What is the evidence that sound tra riq ,9bggu,7hvels as a wave?

What is the evidence that sound is a form ofdii)kc4z6 oga2 ggf+y1 p()e a energy?

Children sometimes play with a home +erl +ogw6glr )4(lcsarok ,*made “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 hearrg,w g+o+rs*c) olaek l4(lr6 d at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes frjk/:2z:9 52 qfvlejkfm izji;om air into water, do you expect the frequency or wavelengej2j5ifi m:q9zvz2 l ;/j:k fkth to change?

What evidence can you give that the speed ofus6y*p 305 8myxcuyc ,t lrvs3 sound in air does not depend significantly on freqyucpy 8l ryx v5u,336s0*tmcsuency?

The voice of a person who has inhaled helium sounds very. 9zv6bq eqnv* high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes?qk;h*g r3*8z1l ft,uaz l pch+

Explain how a tube might be usemy7*hhfrv1 glt *d-y(d as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muff*g( t*- rf7lhhmyd y1vler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you m-yks4 nnaq1 ;(2yd7epi 8il6v l u8rtjove up the fingerboard towardayln8eyl6; su8qin2 r v(1ij d7k pt-4 the bridge?

A noisy truck approaches you from behind a building. Initially you hear is6nn)/+ng v:r8vgdz ht but cannot see it. When it emerges and you do see it, its sound is suddenly “bv n/:s )n6v+dr8zggnhrighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to /d ) d.g3ir vl9/wgddc“interference in space,” whereas beats can be said to be due to “interference in time.c idv/3)ggw/ 9d.drdl” Explain.

In Fig. 12–16, if the frequency of the speakers werf*-suy b,z g/me lowered, would the points D and C (where destructive anb ,*gy-usf /mzd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work inz 1(cwi0r xq9sv 2r. )lry(jbzqrt hjs25l8x( areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphs w( i.8c xqrzh(r 9rzb0sr2)j2(1lx y5vqltjones 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 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 wav:k) m/mxiq5ody 47g kke can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compodkkq4/:gomiyxk5m ) 7nent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sor x5q1jutx a)(ix;m t5urce and observer move in the same direction, with1 5(xxtiu; aqj)x rmt5 the same velocity? Explain.

If a wind is blowing, will wlrpbh 4:2e-6y ;yk uxthis alter the frequency of the sound heard by a person at rest with respect to the w :euphy6 y l-b;2k4xrsource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mo m+ lo 7vhddi:(j8q v2bg.dx1onitor is blowing a whistle in front of the child on the ground.7od g b2vi:mv+hxj1d.8q l( od 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 listen bxd;,j4n9u qr /1g jen7bgln mx1:0vuing for the echo of her shout reflev xj:jg9q0 , bu; bexng4nld1r1m7nu /cted by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side2lbwshwhyt m512 lb91 of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below hwh12t2m5 lsbb9yw1l 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air ,h;(pfs+n: dz7mzotc 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 fijur(,s5* l.w9htd l xoggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elars,*lj5 w9ldi thu x(.pses 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 wh4.so:, yeqa fxi+b suggs7l.0en striking the water below is go,x f7s0..aysesu4g: iq l b+heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a zv 2iojeus k.t;9trsq08r-cms20, dehuge 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 apart.uciqdser 0mjs.2kte t,2v 98sr0 o-z; How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent errukmvgb 79eqs+ + d7 zz.a7hen+or made over one mile of distance by the “5-second rule” for estimatins 7+zzebmhk9g7.e qdnv+a 7u+g 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 sound at the pa3wvh uh i35k3nin 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(q ijbg8s z-: ,rs nalt6wt*3t sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9xd5k6nvli(d53 3svyjs q 4g-a5 dB when fired simultaneously at a cerndd6lkys55iq 3v 3-js (xv4a gtain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four dbq rxe-6ac:; equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the caer -ax 6d:cq;bptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is s27 o /nggasto3aid to have a signal-to-noise ratio of 58 dB, whereas for a CD player is7no 3g2o tg/at is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaza 0 u m;i7zumq8dr)7jking in normal conversation. Use Ta8jummz iqz; dr0 7)ua7ble 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area c pcp x.86 14ummo:jtqv/ozv i-)le0 u nmj,u2is $5 \times10^{ -5} m^2$ (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 iscd +wq,.may rek88swhn43,o d rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound levelc4ym8wsqa +kn8 odd.e,, wr3h in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter regv)q+urp;xfnhi nri8+. p/)z g8u3znu6psi 5mistered 130 dB when placed 2.8 m in front of a loud6u/isqmzi)x +8vu)r3p ppn f nruh;n .8zi5g+speaker 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 typicad:x;egxs wfw4edk6n5-7 z al4 lly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectisxe w4 7xal5kzfn;g-wde d6:4on 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fact.p 2i98(a1xg3cvpf8* bcbixghuu 4 evor will the intensity increase? Increas38p4 cpf8.v 9egb(icg*1uhx biaxuv 2e by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one h5ev xuzx 4y6(yas twice the frequency of the other. What is the ratio of th vue4y65zxyx( eir intensities?   

