What is the evidence that sound tr)nww. sm*hm3g avels as a wave?

What is the evidence that sound is a form ol-v 7tu+awhm 67z al8yf energy?

Children sometimes play with a homemade “telu ffz8tjn.cc -0q3jj8ephone” by attaching a string to the bottoms of two paper cups. When 3j0q-n8 .fjczjtu8cfthe 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 w)drt un.wj1 .eater, do you expect the frequency or wav 1j.nw .edru)telength to change?

What evidence can you give that the speed of sound in air does not depend signi0d6gi ny i,/0arv( tahmh5k.ti/p/yr ficantly on freq 0hr ,y/0rtymg dikht/ia/na.iv p5(6uency?

The voice of a person who(7r; 1;ubrwtelnn*e y has inhaled helium sounds very high-pitched. Why?

How will the air temperatuszshf(u0lht8na .0b 0 re in a room affect the pitch of organ pipes?

Explain how a tube mibx 7a.am m7lb3ght be used as a filter to reduce the amplitude of sounds inb7bal.37mx ma various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move / s*5 be6x 3/,jzsp sdt(farbcup th5sjaz(b e*b63f tsc d/sp,xr/ e fingerboard toward the bridge?

A noisy truck approaches yo84e ypr.g5pxs8h 3qeswc:lz l91 z7ydu from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighte8ylx r w4egeh1yqd53 s.s9p8zp:lc7 zr” — 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 “interfb*o hc7*fvei1 erence in space,” whereas beats can c 1*efvoi7h *bbe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the -iss g6/ rypx **mta3jspeakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togeths6ixgmr*3pjsa *-/ t yer?

Traditional methods of protecting 1 c abl6r9v(xfthe hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inve b1lcf6a xvr9(rts 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.z q wk,( -gm7nbf33jql Each wave can be thought of as a superposition of two sound waves with slightly di b,zfj glnq33k-wqm7(fferent 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 move in sw.isvug xlz 6r+ ,.o5the same direction, with the same velocity? Ei.u.ls6xz,w+s go rv5xplain.

If a wind is blowing, will this alter the frequency of the sound heard by a pro2ip /w;91 lagssyx5q6;j g herson at rest witgyoh rip/q;529j;l6xw sg1 sah respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child+;:/n ( 5ifghprmwr 8jcc2wb l:zxj9a in motion on a swing. 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 cw i5l+/8 pgwzbrj:nhfrjc9: ( am ;2xthe sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening forc 3zy90w/fep:ze n bhb;;o:zw the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s af :pz 9e/wcz:0fb; 3yobwehnz;ter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sidr;u z;vb4k4etr,4oa m e 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. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 k4aor 4 v;4r,zutbm ;em/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavem (j*rcg zn5g8bkh3(vlzu)8xlengths in 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 juqh2h wbm ;93yust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much y9b3 ;qwh2hum time elapses before 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 its meznas+msi .ks3 .gjq7,03d makes when striking the water below is heard 3km m..s7,33szan ije+ 0sdqgs .5 s later. How high is the cliff?    m

  A person, with his ear to the g7fef g9g1z*cg4gd a)j round, sees 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 a91g7f ce4fgdg zj )g*s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent-h. 4h *vw7nib7 al2 :l xo:pgebmkvt8/rgel4 error made over one mile of distance by the “5-second rule” for estimating the distance from a lightnin:8 /wx tvn-:*ghbl a lv.i4bpkheo24rlg7m e7g 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 levegkf0giv4wwjm;v;wk0 s d4 ,m5l 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 le;r vw aq;ld;l*vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound ln.fijqejia+/2sdon;4t4vv*0us+ f h evel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intens ovh .4s0 ji jn*+;quv/4+ffsae it2dnities, not dB’s.]    dB

