What is the evidence that sound 8tfk d:jp:pr9 ,4l-tw46:n elt jadfe travels as a wave?

What is the evidence that sound is a form of.j fq-gja2kl, c2ov9x t. wh4zy 0ru7w energy?

Children sometimes play with a homemade “telephone”.5 hvwss.:h-z)q:z6ln ourx-vf-sl kfef *b2 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. 12–2*-)s52x fsflh qun:w .vsezf:o--6kvh.brlz 9). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air eap fdt:lixno*;m4 0 8un8 )kginto water, do you expect the frequency or waveleng8x t 84o*mefupdina : klg;n0)th to change?

What evidence can you give that the speed of sound in air 5yj;6jms *elo:4zwf:r;ajw t does not depend significantly on freque4f* wzjtm js6r:ly; ;awo je:5ncy?

The voice of a perso 91-dunlad k(dz0y6lgxvo pfq07*)mcn who has inhaled helium sounds very high-pitched. Why?

How will the air tempe j8zqj(iv k(zjv-5d:otp x 61krature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a fg.i)s(n (bgt filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.gn(.sbgfi) t()

Why are the frets on a guitar (Fig. 12–30) sp9r3he.(tpz qc2q zmz ,)cnpdgw (; x(saced closer together as you move up the 3t(r) (e2s nzp;.,c 9dpzqcqzhw g(mxfingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it b/4 z5gz1y (s dq)zsmngut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: Sq ns )/gmyzzg45s1dz( ee Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats dz2xdmok3 3)acan be said to be due to “interference in time.” Explain.odxda 3k)32 zm

In Fig. 12–16, if the frequency of thebtr 4w*)1.lsqbaen d2 speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or c4 21ba) s*ntwedl.rqb loser together?

Traditional methods of protecting the h-99*eraroz-l qkjb,b1g bh kpv**km )earing of people who 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 the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in oh r9-*b*)ra9ebl ,jg- m1bqk* kpv kzaddition 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 txi2g:qmsr)s+iyu5b-rf3s9dl jbso0 ; h j9/a superposition of two sound waves with slightly different frequencies, as in Fig. 1ds rli yji : 9hmf2t-ro)g+0u/ x bsss5;9j3qb2–18. 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 m ycs*tcaj *3x4oper 2qj(d6w8yw; diq,s2. u zove in the same direction, with the, 6jcs2 q twx(2 ay4pewy ds*zi83;joudr*c.q same velocity? Explain.

If a wind is blowing, will this alter the frequencyz- ke d+yyys76 of the sound heard by a person at rest with respect to the source? Is the wavelength or velo-y6yk z+d se7ycity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monit wua 8nfdpz70a+)wod*or is blowing a whistle in front of the child on the ground. At which position, A u )7pdnwdw 0*a +zfoa8through 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 ecszkd;ma t7c/d jn0m7+ ho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.00zm/kj7stn ;dc7+ adm s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below 4/ s5 b0jj68 rlr*b nazaml2knthe waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. *bjr nz jan/0lr2 sb8klm4 a56How 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in9j,z7-nm jcop air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. W3q .z8rrb bzca48 i;wyithout warning, an engine backfire occurs on an4z;w c3 zq ria.yb88rbother boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the k dq5.e1zpw8pcf k8. dtop of a cliff. The splash it makes when striking the pkpzddwc.k 5qf.e188water 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 stroyr-9n q xs.oop9)rr+em4te9ike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impacte oomrs4t9q9r. oxy )en9r- p+ occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofdiz)x 8 8wn6yw mpxq2a)w;,o p distance by the “5-second rule” for estimz nawmop8x28 wp)di6 ) ;xwy,qating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soundh b:b:pva/d8 m 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 who +r yfla9n3i2wse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously aol8(kk04 v:;ov/yz l csu7axct a certain;/v slo 4zkoy(7xla:c v0kcu8 place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wito8* +bs/r8l2syc nmb; wg8wxfh four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensitiwlb2;xnwc8 gr*o+8 sm/s 8yfbes, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas .8 jgmszy;2ul-q5 :0i; m fkiek dva;eu 07hjvfor a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for e d.a jf0m0m27k jv; lshz;8eg iuieyqv -k:5u;ach device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakin*4uxpox8,jlod -mw2 cg in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centeroow ,*l-82jc4 dpmxxued 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 is l rwavz(p/7h 2(0oe oj$5 \times10^{ -5} m^2$ (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 2tj pzgo.d/cd71y;*v.n5t ssip n40 xv50 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 i*op .n dj;i ./ 70n y54ttsgdzc1pxvsvn turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB k rxv9 h;9+,eeottmn4 when placed 2.8 m in front of a loudspeaker on the s 4 h 9v+knt,e;ter9xomtage.
(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 azc7+-wba )f ze difference in sound level of 2.0 dB. What is the ratiozwe)+-a bfz7c 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 wha,.2o rnkf/5 -l0rk yk8nmrvozt factor will the intensity incfr,kn l0vrn8o5o/yr-k. m2 kz rease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equa ov fy45(2lr5ciwpw1ol displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their in1ovw 5 24yrowcl5 ipf(tensities?   

