What is the evidence that sound travels as a omn1)yzr , gl8wave?

What is the evidence that sound is a forz; v1znfbl ,6gm of energy?

Children sometimes play with a homemade.p960d:kl.qjl rnshh “telephone” by attaching a string to the bottoms of two 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 thljn 9lp:hkh .06.d qrse sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you+5fpbsfyljh;w 2j6b2 expect the frequency or wavelength to l2jybbf+fsh pj2; 6 w5change?

What evidence can you g 1nzfn 0 rv92jo(pcixw-dfo*.ive that the speed of sound in air does not depend significantly on frequency- ozw n(n0 jo2ix *rc1df.fv9p?

The voice of a person who has inhaled helium sounds very high-pitchedv*jpcvk l dr*0c)ek :4dl-9o zb85m xi. Why?

How will the air temmi ciky-3o6g+perature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to syn++)/gank tm0 r+fbob,i p; reduce the amplitude of sounds in various frequency ranges b+spb/gia 0)nof;kyt+ rm +n,. (An example is a car muffler.)

Why are the frets on a guita06gii)h- 8cw mu ak2nliv(y4qr (Fig. 12–30) spaced closer together as you move up the fin v2i aw-8qmnhigu0lky6i4) c(gerboard toward the bridge?

A noisy truck approac1-(.(ksajb:z kgxfy olf3 e*c 2w;cvdhes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffractiowco- gkc: d((3z*f lybkfaje12 s .vx;n.]

Standing waves can be said to be due to “interference in space,” wheb3/c 6 u+ynjjireas beats can be said/6jb c3 +jynui to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin-x0wwguj *ga )ts D and C (where destructive and constructive xw*-wu)g0aj ginterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peo-5b*l(blsxn 8 hxs:bljj ( r.ople who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. l(bh5j.j-lnsbo 8(sx*rb xl: With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thouqf*i5/ xo.sa eght of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves q*i5/xe sof.a, (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)a-)gbup 3v.( 3ovki c cshz0p move in the same direction, with the samu0vg c.a)zip(bs 3 k coh)3pv-e velocity? Explain.

If a wind is blowing, will this alter thek+hh*aj r9 ;;7bnu fyh frequency of the sound heard by a person at rest with reha 9;bn7h+hj *kuyr ;fspect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mond y4zx pve..m+.c mwyu)us8g9itor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child he 9yxm..pdywvc4uz)su.+e m8 gar the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listerx89yx m-hsi -ning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the rxxiy8sh9 m-- length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hvy 83y9 ab c* stm-t-o.ylq7vtis ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table ya73tq9tmy .-ct -svlob *8 vy12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in av kgd8mut:0x8 ir at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just wady*.k1udh+p7 4 mrpabove a school of tuna on a foggy day. Without warning, an engine backfire occurs on anothehu +pd*wa r7d4 py.mk1r boat 1.0 km away (Fig. 12–33). How much 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 it makes when striking d,j; g3)l*2f ) prjcjgua3ruqthe water below is heard 3r d3,3gl;jj)j)rp*gu2 f qacu .5 s later. How high is the cliff?    m

  A person, with his ear to the groundaogyb*kn +9x708i/e /reon bl, 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 s apart. How far a e+ /nnroae0bbk x7g o9y*8l/iway did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-seccb og0dae:29 sond rule” for estimating the distance: e0bgsod ac92 from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitkrn:yisddm8 5q8a.pzje 185w blal6x;l; o4 ay of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose9v3v18 oi06p dnbmol u/eqih- intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelrr7p te8gol vkpp ;m r,bva .(b--ts2+ of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,po 2t.,ba rpprvlvrg ;8me-7 (+ -stbk not dB’s.]    dB

  A person standing a certain distance from an aij 2j(:7xjb: x-sowglkojxp+6 rplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wougoj(xl-o xx:b s6j2p :jwk7 j+ld 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 sig 7rkk2 uei7h;unal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the hike7;u2k7 urratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of4pee7npg ,ao pb n 47)n 19r2wxzctnmhc-8 i5x sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mou z9)r1mcpib7one -ghpxcen 8x7anpt5424wn ,th. $\approx$    $ \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 qt:oqa ev;-kfw1 wjk*x02m; )g onjw; an eardrum 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, while4 j(bytih/ tva5 /md6b the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would 64m/j/yai5btt d(bvh expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB metz4m7r )krzf *p/c9tsb er registered 130 dB when placed 2.8 m in front of a loudspeaker on t7f4 t*krsc z/ rpb)9zmhe 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 typic s9t2c -zbh*n/ tq,qelally detect a difference in sound level of 2.0 dB. What is the ratio of the amplt*-l 2en ztqscqh /,9bitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound w9zljys9xs7;h6 c mvbo kir953ave is tripled, (a) by what factor will the intensity increase? Increase by axozrb 5 hysvs;9j796 3lc i9mk factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacerg; y,q4d(t- k)f,wvcye)c (jvs3nic ment amplitudes, but one has twice the frequency of the other. Whv f4cy c)j ,dwrsen3;v ct(q)(iyk- g,at is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds on 1tdx n*7 zc)yd+,beaze0 n x0l:1u t4tj1vtto a displacement amplitude of vibrating air molecules of 4bnn: t7 z0ldx x1o vjey0*ztc1ae +tu)nd,1t0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tog:md/lzk-) c* i m/ o odh,ml8krp)ps6ne that has a 50-dB sound level? :/kp)8cd)k ,s-mhdl*mpgz6r iom/ o l(See Fig. 12–6.)    dB