  What would be the sound level (in dB) of a sound waveu3k:ichf5m j7/ k55ti uy4ocf in air that corresponds to a displacement amplitude of vibratiy:5/ 7i4ucuomc k5hfi j 3fkt5ng air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what.f 1f;qgr6z sx sound level to seem as loud as a 100-Hz tone that has a 50-dB sosf f 1;gqx6zr.und level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ed;yrfwdid i/8c2na6. wgurc 1je : 14bl*o2ylar can detect when the sound level is 30 dB? (See y ijdr2c2;lf 1b1e:o6ary4d*igun dl/.8 cwwFig. 12–6.)

  Your auditory system can accommodate a huge range of sound level*- ix ;,s)a8m8fdpuxhu9(hwh ow 1jcfs. What is the ratio of highest to lowest intensity at m,-sp(j 8 xchxiauud1;h)h *8fofw w9
(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 o.le6e18 pv.(xjc)yao.vqa cp f 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 p 6.jax) qe1.oc.8vl(yp cevabe placed?    N

  An organ pipe is 112 cm long.b:ef j*m(akhw4xax9 ) What are the fundamental and first three audible overtonaa* k 4mf:w(9ex)bjhxes 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 fsgy7ev0b xu2 4rom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed ivubx 27gyes 40t 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 spanning the: qgt/d1ila 0vkzv/b,,mk2bf range of human hearing (20 Hz to 20 kHz), what wolv/zdtakb v i1 ,b0q:m kgf,2/uld 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 harmonic*sr *g bj9+rdt1r,fi3zmghpb;( e t+ g. What will be its fundameh* 9zggrr+mb gbr+ fi,; *psde1jt(t3ntal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar str1g8+ /belijqhing is 0.73 m long and is tuned to play E above middle C (3gb ij+ l1he/8q30 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) v kqtb 5n+rex8ru8a:4d4yz mtg79hr5 when the tq 8rxygda:t4b zk rmvr4u5e7n +95h8 temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune ahbennby.laj*9dh 4p xu+2s 57t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofa2sjm f:.c 5cvpup+7vy* qp;n the flute in Example 12–10 should the hole be that must be uncovered to play D above mip qyp;.2 vs5+*cjp:anv 7ufmcddle 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 cpt/2nh)1(bqa wbw;t zt kcaj08j);i ,q8cce 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whtwhc);at ba e1t8kp/w( )jn;z cc2qjqb0,ci8y 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 ot( iuivu m-.: l-ql1zipen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and u.vz-lii lqi(1ut m:-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 cw v8pa2cqb :2( ooice xp* g;w/x2,et$^{\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 y-f.u+kg+gqzrcys n:ld .9 v; range for a 2.14-m-long organ pipe at 20 y.c+ :;ngzrqg-fuy +s9v.kdl $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately vx3.w8ltg8 4fzai3a) ns/z w fe+hfr) 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 the ear canal. What is the relationship of your answer to the information in the graph o3.v8at8 h)3ws+wrlez x zfg f4)/nfaif 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 strings, one1;83 ; mjacpuq1pyopb of which is1oc 1u8pq ;aymjb3p ;p sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat freq sp 0yun4i6z5hf6ouo, uency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatkbebc c f6 i4sx*2kuzp x;.c;5es at an unknown frequency. If neither whistle can be heard by humans when played separately, c f.x;*sb6ic24bkzck5 exu;p 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 produo * kflgn75s op:shm/;ces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What ismplo5fh*n:s ks/;o g7 the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sameuy g-+yw hyh7/t ;qth9 frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequ/hh 9 yt7tuq-+yyhg; wency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fo,+r xzxiuq8l:0k k .klutes each try to play middle C (262 Hz), but one is at 5.0°C and xo.0,8il rzk+:kuxqk the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hdayq2bw, +bg.8ky c1 /emksfz ,cd5;aas a frequency of 441 Hz; when A and B are soa8,ky;cm2f ya/k5z wqbgb ,ced 1s+d.unded 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 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 per +sa/dchtv:0ov .javbyx7 :r2son stands 3.00 m from one speaker and 3.5yva /vb:croh7 02: a. vtjd+sx0 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 1b/;a/m 0 kwlrk32 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If o;rkw0ak /mb/l ne is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in airu+ceq l7j,zqk fm/)bi6*,nai. How many beats per second will be heard? m,i f/*n)7jc+eb6, qziuk qla (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ogr7 g9zj s/oj.d0pnb0f a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you7rz0dnj g gjob./9 0sp detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fi9k.g yo)d;zdxre engine whose siren emits y)og. d x9;zdkat 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source6 7l auhkc i:)+nub7tl is moving toward you at 15 m/s versus you movingnu6+)t7 ukhlla i:7 bc 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 ho mlh5e,j0 uq)hrn. When 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 horns emit? Assule,j)5hm huq0me T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasont7gd)l xm7z4xic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 mm z4l gt7dxx7)/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 ls h3kz4q 877b4 aysljan ultrasonic sound wave with frequy8kajb3s 44lq h7zsl7 ency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movingribw)v.: jrqe.p7 b5 l flat train car at a frequency of 75 Hz, and .:i)5 w 7b.ebqrrvjl pa 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/s ?   Hz

