What is the evidence that sound trave y*;-atbb;7gcqe83 :o(rcmok3x jpmp ls as a wave?

What is the evidence that sound is a form of ene qt/ z u8nnkd+ks4n64urgy?

Children sometimes play with a homemade “telnc .7g(kj j(mcephone” by attaching a string to the bottom(kmc. n(g7jc js 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 airp2b9ap2cb)+vxti-4 n q g; zxw into water, do you expect the frequency or wavelength to c;4+vqctn )ix2z bbx9wp-g2 ap hange?

What evidence can you give t -ay3hoj-*sm epk (-xghat the speed of sound in air does not depend significantly on frequhe -gjy(*xo-ksap3m-ency?

The voice of a person who hasj8wx7 :4r o qmrglf 1vjqg+(m9 inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the1p1zj8k6 d nnc w+mvnff:zu89 pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitu6+by ijvm/ p6hxt; *juadj-:fde of sounds in various frequency ranges. (An example is a car muffler-j6ba +;/p*j6: xhfijvty ud m.)

Why are the frets on a guitar (Fn4 xv5d89dqn jg6gti*l s +x8o 7yb4dbig. 12–30) spaced closer together as you move up the fingerboardi bbt9vx6nj dx 4dyl ds78q54 *ogg8+n toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but c e(ph3tr1gq5jyq38u2fh a ly;annot see it. When it emerges and you do see it, its sound i2;5hyqaq1gy (er8j t 3lp3fhus suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wtgjvfmu8 g bry7s9v,/ /u f27ghereas beats can be mgs2jt 7 ,y/7frg89/ufb v ugvsaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of thof2m .y0t6 sizvpg: 8ue speakers were lowered, would the points D and C (where destructive and constructi82.y0 g u6zmtpv: fsoive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people ws8 ydbeplya +)(rlh;.ho 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 thelp.bes;+(y)a 8r ldy h 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 b*-tc)3abq5 mti eu.fv e thought of as a superposition oftvq.c5mt i)b eua-*3 f 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? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samez(4 wjixv9kw*6wpnu7- (jxr j direction, with the su 7zxn (vkji49j 6ww(j x-rw*pame velocity? Explain.

If a wind is blowing, will this ajn2vgh9qg 9srdx+/qo ;- ts k5lter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chanj9hndgqvs -2xt;qsog+ r /95kged?

Figure 12–32 shows various positions of a child in motion on a swi9lm/02s l/oinrx 7 s cak(:a8qy5 jdbdng. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whia ad: 825okm/d l9q7/0srxy jln si(cbstle? Explain your reasoning.

  A hiker determines the length of a lake by listeninex2o )1wiin u9g 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 length ofi i91e 2xuow)n the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the6h1hea9 xmx :j 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 12–1) and does not vary signi 1h6exx mj9ha:ficantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airgmr1f8y e1fuz6 l z;id;bs*z) 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 k3yy(vdd.rj g jl7f.3 drifting just 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 t(f rgj7d. .v dky3jl3yime elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from cbxvit3mkhcanv3 s 1 + 72y-r2sv7ez3the top of a cliff. The splash it makes when striking the water below is heard iyavev1c+xhts 2b3rm-7v z 273nskc3 3.5 s later. How high is the cliff?    m

  A person, with his ear to the gyb/hh,,-s idwac( 6d qx t8,rlround, 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 th ,hd6q8tayxibsl(r ,h-, dw/ce 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 one mileai8r8gbud 5c; of distance by the “5-second rule” for estimating the distance from a lightning strike if the tempe uba8dr5g c8i;rature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? rgkn zs x931hwe*mh, (   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 sou7l8h6qf7pww h nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producekwt9bia372d wgwde4cm k 4: q6 a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add icd6aww m32kde7bgq :4 iwk49tntensities, not dB’s.]    dB

