What is the evidence thad lur242;sqg jt sound travels as a wave?

What is the evidence that sound i *m-uol6jwr m+s a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stroe,s:ew,flvhy qfqlo a8b 56 .rs 1w7.ing to the lw.q b5:7 hoe8 lqfw6y,o1sa,.s efvrbottoms 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 the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequenpl7qvsx 0 jxa/vwc,- )cy or wavelengtcpwv,0 7qx )j/vs-alxh to change?

What evidence can you give that the speed of sound in aeq3 -yo1/zujq ir does not depend signife1ujo-3q/ qyz icantly on frequency?

The voice of a person who has 0ro:k -*crlka inhaled helium sounds very high-pitched. Why?

How will the air temperature in a )fvn4ztbnlr 0re 6zg* rn(,7*rz dkoc,*i tp5room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds i,uf6hx1i fet8n various frequency ranges. (An example is af,6i1 tx8eu hf car muffler.)

Why are the frets on a guitar (jffu+y3gw 20g 0h5rnsFig. 12–30) spaced closer together as you move up the fingerboard toward the bridur2sf00 gn3jw hg5+y fge?

A noisy truck approaches you ff2+ oemozrp 7 ve/c14mrom behind a building. Initially you hear it but cannot sev4r/+eo eo2mfz c mp71e 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 diffraction.]

Standing waves can be said to be b .,2 hykqitb.due to “interference in space,” whereas beats can ,k htqb2i.yb. be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsw0pv0hq o:cevye4,:f5r cv6i7wz d 8n D and C (where destructive and coc7vdo,v5wrqn:yz h6v cwpef4:80e i0nstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wox/3xqgbse8zv(tx,q - d0 vu0zrk 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 used3gutd s/8bz0qeqx zv, x x0(v- 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 thought of as a suk5c7r*k k)q0u kzitl5perposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? E7k ct iqrkk05lz*k u)5xplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move b8z4cjzi,isbh -oq qtf0zv68ez 9 0 f2in the same direction, with the same velocity? Explain6 ,qbiqzfoz b0t2iv9fh88czze sj0 4-.

If a wind is blowing, wi xig( t+:r+hiill this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wa(ti+xh: ii+ rgvelength or velocity changed?

Figure 12–32 shows various positi/tzu79+cwjc f9b a7 irons of a child in motion on a swing. A monitor is blowingfb99t +/ac irzj wcu77 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? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her n d/zjcd i1;6bshout reflected by a cliff at the far end of the lake. She hears the nzdidb ;/c16j echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlinvsiy33m 7hr s(k70 qcne. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep isr03 y3(7ni c hvsmqk7s 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 wavelength p0q+; f5g9)ecbx4y z,bzvqzxs 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 just above a school of tuna on a foggy dayc(o+m90vjk 2g jb b my5y0n/wu. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backf0+jyw(cgv/2m0u 5n9 ybjbok mire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from th40 /u. koutmm3gp :oefe top of a cliff. The splash it makes when striking themge0 3tu/ o.kp4 o:umf water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike t b*z-xkud6 3 rej4.(jihvusi5he concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the oth(5- js6krduji*xv4 .iubz3 eher in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over onx ;cnh26 fw50yrq3ceoe mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the tfn 6y;o5h0rcqwx 23 ceemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity gy0dn1ec y2 zyr.b*l; 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 soundsa/ rq l 5oqctf*d96lpi2or/9 whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound le6,wtaws,wq 1 o ;yj- 7jbpxhn9vel of 95 dB when fired simultaneously at a cert91xy;tjnjw,qaw-7 hs o6,w bpain place, what 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 equat6sts; n)vff b *i qt,*9bd9xclly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engft ,ts9;*q* i)6stxd9 bcbfnvine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-tp hk2x 8;tan7to-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 nat87h2k ; ptxeach device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpy :+pr8u1 slts fdna1ad/m*8/eq i ya*ut of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly un/ys8+qr8nd1 ul/sa*yaa*p1t:e imdfiformly 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 strik7*aa:9 3s mah/r8hddmlk iv *ues 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, while the j.0ur x:xh1 9cam9q rnmore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you x1ha9n:qjmrr09 u xc. would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.oxgo;p h/f-sdyp- ykcl1; .vyzi+++a 8 m in front of a loudspeaker on the st+;pfoi+-a v+z- c s ogdl1x/ ky.pyh;yage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of9 p19yy 4r 6nu;xlt;5 txdkids-oh c7g 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ 9;c9n;1 po5t4 dsrtx kh6l 7gyxy-uidby this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by ww.rx4dsg3 /g8do; gsnhat factor will the intensity increwog nd/4sr3g.8ds g;x ase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equagk3 l1hfx: ;tyl displacement amplitudes, but one has twice the frequency of the otheh3tgfy:1 ; lkxr. What is the ratio of their intensities?   

