What is the evidence that sound travels as h9u( arh2vcxtc .i(i.4f9c h2zzj ke*a wave?

What is the evidence that sound is a form of enervfq(5hoyq*d awo imw839 *y1 lgy?

Children sometimes pl w006t lxsrn7say with a homemade “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).sl0xw tn6r70s Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes frr3f4c -c7 xwjwml2goy.9 qpz*om air into water, do you expect the frequency or wav yl.x 3pwzg9ojmf*q42-crcw 7elength to change?

What evidence can you x6lfe*t(1 c f0fv2ng: jhr.skgive that the speed of sound in air does not depend significantly0sek* chxf6 l1.( fg2f:jtrvn on frequency?

The voice of a person who has inhaled helium sounds ver .i6fttn vaby78p j-b6):yaa+ zih5bzy high-pitched. Why?

How will the air temperatuybzjyaw:ef3j0 6a/l4 re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amscq1pt3 2p+ uae ;siz-plitude of sounds in various frequency range3-t +2seiacpsu ;q1 pzs. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cp2q/w n3dedmc*; vm5ks2g pg/-rdk7tloser together as you move up the fingerboard e 2;ddm/3 cr 25qps mg-/nwt kg7p*dvktoward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it1p myr3*glq3l but cannot see it. When it emerges and you do see it, its sound is sq* ml3rlgyp3 1uddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to bnlljma6 yp) 76e due to “interference in space,” whereas beats can be said to be due to “interference in time.” p7jm6nl6 l)yaExplain.

In Fig. 12–16, if the frequency of to p2qrm*9d k4she speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farp4*92mk rdqs other apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wit glj(b (*ar wf8a3 bzkovzb)26h very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headp(6l wjabazz )kf(v2o*3gbbr 8hones 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 c+ y:w b)vi(boa superp+: )bvo(biwycosition 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? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obs e .fe3tea;)roerver move in the same direction, with the same velocity?.a f 3rteoe)e; Explain.

If a wind is blowing, will this alter the frequency of the )s;r1dnaa i 1hq-8 tzdgat q)jo:vl10 sound heard by a person at resgldrj n1-q10) 8hi;a ) za:tstdoavq1t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moti :8st ua xkzyp*b 84rxu3n,)qlon on a swing. A monitor is blowing a whistle in front of the child on the groundy s* )4t ub8 lqapx3z8xnru:,k. 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 k jhr),vc )3rlher shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 kl)h 3jc,) rrvs after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship2fuv:c r:r i: n ;d(uflc 4/xhyz2zda6 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 theru22rafn6 d:y /::li4xcf dvcz u zh;( 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 wavelengg r+x2uek( axr pbfyvea h:()xl-b 4((ths 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 aj)b 7 ,eblvid9 school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away dv)b ib7 9ej,l(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 stue)42pxx4o30d slc v xriking the water below is heard 3.5 s later. How high isx2ecd4p u xv4 xl0)s3o the cliff?    m

  A person, with his ead(8 cv))pj f2suii w/pa6qqy/ cxf6 r/r to the ground, 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 af(yi/wfs/a 6 6 cd)x/2q)vpurqjpic8part. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5lw(7;nmn:nk4 b e ;jvc-second rule” for estimating the distance from a lightning stri n:c7ebwj;4mk;nvnl( ke if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounwyu o x. mp6g5*,g,wvyd 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 whose intcbawe5g )48h6+ tyk ztensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB w,1h ,0gz)lay 8aq4hcwhlq v)j hen fired simultaneously at a certain place, what will be the sound level if only one is explodel 1)4,layv qhaw)g08hj c, hqzd? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpbr, cn 15lts/ ni9/wmqfb b*0ylane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pt q1fbb/9w,5/*0r sm ibcyn lnerson 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 raf7a6+h spix.rtio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and t7a f+6psrxih .he background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speb 41rl ;jls.hx*6 sylohjc+b4aking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere center4r+so *slyb b hjjll;hcx.164ed 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 str/ld ku/t1 t9wzm3u6us;y7qyhikes 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 more modest amplifier B is q0i/a wl hhvt.,:;k mmrated at 40 W. (a) Estimate the sound level in decibels you would expewa.qv/i t,:hh0; mlmkct 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 megue) soaq 2b/64,z zniter registered 130 dB when placed 2.8 m in front of a loudspeakb/g6o,s) 4nuzi zeq2aer 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 differ+7s ahybu++cwbg6sk1yp; x( sence in sound level of 2.0 dB. What is t uph+(1bbs+ g7akc;+s x w6yyshe ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intvfjrdo1g 96 s0ensity increase? Increase by a factor 60r1 jo 9dfvsgof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudeb t8mx(/h8 f,qf*tkibhak, i *s, but one has twice the frequency of the other. What is the rat8qt/ hfkmbk,f ib(x*h8a t*i ,io of their intensities?   