  What would be the sound lb6 71g6utfvzbo bz;o.6tus : yevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of vo :tbbg6ubz;1u of6. z6syt70.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz kf9xuqav)0 oapk 8/yhghd,7 /tone that has a 50-dB sound lep/ ya,09o8f) gkq dkau h7hx/vvel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecttutg/ g9)zorif+ckb kl/5-(a when the sound level is 30 (ikg-lt/ uotbaf95gr/)+z ckdB? (See Fig. 12–6.)

  Your auditory system canf*,ybkm h u-l5 accommodate a huge range of sound levels. What is the ratiolk,*uh5f bmy - of highest 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 has a fundamental fgb(e td6)wlyv9zj4lmi h29p )oz0 7bp requency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wha9bjh974zip(6 )wbl op)e 2vdlz gt0myt tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamev 9.:z:gw g)jx3 dawcnntal and first three audible overtonc)v dn .:wg9awx:j3gz es 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 frequency would you expect fromv:konw (*b/ if blowing across the top of an empty soda bottle that ivbkw(n :fio/*s 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 pd1xju ) 0qc. snbqwo;,ipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would0o) uwj , ;1cdsqqx.nb 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 third);q/z)lf nyq s harmonic. What will be its fundamental freq;fn l/z qy))squency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovqc5t:iaj a3n:e middle C (330t ai3 :a:5cnqj Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whenl1v3 psj :b4cp the temperature l14bv:s j3pp cis 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 2v3 nf)r ah40ml0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpieceh37::vwms g fa of the flute in Example 12–10 should the hole be that must be u3wmv:7ga :hsfncovered 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 ilzlct2z oqh4+32oigq yqe 6/j r92f/resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why th42ozq3ftc/ ioh2+/2q9y lqirgl6zj e is 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 botnxk ft0 (hi0+fh ends. It resonates at two successive harmonics of frequencies0 h0nx+ffkti ( 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 yb-9 7iw cwew;kl0ij($^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-z16 * j( zlx qhj:-jougp-o7qkv/ *niplong organ pipe at/hovunljg1 i-**( xkq6pj7 qzp-j:zo 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 op 5.jg 6kzw;7,7m uogtc wdmyd6en to the outside and is closed at the other end by the eardrum. Esm6gu g jy ; t7d.ow7c5k,6dzwmtimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tr du1gnz-: 2mlnying to adjust two strings, one of which is sounding 440 nzg:u nl12m-d Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (26arl+a nt7 tcq,g )o,p/2 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 opernt,yf rda35z5vp 8 :fyates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 5:,d3fy fpat8ynvrz5 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when h9bw0 8u.px onsounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the st0w8 xhopu.9 bnring? Explain your reasoning.    Hz

  Two violin strings are tuned to the g(jyw7p6;h n ut2qs0gy/818fs,ljtf9 ll lngsame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–/yqfg9 t(j n8 8g0stl,26 pjynlfll1 7uhg;ws13.]    Hz

  How many beats will be heard if two identical flute92.p qab ql(fls each try to play middle C (262 Hz), but opb qf.a(q2l l9ne 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 frequenc j5 d.orgt (xql2a;3lny 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 tg5 xda 2;n3 rj(lo.qlC? 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 pers5u0) 4avez2efexaf bqb 8cr51 on stands 3.00 m from one speaker and 3.50 m frf8fee4zx5e ara0bc2quv )5b 1om 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 vibrat* +(mpo(uzbxve0 /xhying 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*(+eomxzh(xbpv /yu 0 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 2.76 m in air. How m1:k guate lstbxi mwd 9;3+j(ux:5na9any beats per s(5tunu;mx g j:di9 lwt xs1a3:+ bek9aecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certmtd 3kt6v-miony68s 5f () ghsain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if y(soh- kt6t8y 35)vin6g mm dfsou move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stillh )x,/ vjvhutv(9 g7xc. What frequency do you detect if a fire engine whose siren emits at 1550 Hz gxt)vv7,cv h9(hj/ u xmoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequenc:; mlxnf8 0gyynj 0e*tn+yv9 zy if a 2000-Hz source is moving toward you at 15 m/s v0yg;y0mn+fxtyen8 j* 9:zlv n ersus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency nb5kkdfn-. c 6az0bmp:gbxnk q l86.4 horn. When one is at rest and t 8nf lb.0c6 k: nq-gkx5kdbb pzn4.6mahe other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounu86:yp c*qxg 9n.p:d,q0jh o ;xahwbud waves at 50.0 kHz and receives them returned from an object moving directly away ,upp;o:hd yb9ng* u .w6qx8a xc:h0jqfrom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 54s2se uq2 zr kcq5d3 l./pm8wd m/s As it flies, the bat emits an ultrasonic sound wave wisqm2p.c/qwk5 2s zl83dredu 4th frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler ep4.z5+ ug gspyxperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical 4gy5 .pzsg u+ptuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supposnd1 ma/w60p rse the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be/wp6ram1 ds 0n 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequl-xl5 jdk0 5kybb,+ei ency $2.25 \times10^{ 6}$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 Hr ioqrg2r v733*gud n iue)-4jt )scl6z. When the wind velocity is 12 m/s from the no dlurn)2-rgv ecti3j4 sor7*qu )gi63rth, 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 on8(pb8i0+amsognuz 7 c land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Macg8 ug q dg7f2+k*7ob.jfnxm1jh 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makesg gou7 2j17dnb.8 kqjgf*mxf+ 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 m*f qnz (43dtcof a planet where the speed of sound is only about 35 m/s tm3fqdc4 *nz(
(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. Determine the shock wave a6rml2n 5z4a nxngle it produc5ml6 nnza4r2x es
(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 ju94u7b(x 0w5lux rcu$/theta$ 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 *1vxafa 0j17w be9nvjflying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2jbe *xf9naa1v7v0w1j .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 auqf4d -b a6,py sonar device that sends 20,000-Hz sound pulses 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 - fbypa 6qud4,minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human auro1q/wgi()5il 5j jaldible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of jsu eoa:c 0ld7r;k,o- many plastic pipes of var, ue;d70kacrojsl o:- ious 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 persohv/mo.: (q-m l/ybbfm n makes a sound close to the threshold of human hearing (0 dB). What will be the sound lev f-ho v/q:/m yb.blmm(el of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound gn1a psn;sfic u.p2uu (b) o)4are heard simup(ubsgpc nn u iu);a4.)so2 f1ltaneously?    dB

