0w-zng. How long is the other?    m

Two loudspeakers are at t rz-7jyqa 8+jopposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at 87jz +ay jr-qtB, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abi)h h7p b x6.,b ckcc-q2lmemyx1+v-pout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the,6kbhq vxc x.i-m +cp21b-h) 7clmyp e 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 l z cy77uh(c.ftoward the bat at speed 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 r.(yc7 zhlf7cu eflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it by.yn6;kexp .b*:s ctapproaches a moth. The pulses are approximate.6bby .cx;n :*tke syply 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from 9 ) .k9z+ulq-xpdp vkfone 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 fundamental frequency of this horn, and which overtone is close to F sharp? (d-p k)9+z.vuq9p k xlfSee Table 12–3.) Model as an open tube.

  Room acoustics for stereo listen: .:fhu/r. sn2tk*k jlhs;( eqq;oxpding can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wi :ksfo(*ux qknldehthqj: 2;.; /sp r.de, 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 “siat+ ;e17yqgo )opp-c tfjic/ -nging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with thi)yo+cfp ja tq;- tp-eco /7g1e other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frenkl.pc.1gwu1y : l o,uquency of about 101.l,:. plu uwongkc1y 00 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 tz + +wkmh)i 3ofmd6hy8he ground hears the sonic boom 1.5 min after the plane passes directly overhe+of8mw 6khh 3iz+)dy mad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 0utwwuk6n4 / n15 $^{\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