  What would be the sound level (it/h9lfql6iv.-dv. afpl-,as d: m b 8yn dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecu-:v/89lfdm6.-tb.f pyd,sa qal l vhiles of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound f0qmp, z*/6e erp a)queviq, rt:gtrq6(/qy3 level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Se(mepiqvfa)q,r : t6r/qet 6qyp, *3qu0 /gerze Fig. 12–6.)    dB

What are the lowest and highest frequencies that an e vndoh32 9p.vaon-.csar can detect when the sound level is 30 dB? (See Fig. 12dvo n p.9-vsn ch.o23a–6.)

  Your auditory system can accommodate a huge range of sound levele5-7s( 8oi zlhjy+nj c6tim7is. What is the ratio of highest to lowest intensity t n ijc7se -67iiz(oh58ymjl+ at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violinyzphwgz) vo1nhtm cd.)6 e7.iu k 1/5z jo1v.f has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensiof1 / m6ignh.1ukzv5 ..)7w 1zv)ot ohpyecjzd n must the string be placed?    N

  An organ pipe is 112 cm long.: ri/ii655pmco td*,cv1zf mt What are the fundamental and first three audible overtones if the pip 6io/,rfm d vp *ciitzc:15m5te 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 blowq-1.b da .pxix(2fkn5 lk7xkuing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clo..(- 72bqd na1 luixkkxp5fkx sed 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 pipeon7ejd qwe933s spanning the range of human hearing (20 Hz to 20 kHz), what woulod3 j397eqen wd be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string havum0 ku+w(e04gynp1p0u 1/ w,njhzbs s a frequency of 540 Hz as its third harmonic. What will be its fundpp(u0 11mwyzs40+ ukn0,uejh wv/b ng amental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middl*)7elqiki) m8 v;b;upe n7igw 7vx ex.e C (330 Hz).*) 7ie x vx7. ki);q8eipv7uwngm ;ble
(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 e;n. ,uw:+plz8,,x huym vflms gv2xr- mits middle C (262 Hz) when the .2ypw,sznu vr,hm8ug ;ll+m-v:f ,xx 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 atc*w+t tw s:jt1 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shouldph1 zct6g0m,uasc: z5 the hole be that must be uncovereha:6cp z05smu zc, g1td 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, 440 Het r5 d4fh.m e he:5zikbab.ox:90 w0xz, and 616 Hz, but not at any other frequencies in between. (a)f5 e5:ixr m0:0..ae9 k4 ztwbhoexhdb 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 endszrif17 lr 5l .nvv7f:b4cty5v. It resonates at two successive harmonicsr:1.flv5v fzcib 7n7vt5lyr 4 of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 uaa*6s5 5iy ll$^{\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 2.14-m-long orgxg; gy/ +ii,it.vhe5a lw-f6gan pipe atg-g,5w/ 6ig +vlxeiia yhft.; 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal isnqkqh9m 8, p4d yi16gsvpd2zzt) r:w et/y9h ( approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequen4y t19: ih,wer9dq )pgzvt/qk (s2dmzn8hp y6cies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears onp p 2x.m7,4jkcxy97ff f z;hkye beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is tmxk,;7jy 2pzkfy7pc .4 ffx9hhe other string? ±    Hz

  What is the beat frequi .pm2d7 e :m0g;3y4( bgzownnxcj (7brto1kuency 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, wc+n wr1 isc56ubqj*l ++aoqq ,hile 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 simultaneously, esbq++lqur1cociw6q ,+s5aj n *timate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuninaw 3mja ; hlt9qlfsc-g2*t1) vg fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational wmf -g2 tlahv)qs;*l19ctaj3 frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hzwnu0fr *fc*gkp-/:bk . The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recal:0/*-fkkur*gpf n cbwl Eq. 11–13.]    Hz