  The sound level 12.0 m fromvdz(xe i+k)(og5)rh+b.,y: g bzhcqa a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it+e,qv)(roh .aizx b z:gk(+5 bdyhc )g radiates equally in all directions?    W

  A stereo amplifier is rated a5zht:ohja ab8 pbx,ttv rr y1 31q 4rhw4:.sv.t 150 W output at 1000 Hz. The power output drops by 10 dB at wr.5q, 1vt r paaz:b:4htys3hojb.8x tv 4h 1r15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devic x rvy(le ,rr.o32wac )vd)l2zi6q/hies 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 average human ear has an effective radius of 2.0 cm. What would be the power intercepte2a3h 2vo,xi)lrzr /.wevlqi)r6 yd (cd by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,scg:q+9 uo6fkv9 svy( the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violitkoaro0f52n s9 c- f7 23jwqjin 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 fundamental-j9gh qcqm ,0k frequencm-kq , chg0jq9y of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fkemd y d)lis,+49vy (tilled 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 leds +e4km(ldvty,)i y9 vel 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 opj wp6c0 5kslc5rk+;b7z d 6kcren at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in it5zj0 l6dc; 6ksk+5wrcb kr7pcs fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observede ud:jra8 (+ai 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 qs*3jy5 vy0d ztwo sources. The sound is loudest at points equid0s j5v d3qyzy*istant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a 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 sts7 4s5fyi* dsnx7h0vwy2c2 ob ationary. The conductor on the stationary train hears ahf*54x2sy0yivsn2 b7cw7 s o d 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 53f:;x ji eqx8q98 Hz. After it passes you, its frequency is measured as 486 Hz. How fast;jqx:q 9fi8x e was the train moving (assume constant velocity)?    m/s

  At a race track, you chh(okastx 3t)i2cr ,db)( nh8an estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding ctx( (ot8)h isd3,k nhah cr2b)ars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 1 s:3+k .vrjh gd.ltl,r1 Hz. The shorter one is 2.40 mth kd.:.rlsrg 3v+ ,jl long. How long is the other?    m

Two loudspeakers are at opposite ends ofqaab82 h+,tx ut afr;0 a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig;,2 r0btq u+ fxa8haat. 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 have passed him, at C?

  If the velocity of blood flow in the aorta ildz:4 iv pavr5rrbor0(v 8q -;s 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? Assume that the waves tra0qldi z(rvo:-5;a rpv4vbr8 r vel 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 towq l7m:1/g5yas gsyo*xe:6ef dard the bat at speed 5 m/s The bat emits a sound wavsfg 7gdlm6e ys::xaqe o 5/*y1e 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 asp1 th2s4njv( c it approaches a moth. The pulses are approximately c1pn 2( tvj4sh70.0 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. 12–387y(5ctf;+ oe4q,z o wldbunr+ ) 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 ac+ le n;ur7t5zwyoqd bfo4,(+ bout 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 *fv1 )y-hbgx hcompromised by the 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. Calculate the fundamental frequencies for the standing waves1gxvhf hy-b *) in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a dyy / cpmmbjrugjb2 /d, 0-n*0;/hj sllong, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With bmjlj/nbrydcu,p 0/sjy;/* g2 m-0 hda little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for 5lh;a*oa2hpxx8w iyqw-9 h/k the human ear at a frequency of about 1000 82 5 kxaohw*wy/-lp hx;ai9 qhHz 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 a8or7cha6 i:pv t Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhr pv7:h co6i8aead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat z 6fz5mwortv8 kl1; ,dis 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