  A Doppler flow meter uses ultra3u;zof od/)q0ypd 9gr sound 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 9yz3 o)qd ;fr0gou pd/blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ulm o2cjsgvdsa0+( e2 9ttrasonic 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 frequency 570 Hz. When the wind velocity iodvb* 8ga mo.)s 12 m/s from the north, what frequency will obse.v*bg 8odmo a)rvers 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 a gnu a,ew poju8-a -id7j62ym0t 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whatv 6kmq m1dgn/5 is thvdk6gm1 n m/q5e angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of hk)b8cezq nj jr b/(/1sound is h)e8b bcn jq//rk1j(z only 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. Determine the shock wav7uxvoy, q7gf mao-z;b(ru3m .e angle it prov,fo om ayux( b3u7.;7gr-z qmduces
(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 dp16s 1+bxdx 6qtrm,n$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and4jl ,rrw gal96 see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane hawag4jllr , r69s 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.g4b 7lnjo- +j+dgojb that sends 20,000-Hz sound pulses downward from the j .d 4g lj7no+bb-g+jobottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humauk l k +uziwgpa:4/)o6n audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphtg cnm(e u-30c v1dj q 9zphrov36a/x7ony. It consists of many plastic pipes of various lengths, which are openvj0-en 61ztc9(uvcxpdgqo r3amh 73/ 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 ma,f-8c yypwq)p kes a sound close to the threshold of human hearing y)w f-8cqpy,p (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are h-c0js.w*wvs r eard simultaner0*swsc.jw -v ously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whkcguy h 20) a)aj5lb;xat is the acoustic power output (W) of the speaker, assuming it radiates equally in all direction;ljxba25g)hy k) acu0 s?    W

  A stereo amplifier is rated at 150 W output at 100zd -b f-w5abt70 Hz. The power output drops by 10 dB at 15 kHz. Whbd waf7tz5-- bat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over 1 nvg5usyn:3 btheir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airpyuv g35n b1s:nlane engine?    W

  In audio and communications systems, the gain,,oe.f3k cop4w $\beta$ 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 )js 59w yhhp5.-ebiwvis 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 9qz c9p5li3es with a fundamental frequency of 440 Hz and a mass per unit lengt9cpq39szli 5 eh 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 n*4jfv3bq d d.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 dqf3.b4d*j nv 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 t x94j+eo6gyb-lcf3 omq v o:y;ube that is open at one end and also 75 cm long. How qx:f e oy6bc+ o yl9-;34vojgmmuch tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loj/yip-nax o n1arx5. -op ($\frac{1}{2}\lambda$) 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 sources. Th0 t6-t dchsks8e sound is loudest at points equidistant from the two source8sc0 htst6 k-ds. 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 stationary. T( do j0hpz)i,vwh:jc o-09soq he conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traihpz0o9d)( v: -ojih sj0cqo ,wn?   m/s

  The frequency of a steam train whistle as it approaches you is 53j-ad9f8 ;les z9y pib38 Hz. After it passes you, its frequen8 dj p al9f9iye3-;sbzcy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you ca1:/oox rexsqys.59s 4hl;bvb n estimate the speed of cars just by listening to the difference in pitch of ts.hq/s94oxel x:y b o;s b1rv5he engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of ad9 g1y; 4xtgvfx -hz211 Hz. The shorter one is 2.40 tyaz-21v4;gd xhf 9x gm long. How long is the other?    m

Two loudspeakers are at opposite ends of aw f0/jlb tfj)h b5qu(1 railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) hbl q)0bf5j/jwth f1(ue hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 7x;ixnub gt(- b/rl.t 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 bloo. u (r tlxbx7in;tbg/-d cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 vy.cki1b43 od;ja,pj ,nj)l: * ykqr hm/s while the moth is flying toward the bat at speed 5 m/s Tyykc1jn3vr)op;,q*lah k. j ji:db ,4he bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it appr:jk rb (,gi7ytoaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be d b:ktri( 7,jgyetected 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 p4 ck+):u6wgdll1 6cbux1h n.led ncaz ;zz,+ 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 it is calledc,)cl1+dzd6zgpuh4uxwn1+nl ; z eba 6l:kc. 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 ixa-a5s*kmo .yb.z r 38v2qgmpresence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m ls5-a yg. o ki8qxbr3mmzv.*a2ong, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing9 ld/cs;7wnp;npiq,s9r rwr : 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 roiprsrp ,; 9d9/l 7wqn:c srwn;d 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 the human ear at a frequencs1p 7m e cej:*lw.tod;y of about 1000 Hz is e:7 w.;tjdsm1*oepc l $I_0$ = $1 \times10^{12 } W / m^2$ 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. A.w (o 5 qodsm7hdom0(in observer on the ground hears the sonic boom 1.5 min after thoqd o((0.iwd o sh7mm5e plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat hve .)hib;5w,i/;a n:tcjy yi is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h