  A person standing a certain distance from an airplaneo f0nxk/m wzk-yh*5eo,zjzse+nl 52k/nq4o 6 with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What so2+oyw0jx nes ln6 4o5k- /fzmkq oezz*,5nk h/und level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for6v exl0 7rvf9 w6yqn3o a CD player it is 95 dB. What is the ratio of 0wl37v6 yx9q fr6vnoeintensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fp)- m4hk*yhpfrom a person speaking in normal conversation. Use Table 12–2. Assuhkmhy *p4-p)f me the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area iymk)h8wx oomh9 3+y )us $5 \times10^{ -5} m^2$ (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 9 a2wv7 s5iawxd5( apiiu) up9250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each u (vw9ipiaa p5u s527)i9dxwaamp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter ruu gnz *5d 2j:mny5qdp8 a1:viegistered 130 dB when placed 2.8 m in front of a la8 g5v :5ipmy :j*1ndud nzq2uoudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level* zd6b q8jm hs5;s az9w2bk2zk of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this ajs ;6 wdha5 8bbz2kz k*mzsq92mount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (u9/nt4bh m ru1.n7dll+yf j3u a) by what factor will the intensity increase? Increase by a factor ur/dn hbt 1ul3lu n 9yf.7j+m4of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twi: bvrjz wf. aj;1f9rx-n-8ydqce the frequency of the other. What ir-d-ybzw8ar :19xf.qj ;njvfs the ratio of their intensities?   

  What would be the sound level (in dB) of a soundt9pul5s7hub + wave in air that corresponds to a displacement amplitude of vibrating air moltb95hps 7+ul uecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level s+lky )f7k 9f2dl xibi :;7,k6hrpobnto seem as loud as a 100-Hz tone that h)bibxlhp 6fyrkf+ :7;s ,lkk d2n9o7ias a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest fk 1aq g-ed;4knrequencies that an ear can detect when the sound level is 30 dB? (See Figk4g1 q;-nka de. 12–6.)