  How many beats will be h,-ckz v9 +fnw x6fc i7w(mnq8weard if two identical flutes each try to play middle C (262 Hz), but zn+ncfv(wm wi67xq k8 fw9c-,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 a frpubcoe :)fpz l r2d95)equency 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:f 9 )5 pcrzuelbod)p2 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 pers pfie zlk 5v,sq65amqmnk).* /on stands 3.00 m from one speaker and 3.50 m from the oth*qk) lz5m .sk qa5f nv6pi,/emer.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tucoi8;ee.:dmu (nv nh v0o1lh )ner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must beu:8 il1envo o.h();d mc 0envh the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 ay ,rzqx4m(/ebq7ds 5m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 /,4mqyqra x7bsz5(d e$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fi,e*3v1wefza c3z )qchc5w)r d re engine’s siren is 1550 Hz when at rest. 5qhr cz)w1eaw)fdcv33e* c ,zWhat frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eng9y 0mw mf22:s8ts2/:javr+dqx psj ykine whose siren emits at 1550 Hz moves at a speed o q: +v/da2tyjj02yk29smw8xsmp rfs :f 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movl0pu.vlsy5rs vn- r0 ,ing toward you at 15 m/s5ysu r-0llp.,rnvv0 s versus you moving toward 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 nlnl av6bo iw07(ndh8b938 l5mf,fa ksingle frequency horn. When one is at rest and the other is moving toward n aivn 3ba(ld f ,m8l9hn7ob658lfw0kthe 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 rec+p rf-ondv(j 7eives them returned from an object movinr7v-n od( pjf+g directly away 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 it flies, the bat emits anl;xy07.uu4 ddv -uf uz ultrasvuudfxu l7d0y z4.-u ;onic sound wave 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, 0l2w2r: xas hda tuba was played on a moving flat train car at a frequency of 75 Hz, and a second idena22lhr s:0xdw tical 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 rcpr( ;or v4w5to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sou4r;o cr(rp5wv nd in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr lwungvx8wo q -8t(l7+equency $2.25 \times10^{ 6}$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 9 1 srf/-jjg -5hmj.q0e) dmdaddva7 r570 Hz. When the wind velocity is 12 m/s from the north, what.d1 ef -)qmamdjsd /jhr79a 0r-vg5jd 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 movin0;grdod; ckriq :3 1yxg 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 of sound is 310 mhba;8gmer*boo + * /so/s (a) What is the angle the shock wave makes with the direction of the airplane’s moa*o g;h/*r8s+e bo mbotion?    $^{\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 sp )cz(ur-c ta(veed of sound is only about 35 mac( -cr(t zuv)/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. lo (uoixe4 k48,;g vbbDetermine the shock wave angle it pro bbou, ilvk8(;44exo gduces
(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 sxi vhrj3 3)v (bxw*g*m4s7ge$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plancw )mprk4 3em(e exactly 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. S (wp )kmce3m4ree 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 tud ur ,wv(q21(mqe.g x/ixl8 20,000-Hz sound pulses downward from the botig ut8 dxq(l,q.e1wu/ xmr (v2tom 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 tr d r8 xrk0mv,6f)*cqvhere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displaxdh- h7w3u8xemo-7cty called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are opx 3uhcm-wt x77heo- d8en 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 pcml i*uw :y:+,llw- jfrom a person makes a sound close to the threshold of human hearing (0 dB). What will be the soc*:illjpm:uw ,yl -w+und level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound x 7i:we(qec fe .r/bg4and an 87-dB sound are heard simultaneouslg4rbqxie(.we 7e/: fcy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 q5lex*c )/k wgdq8y qjn6c)n3dB. What is the acoustic power output (W) of the speaker, assuming itg 8jdexyc k3nwqc*q/6l )nq5) radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 H n k3(illo(/f/u4mun/c7pwf fz. The power output drops by 10 dB at 15 kHz. W (3(p/lkl wu c /ifffuomn47n/hat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices gl dke f8)pg.x8t:i-rover 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 pglrdk8)g.t8ixe -:f human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, a.iuoq) ev2:-l9z dz j$\beta$ 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 f+o pd93t6 zh+l:qgton) u ;,ffwxr a*zrequency 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 +dq/l58.wmdo vch)cofrequency of 440 Hz and8h+ )om./olwdd5vqcc a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verticaawb,j vatsy3,/:qmo 6o4 /vmnl 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 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 frequen jnw,a3 ,tmmv/ b:v/qoya4o6scy of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is qt3a. ( mg;-fmh1 aif( 8mdrqzopen at one end and also 75 cm long. How much tension should be i h - q( tg1a.irm(zadmqff38m;n 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 loop knw t;/ a l3.medq.4rv($\frac{1}{2}\lambda$) 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 coming from two source18-zhsy p3m7 wmi3oxd)io z /ts. 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 do/w-z8i3 3t)mio1pxzsh y7 m 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.h a6wx7f 89uleq tah28 One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mov 2t8xheuq98fahw 6al 7ing train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. A).q3ov6-)v1 :dveyrrs kk fpx jp;i4 wfter it passes you, its frequency is measured as 486 Hz. How fast was the train mokvp-6 xr :.jsvked)ip; yfrq1w43 ov) ving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed f2lz91o)g ;6flcuh(g svu) 42yex vubof cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast ; 24bzv f1u)(oy gxf suc6eh)gvlu2 l9is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequee( ;yxx0h6mqfz b*zi+ncy of 11 Hz. The shorter one is 2.40 m x;y*(+zxehb mzi0q6f long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car a : irwlph*.tz)mz .kc.s it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. Ifzklhmi* :t.. pr.cz)w the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s whata nx*on;hv-:l beat frequency h l-;a:vnx*onwould 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 whwz9j. yb0nc (oile the 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 detected by the bat after that wave reflects off tojw9(cyzb 0.n he moth?    kHz

  A bat emits a series of high frequency sound 0,yk7t jniz k)foxt*7 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 be detected by the bat so that the echo from one*kf70nx,i 7y kjot) zt chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. y/rvl8 b) ks+q12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The srby)v l /+q8kmost 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 1mzhz oa8*mc yyjy2*h6.i+1/ krk ufobe compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. zhy1+ m yhok k*rm62 ijc8.oyaf/*zu1Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender sekz6 0jhfkx)1s/s p4aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. W /sz14)f6s 0k sehjxkpith 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 hea:orh,j7dt) ltring for the human ear at a frequency of about 107t,oljr:h )dt 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 the gpg7nm 0;u :qbm2sm 23n*almj pround hears the sonic boom 1.5 min after the plane passe p * lqnjms2gm 0b;umn73p:2mas directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 7235 x/mrnuegfegum 604pin 0 bca;xs15 $^{\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