  What would be the sound level (in dlm gubeuwrw5 v wu /+7kqn5fnb -;*g4:B) of a sound wave in air that corresponds to a displacement amplitude of vibraq/: g -7nlu+euw*w45;ubfbm w n5kvgrting air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level 3sracl,/xyy-to seem as loud as a 100-Hz tone that has a 5-y 3lryx,c as/0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequeu 63us :)bucvsncies that an ear can detect when the sound level is 30 dB? (Sec ub )3s:6vusue Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound n x3;j hv4e2gulevels. What is the ratio of h3; ng2 hjevux4ighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin cixrhl. ccte/6+ 4dk+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 tension must the string bet 6e k.ic+4rdx+c hc/l placed?    N

  An organ pipe is 112 capm/+rsr ,a ign4f8vs-62hng6 eiu u6m long. What are the fundamental and first three audible overtones if the pig8hv ssri4+6u-6/n m,pi2g eaarunf6pe 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 e- j 1lqlq-0(4fb cfv w7aofkn9xpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tub9qfn1 l j-l(oa bkfqv-f7 wc04e?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe ord, 1/uo y*x. q ega4x+bqbu.plgan with open-tube pipes spanning the range of human hearing (20 bxl+p.u 4d*agq1,. oxyb u/qe 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 j+oo l3d 19s2y7odh lkfrequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered ako+ l32 719oodljhdsyt a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunat *m2 .qk9gn,r qw6lced to play E above middle C (33acgk* l wq6tr,92 mqn.0 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 ope78uf1 f, rvbqfn organ pipe that emits middle C (262 Hz) when the temperat f8ubf,1qf v7rure 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 at 2apc l,qr6hry2 bl 5ke ens+6*30 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ovj-**9 ztr d+ 0eghjp x:nsq6af the flute in Example 12–10 should the hole be that must be uncovered to play D above middle+6 x-n*gqrvj*h j9as d:0 ztpe 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 n w xws2xc0 di)s ;8e)( aftutf*y:bm:can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other freqax*(2ife8bwn f: tus0d)scm; x ):twy uencies 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 aa3zlg)hq z0 d,t both ends. It resonates at two successive harmonics of freqdhq z)alz,0g 3uencies 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 -/ +h(mg ezynxdzg0l6ql/ h m($^{\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 wit h,z.fz rrm).ln3mqr. hin the audible range for a 2.14-m-long organ pipe arq r3)m hl.r.,zf nm.zt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside atu7o):lo ssc ;ifpzyw 8;47hwlnn)umg9-h *hnd 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 answer to lcl)o tm*wsy7zh;wf;:gu8nhu9-7ip sh )n4othe information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two s.u sbwl1nvz+/ trings, one owbsu+.nz/v1 lf which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 5e;bjbv +c.xmm )eso 0Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brdn 8rg/cj5pu (s gzd.v21gt*dand X) operates at an unknown frequency. If neither whist.5dg2j8gz/dstv(1 c*pd u nrgle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3wzcb1fxx 0t,6a*ils pln8 . t:50-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fr6.8l*xn,cfawls p x tbz:ti0 1equency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29xhbiv/;hp:* rm6 pu7q l(qb *nl+u7go4 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency her *ih nbppohq 7u* 6l(: v7q+gb/m;ulxard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle * h4pq jomwl 1-t4lwj1C (262 Hz), buth4m o-llj 4w*w1 pjqt1 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 f1 2 tufr5kbd. w*xr)eurequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. b1x. 2 )utwe d5*urfrkWhen B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m fromslecj)( 5lgsng,vp ; ( one speaker and 3.l(5)v ; e,sjgg(lspcn50 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 supposed to be vibrating at 132 Hz, but a piano tuner de-61tw cm 0qnf*h0sx 65lowvhears 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 otherowfcx6mv tsn 156-e *0hqd w0l ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Hoc +q h9xqg5(a8po.pdqw many beats per second will be heard? (Assume T+c(h q dgp8.qa9p5xoq = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at reovr+)z m69lhw rvc(t7 st. What frequency d lzv9 )6 orwrvc+m7(tho 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 d7tu: (q.1,ik yy ka cdgcbklx 2u:k59if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/sck2kx, lk qt17cd:au db:uy5gy9k.( i
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving tj ui2(c:zcbc/q15lqmx gi:*mbap 0e1 oward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exact2q0bcmei /(u 1ic*xb1qmcj:a z g pl5:ly 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 +rtp;5 5x lwla+mwj, iequipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 155r mjp+,l+ww ti5lax; 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 c0is1 idjvn,pgue 3i )e f(d3f *aws;8ky6*fpkHz and receives them returned from an object moving directly away from it asdfgwc n8(; evppf613if*si,k juy 3da0) ie*t 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ult1 qv rp: b+vidg9zbw(;rasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the+9 ibv;w (rd 1pqv:gbz reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen+rc ;5mfuh1 z q( +cff(duukh(ts, a tuba was played on 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 frequency was heard if the train car approached the station at a speed of 10 m((;fur5f m +(+1 hqczfuhk duc/s ?   Hz

