What is the evidence that sorzd*.rnh corfs)qqzr-2 2i6 4und travels as a wave?

What is the evidence that sound is a form of energy?6nm,kh p+o gy*

Children sometimes play wit2p ,rhtse19 n(hmn0myh 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 (F (,2yn0r1mnh ep9tsmhig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from a/54mkwxkb ;h dir into water, do you expect the frequency or wavelen5/wk m4h;dkx bgth to change?

What evidence can you give that the speed of so:3yfvf1p r5ovfyyh; /und in air does not depend significantly on oyp15 rfhy 3yf;/vf:vfrequency?

The voice of a person who has inhaled helium sounds very high-pitched.cu 7.dqzi 5x35r gepx()t8xcz Why?

How will the air temperature in a room affect the pitch of o.:xo --idn3e vlrn-f ny.cu1lrgan pipes?

Explain how a tube might be used as a filter to reduc7sur f(-ic/yn5zwbp*e the amplitude of sounds in various freque/5b rn*z u-ip wf7c(syncy ranges. (An example is a car muffler.)

Why are the frets on a guitar (;*tyl-fw 1bm zFig. 12–30) spaced closer together as you move up the fingerboardl*w 1tyb -z;fm toward the bridge?

A noisy truck approaches you fronnqg) l5jsi87pg18xl m behind a building. Initially you hear it but cannot see it. 7i n5q81ns8p lggx)jlWhen 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 sail 1wi: qceqtpc3b o*s, )6aml.d to be due to “interference in space,” whereas beats can be said to be due to “interference in tip.sclw 3 16qotalc*q, i)eb:m me.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, w3n6r rpa*yu5tould the points D and C (where desu3n ty56*rp artructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in a4zgt2m9 2svfk0 u5of nreas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, ikot42 mn0sguz9 f52f vnverts 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 s;lozj501 y ioluperposition of two sound waves with slightly different frequencies, as in Fig.1z0;5loy jlio 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 shi br-rtsnl 2o .2w:ikmk-i- ,:fayvx6 kft if the source and observer move in the same direction, with the same velocity? Expbokv2k6, - -kwa:rmn :rl.fts-x2iyilain.

If a wind is blowing, will gcdosie,)+q 6this alter the frequency of the sound heard by a person qcio+s e g6,)dat rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions ofhdo 7p6f873lp/dbuef a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear t 3df6h7e p/lb8upf od7he highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lae hi19c0y,wlistening for the echo of her shout reflected by a cliff at the far end of tawc, lh0ie9y 1he lake. She hears the 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 th 4)hsfvrnbrx, 2tvp7uiz 6+g u0 ey7n1e waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound nv 2fgb 7v4etr6)u +n7,x10sriuyphzin seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airh 5:ue2v:vowpybn6 j- 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 dah056a: wywu zd-r8zto*b.- elq scv/cy. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfic z/ywdc b -t e-06zuro wlh*5q8:.asvre is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking(mebrl 9q.qj) the wamj9r.lq b) q(eter 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 n fzk(-g+rbo7uu5 bs3he concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, g7k b3f r5ub+so n(u-zand 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 mile of k rmucbfk)3yj -io(a v)j16y; d.l lr3distance by the “5-second rule” for estimating the distance from a lightning strike if the clr)y jiao(u)3.b rjk6v-;dy1 f kml3 temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a )h5owzb4f0,zzhuyyb d y h/ wxl- 8e9(sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whos si qb996d9cfoe intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fia 8i -q(4wmp+vmavrs (red simultaneously at a certain -sm v4a(+(awm8 vip qrplace, 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 equally noisy jen)p h.qx,t.3 pxr5jt3dex5by t engines is experiencing a sound level bo ,.hpt) pq3jxb55t3 x.d yexrnrdering on pain, 120 dB. What sound 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, whereas1 uxzi xfz;-v+uzr;) 7syizjd)c1q o8 for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise fivzq8 df;1xj+ru1o zs-7)yx;z) uic zor each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ouftk /l9/qjvmlm z1i -7tput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound sp1m l7iq m jkz-/vlf9t/reads 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 strikesybssb7nx6 uiqni99 -: 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 amp-q0lobzy 9 ;1v .kfjiolifier B is rated at 40 W. (a) Estimate the sound level in decibels you wokq;0ib1 lzvo9fj- yo.uld 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 it4z j7 gk0ac/dB when placed 2.8 m in front of a loudspeaker on the stage. t4kgz 7/ij0 ac
(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 detec( fst, 7qv*hclr sda irby;.;0t a difference in sound level of 2.0 dB. What is the ratio of the ampl ;vs y a ;.cd,f*t7bilh0rqrs(itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave jm anu5+1l 52qvomq/on)p0bt is tripled, (a) by what factor will the intensib55 / m o+u0pvnn2j) qaomlt1qty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicf9.mnt1bge / 9it;bzdlab*i ,e the frequency of the otherbt il;f tae9m,/i 1dbzg*.bn9. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspond* pa4m-fltgq(sl y 59ah9r-x fs to a displacement ampl-9hf( fmx9l5 l p-sagy4 ar*qtitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a csi+i px.wcans)q*;*100-Hz tone that has a 50-dB sound level? (See Fig. isc.* pwcn)+aq;is* x 12–6.)    dB

What are the lowest and highest frequencies that an eaihyog 6s:int3 c wp391r can detect when the sound level is 30 dB? (See Fig. 13hsywgt 3i:np1 6c9 io2–6.)