  Your auditory system can accommodate a huge range of sound lhv /titz+f) st.1qom(if x v(9evels. What is the ratio of highest toi( t.ttx/q)1+ (hffsv ivm9zo 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 frequencnviw;hx*c ) x0+r8blyy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wha+*8v) ilr ny; cxxwbh0t tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three orr*xlax).7 ojyy)w 18sq8 sxaudible overtoax*).srxo)7lw88y q1 sj oyx rnes 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 frequenemez+yuek x7br68.gij(yo , ca 68.d hcy would you expect from blowing across the top of an empty 7ie6a8hzxc.ydy ,eku8(mog .r b6e j+soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ w0a/k91 howewq1*.tlvi 9nek k ith open-tube pipes spanning the range of human hearinga1ek0/*9nte k.lww q khov91i (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its d8pvn5v b/1gbkb:a p lwb2f+q1z13te third harmonic. What will be its fundamental frequency if it is 1bbz1bekbvw/l8p+ 2a 3fqv5p:dnt g1fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7.g k0un.4 d3xj2sm nra3 m long and is tuned to play E above middle C (330 Hz)mrg nn2 k.u4asx3 j.d0.
(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 middlhki: ijt/m:bqhg87z8 e C (262 Hz) when the temperature is8b tg7m:8 kz qhjh/:ii 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 atg f2twa bk40p2 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 Examplnv(fp(mwf03isab d v ).ld +74f0 gpvle 12–10 should the hole be that must be uncovered to play (pb04dvvl fdwsf7.l(n0 +vaig3pf m) 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 resona2y3efhg3xz(jucu 9:i te at 264 Hz, 440 Hz, and 616 Hz, but not at any othexih(c3 g9eu 23yuz f:jr frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both end4cg9km:5de sz9 iw.xtvw8i6 ks. It resonates at two successive harmonics of fewi4sx8ikv596g z. k :mc9twd requencies 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 d j67q3.kprdjdm0 6 *,cli zgh$^{\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 audiblm osdg0k. me:2h4c/ vve range for a 2.14-m-long organ pipcsm /d 2v4g.vomek:0he at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.h)+5rm8 gub p.amwzu05 cm long. It is open to the outside 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 relationship of your ansmu )805wrahz mp.b+ ugwer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one b1ykx e*uk dlazgk3)f3 h25( axeat every 2.0 s when trying to adjust two strings, one of which is afu 53a(x13 lgkkx2y hdke)z*sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2 mi7+1l-lrehhx pp4 d2-xw s6w62 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 operatesf;keru 8fksn a(tffo -2ayf+f +.5;nq 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 5t f5ka+(fnqu-k. fs+;ea8f 2rffny; o 000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fornv9szs/n/ us8k and 9 beats/s when sounded wit v s/s8sz9nu/nh a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Tyafm93:r ff m;he tension in one string is then decreased by 2.0%a3m fm:fy9rf ;. 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 identicaln76.s6b xqnfwwz0 2oh9zb *ku flutes each try to play middle C (262 Hz), but one i. xsz6*z9hq wfbnkwun26ob7 0s 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 af-w85 yeiw )96sjaxifrequency 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 f6 fjyw5 s a)8xw-e9iairequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stu 2lrltfjt1jvm 2 n709ands 3.00 m from one speaker and 3.vrl tf ujn7 m912jt20l50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are suppoc.ua8,wk5mm qsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratimkw, .muq8 a5cng at 132 Hz, what must be 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 m and 29 l4k7ew e1roiqo,u cicc2 32bj xp5l*.76 m in air. How many beats per second will be heard? (As2 * c79e35 lbeo2wcu ,crii1lxok4jp qsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaic8hi8 ft(8+k :;uhpxg.erl zhc d;q* on fire engine’s siren is 1550 Hz when at rest. What frequency do youx+iu 8hh.z c8k;:e8;gtd( *pr qoc hlf 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.ka -ku(i.mwb you detect if a fire engine whose siren emits at 1550 (bkuawmk. .-i Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movi1(qoihh9 hj4j dgus7 h+oz+.ing toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequend+ui4g 7 h9oh(+jzsqi hh. 1jocies 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 urt/(xqj:e bh)fp1 jy k )r-g2single frequency horn. When one is at rest and the other is movingp 1 2-g:rjfeq/hy)(ukr)x jbt 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 bn )jgj5;pxgnjsk aapdu- 1i*d5w5 2 0out ultrasonic sound waves at 50.0 kHz and receives them returned from an objecnunj1wg5p* 0- b5sjikgjda); 2pax d 5t moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a se+9dsvi aw45fb. ;pnh b/gl1/0vpniwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Whapvva4bg. sp+ h n5id 0swe91;n/blf/it frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played i-f vahi,*2 ebon a moving flat train 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 freq2biiev,ha- f* uency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usesip 1-,x9mzpbz ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries apz p9mb,xi -1zt 2 cm/s directly away from the sound source?   Hz

  The Doppler effect ub3uvfc a- nux7bw(bn77.m( prsing ultrasonic 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 eml ih9.0ep )3sei/ phffits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, w)3i /hp 09lis.efphef hat frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed abzo;i 2s6 p1 fleuc(8et 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 o0h )pw4mg* qtyxs *pp;f sound is 310 m/s (a) What is the angle the shock 0pg;hspw*x pm 4)*qt ywave 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 w yjr.zaasv; pnv452jt r13v 2fhere the speed of sound is only jv n3fv21 2s4j.atarrvz5p y ;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 bmy,m2.*f +7rj4tcv2t x uzut 8500 m/s strikes the ocean. Determine the shock wave angle it pu2uf ttbty2*vmjxcm 7+z .r4,roduces
(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 2fbd)i; rk)djo bvd /;$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and s2ye i96 x6wfsfee a plane 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 tx 269yi6fse wfraveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound puls2g7fdq) t-d:qj qvwna/9 )w+ y8lyvakes 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 is the minimum time between pug8) fvyq vtqljkwdnad+ay :7/q -92 w)lses (in fresh water)?    s