  A Doppler flow meter uj 2efl6 ix06w9mq zuafo(-a3g ses 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 at 2 cm/s directly away from the sog0emi3x6( -aza 26 uq9oljw ffund source?   Hz

  The Doppler effect using ultrasoni uu cooem+(,)uc waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequen(n.yifb(fg 0 vcy 570 Hz. When the wind velocity is 12 m/s from the northv nf(y(ib0. gf, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed 1rznwh7x y9. xat 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 t .ec+-)gqph cohe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motionh.) eo+-cgqp c?    $^{\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 islh -4qpoe9rb ,m2d +n-xa 7pxs only about 35l4b9n,mpp -2a q +xosrx de7h- m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Deti)p(ucm8s;b,ndn yql+4s ) voermine the shock wave angle pd ncs;uonli+)m8),sb (q y v4it produces
(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 qhaih30sgpe74n1 h )w$/theta$ 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 1.5 km above the ground flyxo ed6)1c; l f+g+a7nr6 ddlleing faster than the speed of sound. By the time you hear the sonic boom, the plane hlleo )+gcn1ex7 dlf 6 d+6r;adas traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward fro udiqp4o7 8,yzm 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 pq,iuo48pyd 7z ulses (in fresh water)?    s

  Approximately how many octaves arclu d-s0tc* t/e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Iuyy: iyww+2 fp(k2i1 qt consists of many plastic pipes of various ley+i w2:fk pqu2yiw( 1yngths, 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 sound close to the thresho fxno k i/x9fi1x)s6t;ld of human hearing (0 dB). What will be the sound levex6/f xxn ;fi1)it9kos l of 1000 such mosquitoes?    dB

  What is the resultant sound level w19lem.g(oa fphen an 82-dB sound and an 87-dB sound are heardf .aeo19m lpg( simultaneously?    dB

  The sound level 12.0 m from a loudspeakzf ps/de7h+q6uu 5mpi3a7 c,jc:+epger, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directionsu3dpej6z,gp:qh 5fic+u 7psm7/+ eac?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The p)(d6t 0 tu3+f,cebzqhau + xkiower output drops by 10 dB at 15 kHz. What is the power output in wa u ek63a()0 fciz dbx,++qttuhtts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective( xlwwc91:waqo4j 2 fi devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB91i jwx4fqaco2 wlw:(, 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 communications systems, the g2js /;fjfjk6cb/2k3 g npju g0ain, $\beta$ 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 frequ0sxh0r(n3h 59 u zyrdm6 i*4-fwupp dqency 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 betweenjenllwd. 8 y78 fixed points with a fundamental frequency of 440 Hz and a mass per unit e8 8l7wnjy d.llength 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 set8unexutfy96cp 8 n/0,f l0 tab(s,h ti into vibration above a vertical open tube filled with water (Fig. 12–35). The water level is6x,0(tuus tp abi9e80lcnh tf, y/nf8 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 that is open at one (fts,mfrq/vzz g (-:j end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with q(f:/ mtr s(z g,zj-fvthe third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as ,jjj 4 xr5k,:e+uoijz 4.qsj kone 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 500–1000-Hz range coming fx t4+2qc crq)orom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound +c 4to qrqx)c2level 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 on thesfi 3vv1;ut-q stationary train hears a 3.0-Hz beat frequency when the ov1q u;vfti-s3 ther train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whis;;2pwim /,w.vpmafn htle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinghm/i; .n mw,wp2;pfv a (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of n9 :5 rgqbzrtbwu,:l0 cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppozrbw50 bulg:: qr, n9tse 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, soundci1 ot jey)r q1:v70hting together, produce a beat frequency of 11 Hz. The shorter on oy:)t7t1ie1h0crjqve is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a2d4 qg( j6m 0ciz 7/woci. zwqcz25et5a m+zfw stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they hd7 5joqzgc (02zmq.mz4w +c2c6ew/5zaif t wiave passed him, at C?

  If the velocity of blood flow in the aorta io, z20pg(e pijs normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assumei p0 jg2p,(ezo 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 wjny1 fu-a afjn21+u)c9agt (g hile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 5 j+-tn 1ayn9u(jgc2agff) a1u1.35 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. z(g t ;uq:vzx4The pulses are apprgu zvtq( ;z:x4oximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to-auj 2zilg26qr2- phl 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 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 wh2-g-rulpiq2z a 6ljh2ich overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can bez. *q4imxv h9g compromised by the presence of standing waves, which can cause acoustic “dead spots” at thmz 4q9h.v i*gxe 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, callek k3 w1lhit13dd “singing 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 can be made to “singdw3l1 1 hkkti3,” 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 thresho ytte5 /fa5a7qld of hearing for the human ear at a frequency of ab a5a5y tft7eq/out 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 2.0. An observer on thrg ze7bnsil jb8 2:f/+e ground hears the sonic boom 1.lr7nbej :f+2sb/g8 z i5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat lq n 9im k;2f6v60ai25ac fmubis 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