  Your auditory system can accommodate a huge range of so-jh w j)g3pq5ound levels. What is the ratio of highest 5w-go3p j q)hjto lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. Thectd3433 y ylqyj+z)n) opg6v e length of the vibrating po33zy)y43)cqj gl+e n6od ytpv rtion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firsts(.4o, vfixy n three audible overtones if th(,o4.fs yi vxne pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would0c ir 59mhjs-h you expect from blowing across the top of an empty soda bottle that is 18 cm dee5m ijs90hcr h-p, 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 with open-tube pipes spannpf 37ko3jz )zhing the range of human hearing (3 3ozh7)jp kfz20 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 agl q9+ k*+yvknvf zk;+s its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its or*+qk9+flgvkkz +y n v;iginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abo4:o5qdfa:fac5hxyd 7 ve middle C (330 Hz). :7: dfqcfohy4a 5x5da
(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 emi b4eepnmb 1d.3ts middle C (262 Hz) when the ten4 db1pmbe3. emperature 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 4h ,-a3xwsrlsmjf (2r20 $^{\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 should the hole be*bqsyb6k i.d;3.prb z that must be undz.bk.6r pby 3bsq *i;covered 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 Hz, and 616 Hz, but not .b2ba(lhke5 y8f t c.sat any other frequencies in between. (a) Show why this is an.. abhtlc 2(8 sbfy5ek open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonatesiw;xc t7ok 2+e at two successive harmonics of frequencies 275 Hz and 330xi7c+ ;2eko tw 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 +d3mba(p/jpm g5oh3cz /h y2a $^{\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 :qcl-i v6z-vl ul, .mljye*y--m-long organ pipe-ll:6 zml,j cv uvy*l-i ye-.q at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximf3sk x(opi;q x9ou82d wj :f3cately 2.5 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:q f8;fx2 k3cpo(usij w 3odx9 the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to wxu e0kh1 7akm.,3nfq adjust two strings, one of which is sounding 440 Hz. How far o3nk kh.af, 0 qew1m7uxff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) apxxvkz xf53ay9,3 w* s8 3dhih:6euuqnd $C^＃$ (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 (bra; kwo mh/s9dtmmw7+ x.nd X) operates at an unknown frequency. If neither whistle can bew ms7o.k/ xd+;tw9 hmm 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 350-Hz tuning foue70. cwce jm7he:u 9y89d -h/ivcjbe rk and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrabdhy8.u cw9ecjme e7j7ie u - v9:/ch0tional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequ8oy++ mno/w uo q u.suk5o/sa33w +aeeency, 294 Hz. The tension in one string is then decreased by 2.0%. What +oqaa +mewno e38kuou.u//o ws+s35ywill 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 two6h td;w / 1escafdlog(wq x/41 identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othxqwl(1e/d4tdac; hf s/go61 wer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency q15v5f /r 7tao8wrqzq of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and Cfzowa78qtv5/ qq 5r1r 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 from one speaker an8a p7v/t9pmi qd 3.50 m from t 7pi9a8/qvmtp he 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 suppos4va a*s:p4 ilc0n(tx led 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 vibrating at 132 Hz, what must be the fre4s* vx(a4ln cp0:tila quency 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 2.76 m in air. How many beats pea/(1 38cvg qodw lbxsra/2cf; r second wia/sq1/c fvr d8gw( 3 aclbo;x2ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire ejs z ;:aeub l,l rh5hc*pcsp4crr0;m1:y*:uzngine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 cr m*h4z p l:uych;rpz*jre 51 0l;s:bcu,a: sm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do x5f4)uw pk2 ezyou detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32) 4x5euzfkw2p m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fre; yj;8y:w 0xazuh3 ,bbjn e28aspgli*quency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the8wx ghuepa,8zb2s a0jy;n*j i;b3l :y two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When,c+ylq*yi3kf 7w ia +a one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horykcf37,y* aq+li +wia ns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rr+sd x*hl:( adeceives them returnxad srl +*:dh(ed from an object moving 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 p9:ulvhq4mhr17 bvcev30 2lbbat emits an ultrasonic sound wave with frequency 30.0 kHze4uvb9m2q3l v1h:0 cl7rpvh b. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played ongkc+lqsjg,j n* (65sy p ;0whp a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest g5(sj ,j*c 6kgln0+y ppwqs;hin the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speex1wo4 dzo 8+a.uns ,pfhj 73agds. 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.s8w ,uf g7pod+a3ah 14xno zj leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wau,1+6zlb kdq 3izw0qjves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity isn /mqes 63.rgd 12 m/s from the north, wha gm r3seq.nd6/t 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 s.mo xwqr t2q85peed 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 isf1-9 (a tnm mb avpxxvl*el ux4xqd t7j().i70 310 m/s (a) What is the angle the shock wave makes with the direction of theb txna(x9(mx7*i. 7xl-0 mvlftv)4ae 1uqpjd 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 ))7gb( gb+px)l rurfkatmosphere of a planet where the speed of sound is g )l 7r+u)b)r k(xgbpfonly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Deterd)r y/0:o3e*9h* q-ii znwymykpvh r+mine the shock wave angle it producephm :i -ke/*zrw hyydn9 oqv*0i )y+r3s
(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 g noxb 5hdu6;g1jkx6 4$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and i4 u /jq :ci/ rvkuxzl-aw-1v:see a plane exactly 1.5 km above the ground flying fasterv/uc/4i1klx- jzqa iv- :ur w: than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device tham vz: asrg4z +/s6p/xrt sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects //64+rx:pmv gsz szar 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 there in the nj.)-erwb,fnci28lg6 /h prt human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It b2 y,+ +ximsel .:yi0yt1ol xfconsists of many plastic pipes of various lengths, which are open on both en2: m+ieb1y.+fil xy,x sl0tyods.
(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,eaw56oc0w )izb*+opt u, l0isz)dn c makes a sound close to the threshold of human hearing (0 dB)owdn le ti6b50 aipc0z, ) cw+),*uszo. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sor/upop2jb ;s +1d7 mp(/ qgnmjund and an 87-dB sound are heard sosj/ pp bpd n1mju7m/2q ;r(g+imultaneously?    dB