  A person standing a cc-tc/ 4+b0 -e b8t x(/svdsdunorro*aertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would the ou8sta(o-sd t0/c4*vnd+ xbbrr/c- is 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 o,(k.+ydp (dn d( khrg3udjb v5v-njx+tyb*4 bf 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiesdnt(y.uj+r,k4bv(vd3dd-( p+*bg5 bxh yn kj 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 speaking in normal c n2c g1)pl0ovvonversation. Use Table 12–2. Assume the sound spreads rougc1pv nv2)l o0ghly 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 eas3f*wh3(s 1w6 mveddq rdrum 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 ampli*sk p7tuf(4 ydfier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to ktfsd(uy*4p 7each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 d ;-rp8d5mlzf0 u2v0j5 dqcgk kB when placed 2.8 m in front of a loudspeaker on the stage05zv dq p0;gcm j5f28urdkk l-.
(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 sou/zan)e bk, 7 myh84euhnd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectio ebn)8 mzuh/ey74k,han 11–9.]$\approx$   

  If the amplitude of a sound wave is trimw x 8u59e9:edz9ju;a rq wo-gpled, (a) by what factor will the intensity increase? Increase by aumqe8;9 x5r gwaz-woj9e 9:d u factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one lh1o0wgk.y q okhn 3 mz5:jg(/has twice the frequency of the other. What is3noq (zo jhyg: k/ g15.mlkhw0 the ratio of their intensities?   

  What would be the sound levewsr(:*i tcax5iq 45)i-wwxa .zt u2srl (in dB) of a sound wave in air that corresponds to a diswa w4.uxii-r5 xzt5 iss*(awq :)2crtplacement 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 v1qt6cn m c(o74z vqv-100-Hz tone that has a 5qot714vcn cz -v(m6vq0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest/ occ9s qo;uixy9cd,. frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.yio xs/,q; c9co d9uc.)

  Your auditory system can accommodate a huge range of soktdu+si *wf t+d )mxm):9mc 8eund levels. What is the ratio of xm+* dc)+f9km st:mtiw)u8edhighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengthw;a 2 9uplrd/lno sfo04;9ruz/oc7a k of the vibrating/4 9;9adrk7lw;ur /oapno of2lzus0c portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the funday6nx(g,apj+kl z/t:xvoae0 - mental and first three audible overto j6(-0y x +ko:ep/l ztgax,nvanes 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 blowing across d2- ab;cihd02 lm*bm2fsb8uk the top of an empty soda bottle that is 18 cm deep, if you assumemb*b u2s28; b mfdhikd0l ac-2d it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes s -.5wffz0+a j62ueq wr ws;sxlpanning the range of human hearing (20 Hz to 20 kH 6 ;wf0ujqr s2s-e.wzlaf5 +wxz), 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 p -zf1+8innyq)/izl ht l9+ hlHz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% pn i+ll ihz)/+y81h-zfl9qntof its original length?   Hz

  An unfingered guitar strd, n5 d3v(3wucu *4plag ;pluking is 0.73 m long and is tuned to play E above middle C (330 Hz). punuv *3p;d uwkc4 a5,lgd(3l
(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 orgg +aj-0 kukr ro9*/s (hku,xksan pipe that emits middle C (262 Hz) when the temperou/ kkgrs*x9-ru+sjk0 k, (ahature 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 a2yn qck k d98mqn)1e12aotq o7-upfd(t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute icfb, 0pzx .t8en Example 12–10 should the hole be that must bez0b,x pt8.e fc uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can xl.td7084gq nd1gaz qdwke, uph*x0+ resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencie,+*tlg.dgnpa7x u q0hddw qz14x80ek s 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 s-6c ajip7 qe-at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is -iq 67ajpce-s
(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 -b,x5)7e/okwbn x h ud$^{\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 2.8kb0 t v 36pkfl-mep.g14-m-long organ ppke6v-3. f8 tl0p kgmbipe 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 ou0c etv6ik4q.xgdf( 5 itside 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 relaqi4ec 0v5 dxf. (kgt6itionship 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 adjusezkibsxp8t1(m .sh.9tc -:wit two strings, one of which is sounding 440 Hz. How far off is98mect1(s-xib:z khtpw i .. n frequency is the other string? ±    Hz