  Approximately how many octabbd4if. 2; h *5 *dqrsv6ngphmves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calleu/f+ b: o-7aj2b ky2: bbsdjjhd a sewer pipe symphony. It consists of many plajah -yb fjdkbu:+bs2j7bo/2: stic 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 makes a 8qne5n;qbrcz* gmzm pcs5v*mk5 3 +c)sound close to the threshold of human hearing (0 dB). What will be the sound level og55c ns c* ;emqc zzqb 3p8n*vr+5)mmkf 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB + ).ql mv 3m.xfe1h:eb udoi+xsound are hear:lm +)d..h3 eemvif buoqx+1xd simultaneously?    dB

  The sound level 12.0 m from a lour d8l: .btaxd(tofl+ )r/)klcdspeaker, placed in the open, is 105 dB. What is the acoustic power outputfkxd/ (+l8otd :)) brl.l trca (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated awo/q:3njm ut -h*mj)gh n8aejp98 9abt 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wattspn j 9):h/wthjgm-uoea 9n *b j8m8q3a at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thei x--ip wg8dgp2n/ud-b r 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 bg-pw-ni2-p 8gxu /d dear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, -9a ocjmes )nla 14an3 m-xc3p$\beta$ 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 viol wzzxlb/e+*f jla,t6ofd7q x 5 fr--7tin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a f wdmvmuq/+*ohf*v0 m)undamental frequency of 440 Hz and a mass per unit le/mmh*uwv)+*fd 0 qmv ongth of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wiy c9 qxep/5x3vp h(;cnth water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the (/9 5hnpvqy;xe ccxp3water 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 iskms 7de);j b41i0dw7 p-tufrf 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 reson 4)em tdk7pbf1j du0- wi;rfs7ance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as ooh(6o9f.*pbcu6 m: mlcfj0zvne 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 tone in the 5ltnl 2j .t1zzeaf9 f3iuqo:vy+2 t4 x-00–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the tw32- 9z.x u+2o1il y: vj4t ltftazeqfno sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whis.y ;elif8ns8w tles. One train is stationary. The conductor on the stationary train hears sle8f nw.;y8 ia 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 you is 538/ts05 9bfqz bj Hz. After it passezbf t5 /s9jbq0s you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate+ld onvj95yxf g;4nt . the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Su5;.yot n9g4 n vdflj+xppose 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, produma,l,-r hnp5h0pti i-v *:aguce a beat frequency of 11 Hz. The mt0 h igh-navrl:p5,*a,-piushorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mov3y-ey6* n1c6mqdu6p3wty uay ,xsyd. es 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 eyuy qaw1.x6dcp n6s,y *y6u3y 3 m-tdobserver 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 what 77 7dl0xpumyf* c -q th+*sxeb-sqqb:beat frequency would you7c *-qb bf l7 t-0*yhdps:u7 sqqm+exx 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/sku2+c y f)lg.2 ijwie2 while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wa +g2feil22.i )jkyu cwve of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. T2we)os9.9i,ta;d4gcj o u oowhe pulses are approxi cdi9o9u;o2. gos o,)ewtw4jamately 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 t l o+7 k2 k4dgnb3j ojufeqo0qh9j10x7o 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 most poq747gh1xo qko+kbedu 2j0jn9j lf 0o3pular 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 thtfnsi vh(7x xzko65:,e presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calcihx (5f 76 zsnto,kxv:ulate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singis72atue /z1iyv 7m +3p e1yembng rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod m71p7eiaz vu+ m e3ybet1/y2scan be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the ra9q89-5 bcdx* y de rzs3jo4ahuman ear at a frequency of abou9*x yjq83azb sodr ra 4ced95-t 1000 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 2oeurv tnq.r grj/ a+3; j;99fj.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the pr.g/j o+avr9 ;j3fjn t;qure9lane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo j ,yh,-f3:asiebl3yrqk*/e jat is 15 $^{\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