  The sound level 12.0 m from a loudsp 5z4j spdd1w.r;qkhl+5j1rnh* g j; uqeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, asjrw+z4jq d*slkh.n j1 p 1qg5; r;duh5suming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dro53 f ira7jf,z*eem pa) 3*lvdkps by 1 rv k*5ffld 3j)p i*ea,7emz3a0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective glg( llj/iixrm,dus (6x2* k/devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the avera/i m gu6lx,lglxr(( jk/id2s*ge 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,shxgk+ g32pa / $\beta$ 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 freque:n * my2ufm0kincy 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 poinwqg t y*-;g(xsts with a fundamental frequency of 440 Hz and a mass per us;w*(g y gq-txnit 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 int epd+rx,6ij9hu o1 puso k77h6o vibration above a vertical 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 7h+r p pdo6 k,hxieou1 j69su7frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.1 6sheq6m wild 7r*.a no);i*ul0 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (i oqwmu6e*inli7s) 6d.hlr* ;an its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observvontj3 )b uf,.za4n( cmxr f3,ed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sohub:5d2 qh4yubt1e g y)v4 -tources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequenc5to 1ut4: -e)vuy2dhbgy h4q by 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 wh8 i/n n 9jpc0q(g0yszhistles. One train is stationary. The conductor on the stip0hqj/0(9zn s8 yg ncationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachesx*)x1ixbo0a42gxo ,qs8 fwfb you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the*oxg1o sawbf bx)fqx2x 4,i80 train moving (assume constant velocity)?    m/s

  At a race track, you lp42v:dy .icjtn mc z6l)z a6*g*gtf+can estimate the speed of 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+ 64tpd zy:czt.vgn)l*fi a *6cl jgm2 straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produ0 kim ftw(rayq(e/nm*syu 449 ce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the oth 4smyfq u*9nyt (ekam(/i4 0rwer?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past 03cp(kq q( uunl bai;lh0pg98a 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 beal p8anpuu ;h3g9((b0qc 0il qkt 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;kx;r+c( v+tt ah 0un9hv;ix z 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? Assume that t0 rh9+t+vz; xnivc ;th;ux k(ahe waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying txe5 a*7v ervqf1j g93soward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wxg9f3ers 5vv 1je*q7a hat 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. Thh 24o:n,bmb )opb-dkge pulses are approximately 70.b:g-om2obbh k) pd, 4n0 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. 2wj iv 4,h-j *l c.u..riam1pdnlm)ln12–38) 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 most popular alpenhorn is about 3.4 m long, and itihj1li-cmml. na uv,w p.*n 4lr)2d j. is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pre d/k ,d.9fyogqsence of standing waves, which can cause acoustic “dead spots” at tdk,.dy/oqg9 f he 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, ca-w0/ pvk1owzux) r3 jjlled “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 “sing,” or emit a clear, loud, ringing sound. Fjw0/jwk uv xp3ro)z1-or 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 thresho0 .syahdh ns0+/kqpk2ld of hearing for the human ear at a frequency of about 1000 H. hp+dk0 q/hsa2kns y0z 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 th+fk yu4 nd 3b (aun+hk8j/tfbr8;dph0e ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the pladyph0f u;+utb /8b84nhr( kn fjd+3akne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat znfc- 9mp (ji1k/ v-o :7ru.gog y-rxeis 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