  What is the beat frequency if midpv60 5vd0+h l.zooafrq s)sq 5dle 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 u/dh ,2gju5djscav -1er (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 Hz occurs when they are played simultaneously, estimate the operating frequen/5cj 1ag d2,uhu-svjd cy of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork a.1kd+ qsd*mpymoqxn ), 2yhr3eu zx(0nd 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strinos2 )x.z10y(mxqeydh p3mq*dnk+,ru g? Explain your reasoning.    Hz

  Two violin strings are tuned to the sa/jporu*9se1 h3/vik, z n5gshlo+zm p02 jr4nme frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strnlu oe 2n9zo0rs+j5h mh/1k4ijs3rz pvp ,g*/ings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middl /2,j3aejill ke C (262 Hz), but one is at 5.0°C and the oth,jekl/ lia3j2er at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and rosrspd.em iwbuzr -/04:j ,)C. Fork B has a frequency of 441 Hz; when A and B ar/ -sdziw4:rbm p,.rjuos)re 0e 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 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 ja) swuw :i75 s9(v kllcwd(w6apart. A person stands 3.00 m from one speaker and 3.50 m from the otheri aw: w7c9w (vdj6l)5wu(kssl .
(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 )zbn:(dqiil)nuuk1,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 frequency of the otheln(,iunqk ))uizb d1 :r ?   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.e exd8 58*m sg5mk6 yuxkyw;a264 m and 2.76 m in air. How many beats per second will be heard? (Assume2; mmeus58xe y*ky5gkwxa 68d T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ods7jk i1*(mea f a certain fire engine’s siren is 1550 Hz when at rest. What frequency do yosdi*amk7e (1ju 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 fruz+n wshqy30ljsc w9s395( rdequency do you detect if a fire engine whose siren emits at 1550 Hz movz9wcl30 d 9s5wy(+u 3hqrsnj ses 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 et4jcf4g6m c 9you at 15 m/s versus you moving towm4ccgj64 tfe9ard 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 o8zky 9 gsvg8y2kwg vd2ry,68 zne is 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 the frequency the vy,2ggvk9yzz8 g8y6dsrwk2 8horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives themj,2/ hw nt /g+u1fidmp returned from an object moving directly away mf,wh n d i1jtp+2u/g/from it 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 b7jrf o4dp vc e9;78zwit flies, the bat emits an ultrasonic sound wave with frequ ;r7jwd4zoe8 vfb7 p9cency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving k.; fpfwv.*cbiu+p( s flat train car at a ;pf( pf isv.bcku.*w+frequency of 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 ultrasound waves to measure blood-flow speeds. Suppobiwcc ), c7kk h6.gx+kse the device emits sound at 3.5 MHz, and the speed of sound in human ticx6 k, cgh.kcik7b)+ wssue 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 ultraso6xat9rg3ce ffhrsv)) y1s z(-nic waves of 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 d5+y2mjbrm 11vlu+ etwind velocity is 12 m/s from the+1mbj1+u2yl5v dtre m north, what 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/i 7mp;ca-yic moving 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 speed o g2he8ep5gl6yk. l*z cf sound is 310 m/s (a) What is yep z 8lgchk.gl 5e62*the angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmu8,yovge8rn me * 7-ewbw/* rk8ln/jsh,e d0sosphere of a planet where the speed of sound is/he8e w d e0m,,gk8uwb*-nrseo8ls7r*/ nyjv only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shocka xwsr47cb+dw7md ,:l wave angle it dwr,:74xb cdl7s +wm aproduces
(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 +t4*m w a2uelzl.)qy.e-z fwh$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead an/9-.ks +b uz z/ psacsulkez31d see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the ti z1s//za3cs-el9kk+su z.bupme 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*cov(gf srdwe0aqx*te,5j+ sktpl; )il 5- n 2 20,000-Hz 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 200 m, what iss(pi )alt*t2owgfnk c 0*v-qx5dejr + ,ls; 5e the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibl3jri: hox,4s ke range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It con5:mqf(rey x c+sists of many plastic pipes of various lengths, which are open on both (+y5m: qcefxr 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 thresholdydjl)g )u f )18tyay 5 snf4,nv0c:zid of human hearing (0 dB). Whatu) 4jn dldy,8gv:tf0yn1y afzsc5)) i will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whenc(nz3+hpp5m cy.;w p u an 82-dB sound and an 87-dB sound are hearn +pz3hcu p.;(wp5 cmyd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plgi //nag3 j bvtbqbyd13 u sl.)u-7ly8aced in the open, is 105 dB. What is the acoustic power output (W) of the s1yu3qjs-./bbv ugy)l bg i3tal/ d7n8peaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rat oiowc, z7u49xed at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHzc7 ix9 wo,4ouz?    dB