What are the lowest andihq eck/1oy-:.omk/xi) a; ro highest frequencies that an ear can detect when the sound leve mohir-q )c;/kx :/eo.ya1ikol is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hugx;npukl*j p3y))7 tnce range of sound levels. What is the ratio of highest to lc;nu )j yt*7)pkx3pn 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 fun--7 x -o7sssahc0whr ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the str crhsw 7hs-s xo0a-7-ning be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first tikc1lt-ywa b9g; 5sg* hree audible overtones if the pip- k g;wi5*gab9 l1ctsye 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 acrossg9 s9tg/zbu,w the top of an empty soda bottle that is 18 cm deep, if you ass9zgb ,/ugw ts9umed 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 orgg:a4;0felrf .4n y:2p rmqykian with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range ok m.0 nra2:4;ef4yp ylqfi:rgf the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string haxoci kaa11-e4v 4psb4 s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is v4i4s1 poca kbx-4a 1efingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m q+9yop xr+)scf;:u e5xqj c v0long and is tuned to play E above middle C (330 r+cvu) cxsj p5:0qxy e9q +fo;Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middly+ 4 k rgw32p6c4o5:vtxpjc rle C (262 Hz) when the temperature isw c3:v4+rpo p5x2r gcyj6tl4k 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 20 0)zbdzc+t bum9u d:l9m2:2idvl5fy p $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flr gix ,1ky085e/pxiu;myzh t 9n/ yhi6ute in Example 12–10 should the hole be that must 8 0epum61/n yi z/hy gyit;r9ix,xh k5be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, kl0) x2v7)t*ujm sjhq 440 Hz, and 616 Hz, but not at any other frequencies in betweenstlj0)q7 mu)2k vj *xh. (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. It resonates at twoif 308a/nav fp7amf4 h/q; yyh successive harmonics of fre yiq/0ahf 3fav47n hpa8/;y fmquencies 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 f mmt(* ym58pgcg; +ks$^{\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 iot b0f/i pi)bruop i8 p /)g/*d.op7grange for a 2.14-m-long organ pio)/ppi i*i)bor0/ gug7oippt/b.8 d f pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cowq124pmbwoi3 d1jy 8 m long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the 8moiwy4pwjb2 1d1oq3audible 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 dpvyw*hi sduch18; --trying to adjust two strings, one of which is soundinh;wd* p1dy svc--u8ihg 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and )zt v 5dhd0ddq6 cb*6q$C^＃$ (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 operje5cz1g .yxdf+/ 5*5nirvz j:wt wf s9 iyld21ates 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 Hz occurs when they are played simultaney2+5wx: jzig*/ jdy .d5fl15 f91ewrsiztn vcously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuningazfg,zmh :r c9edt+:, fork and 9 beats/sr+9, z ,mtcehz:ad:gf when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tunedd(b w; 0v,leb/s *n jklq4xn4r to the same frequency, 294 Hz. The tension in one stringr(wke/ q;*, b04jl xlnbsn dv4 is then 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 identical flut : kj3hm,zv*oc8c 5*(ewhhxp,lftuc7es each try to play middle C (262 Hz), bujhe, of cx mzc7 lw83kcuhptv5, **h(:t one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has w;tnm83m ef 7i 24obcexp;:zxa frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies arxmzo e 2f4t nb7;mxi:8;epcw3e 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.1nsed+ c.bmfa a z(du.3+f qh9 A person stands 3.00 m from one speaker and 3.50 m from the oma hu asz+n93b1fddf.e.c +(q 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 be vibrating at fd/5( qq+q; bnux) bof132 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 frequency of the other ? 5)q;+f xdnbq o(q/buf  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 (*w0ijdcuo 7zo u3vx1z .vqe7m in air. How many beats per second will be heard? ( du0vzq1o*37vi jx zo7e .wuc(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when79aawcbu de kz8+3o 5x at rest. What frequency do you detect if you move with a speed of 30 bxdcukz5w+o9 ea783a m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect 8v.zn+mne:t dif a fire engine whose siren emits at 1550 Hz moves at a speed mn:te+8z.vdn of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequqccx)v);t ,a;m krcz- ency if a 2000-Hz source is moving toward you at 15 m/s versus you moving tom)cz -qt);x ;akr v,ccward 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 freyv/+zd k36fj,z9)l6j fp0w4 y ejsh zlquency horn. When one is at rest an kz9/z6yff 3y jlzs ,w0)vj+p46heljdd 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 horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rece6z+kuynt dm;0ives them returned from an object moving directly away from it at 25 m/s What is the received sound 60+kmy;d zun tfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits anq(iy* lu19l ot ultrasonic sound waveu( *1oliyltq9 with frequency 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 flat 3rxq m3j t7+mytrain car at a 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 ?q73t rj+3m myx   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spe f4lke7 :bklzh okn72 h*jq8r.eds. 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 kkhnj 8z. rh7eq f:4lbko2 7*lbeat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of f /cqbhr6tnlr w vu*(f27xi)- 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 frequenk kusfnh ,+8i6cy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers h6+f hni k8kus,ear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land ifvvk k,x;e-:*w gsun-lak.5kv its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Wharvftaxx 2ebon92jgi,ro1 bcp7 k ).5;t is the angle the shock wa 9ar ox , obb ri5c)kt2nve7;21gjf.pxve 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 atmosphere of a planet where the speed of sound is6dlkd 7tm4 +g9hs*mgiy p eco:h)b:.n onlym 7y sbmkhtd+od*h4g). pnelc:96 :ig 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 travelin(deel;ig1 5q gg 8500 m/s strikes the ocean. Determine the shock wave angle it produces 1g;i (geel d5q
(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 4x/w(sfob nyd)vw 9y3$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly d/y39ax g* bgpr(d-hz 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. Seg3r/ *d a(dp9zxhybg-e 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 s3-/o c.lbezqj3,sztl ends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects ec l,3jeszcloq tb 3z/.-hoes. 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 uhz 6 jjipe .o*yz,5p0human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a shjzn,u+qsb p4ql 15j1a a8u+sewer pipe symphony. It consists of many plasuj5a8p 1jzb qalq14n ,su+hs +tic pipes of various lengths, 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 man8r j(3m unq5lkes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such lm53rnn8qju( mosquitoes?    dB

  What is the resultant sound level when an 82-dB hhlhe-+r4)rj6 rxx c,sound and an 87-dB sound are heard x+re)6hrhc,jx-hr 4lsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in thouy,d-hw1 ci4(4yf yye open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming i4y wiuh,1d( fy y4co-yt radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ouwb 8y;a(z7wgg;o 09r ka-k bxxtput drops by 10 dB at 15 kwy;x 0bwgko-aba87;z rk(9 xgHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. A nf:)1pdi x/y7 y/p6 vxkh:zmessume that the sound/ : xe/fyn z6h1:xydv)m7 ikpp 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 communic jz;ggst; wgd:.i-*u-g.hk8 gisr9kiy ob9k -ations 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 to atdm2rbw +uw*p )d8g0b 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+7 x)9ujeofm f long between fixed points with a fundamental frequency of 440 Hz an)7+o juxeff9m d a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibratwttr v; 6ve0( jm(q*etion above a vertical open tube filled with water ;w* (mtq0e t6vvtrje((Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube s.qv3qlyi+i0 tg cku 0g-v6x, 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 fundug3, qliq -.yx06+i ksvc 0gvtamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was q grei1a,grcd );3 2maobserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure ) m42to :/iwfirpy6as tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency isw 2y ti/ :)i4opam6rfs, 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 8xpva 9k++wqawjn + q7 rar5c.on the stationary train hea+a +a8wr 9pajwr+v nq7ckx. 5qrs a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches y 9sb,c 9qnavw/ou is 538 Hz. After it passes you, its frequency is measured w/ac,qvs 9 n9bas 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 liste0ox((bjry- qcj*bb r9ning to the dif y-r0jc9x*b j(q obb(rference 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. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat k33cmq.13cr/fv ef qyjz g2+8so6 ndp frequency of 11 Hz. The shorter one is 2.40 m l3jg 2emq8vfo s6fd+z k/1 c3rn c3.pqyong. How long is the other?    m

Two loudspeakers are at opposite ends ofhfh h)vtzq9 o/gblrs( 9u( t4/r zt.951ljt st 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( tsb9 jro1z94lrth9ftu/ vz/th g)5hs (qtl. between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of bloo m8lr9louj*q 8d flow in the aorta is normally about 0.32 m/s what beat frequency wo*lo9l j 8u8qmruld 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 3z nvgmh/. tfzu/na+p )t6t v ac94ap*moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detectpta3 +z*g/tanm 9phc4n.) uafv /tvz6ed by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of *g h7mzm 8hs*ohigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth m h*hom*sgz78be 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 Alpu1i;+ojl*kek 3 sjz udc81d5pine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to ze1k8ju3 *; c+p1ddi sjkulo5create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the p z3 rwt7oxoc dz(bg2:1 z8 nako-nzoci/k(v 77resence 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 wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roo37zagox z c-db7nkw1o(nov8 z:2 rio t7/(ckzm.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves)jwy 2o qx f(0uk:3spy-9 tr+fc9qcgl a long, slender aluminum rod held in the hand near the rod’s midpoinsf+k g ol0(yu)2jqcpwy9: rc9-xq3tft. 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 hearing for thq797k/p: rp fue tkx,ue human ear at a frequency of about 1000 Hz is pkfxeu ku7pt,:9qr/7$I_0$ = $1 \times10^{12 } W / m^2$ 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 obhj-e2)m ptlk.server on the ground hears the sonic boom 1.5 min after the plank. mjept)2 l-he passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1(d0 qx;*ie.ve .b kmsz5 $^{\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