  Workers around jet aircraft8tj4(dec*ai)zlprn e -5wpl m,uh33 k typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the 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 )43t u* 5dr8wkz,e plc3ni-( ajehlpm30 m from a jet airplane engine?    W

  In audio and communications syslfg6q- nq)c1 utems, 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+zn5bx9q.) oxvj uoy*jxi53 wyh;u v: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 long between fixed points with a fundamental nkj)6u p)ro t7pf9wu( frequency of 440 Hz auk)pu6r)fo (79jt wnp nd 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 setbj f60c 4+7fy/npbgan into vibration above a vertical open tube filled with water (Fig. 12fjpnf6bg0y b /74+nca–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar strt:2yz yan7ib*ing of mass 2.10 g 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 t 27*iyz:anby the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full 7jf0awekfu8v 4)1 zw iloop ($\frac{1}{2}\lambda$) 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 50dnta;*;irop ldtwf23s )n,e40–1000-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 soiwot3den fn a,s) ld 4p*t2;r;urce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationad, ru3e lz16xory. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mov6l zor,31u exding train?   m/s

  The frequency of a steam train whistle as it approaches 3mn,84um hoveuwt*a jgf *v;8 you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast fj*4,g*n88matowve 3muhv ;uwas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just bynp+,sz2vf8n2ps i/ uh listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a cihvfsp82 nup/s+z n,2ertain 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, sounding together, produce a beat frequency of 11 Hz.pvak-9 7s pk1x The sho-x7k svpa 9kp1rter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rwh(op1v 0e,wb:s p u6oailroad 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 B, and (c) he hears the sbo(0pwh ovu6,1:ws pepeakers after they have passed him, at C?

  If the velocity of blooij*3i -xcdto 9d flow in the aorta is normally about 0.32 m/s what beat frequec*i 9jx-i 3dtoncy would you expect if 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 speed 6.5 m/s while the moth is flx (pmqhh iii8l/uy5,7ying toward the bat y(5m /lh ui7ii8x,qhpat 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 reflects off the moth?    kHz

  A bat emits a series o;dw k.x d4gus;f high frequency sound pulses as it approaches a moth. The pulses are a k 4;x.g;usdwdpproximately 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 ehb6).j*+ oheib,m/zwh jt w5-xqx 2kfrom 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 x.+- j*oe ek)hjb5btx 26qw,hmh/ izwmost popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can cutc)xr10v ii. *kg )kz5 qed;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 rdzi u0tqv1x.) ;cc*)g5ekik m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invo u44uk3 auosvrs +fuc:,)szz )lves a long, slender aluminum rod held in,szu vs u34)sro a :)ucuk4zf+ the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long 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 hbm0zh5hmgakolk/s(s t/0(gd* ou7* z earing for the human ear at a frequency of about kg sl(thk50*d/z /bzs7a (umm oo0 g*h1000 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 t/0bzl8 73c8i m pmmbwthe ground hears the sonic boom 1.5 min after the plane passes directlycblwb/7 8zi t 0mmpm38 overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is wxt6 xtn-.; qbfh t:gb9w;*/had k*av15 $^{\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