What is the evidence that sound travels as a waveown(w:b k1v9 q f3bvz)rqn,- o?

What is the evidence that sound is au-q -))ng0e wqpodzk- form of energy?

Children sometimes play with a hommn1i9)l kp :k7 z 9i.aate7aomemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29).olz:a 9ne7ia . m1t)mkpa7i 9k Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passeso ro x-af)g:w0 from air into water, do you expect the frequency or wavelengow)g 0or:- afxth to change?

What evidence can you give that the speed of sound in air does not depend sign2tq6jl2(0ga( eggklf ific602ggqkte2 ag jfl(l( antly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched.4 djbs;j cps*. Why?

How will the air temperature in a rotyaf a te1k:uy9.0pp5om affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce / 4 zd(9mc+ )m s1qj8jp2s/ voeviinmqthe amplitude of sounds in various frequencyi(m )mijjz q2qm41s8e/c /p vs9o+dvn ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clozcdd47hn2 xp a9xd1t +ser together as you move up the fingerboard toward the bridgex2 h9n1xd4dd cpt+z 7a?

A noisy truck approaches you from bu(9eqykk*l v i1;o fz c6(gzl*ehind a building. Initially you hear it but canko9kvl1e (c* *yu(zg;i6 qf lznot 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: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatsp a0u *r-asaf9 can be said to be due to “interfer 0araa*fsu9- pence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsw qb 8klkt7guw:p(y5, D and C (where destructive and constructive interference occur) move farther apart or closer togewpgy(5tbk q ,7w8luk:ther?

Traditional methods of prsu z4./,ra esiotecting the hearing 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, headp./4,srs uaz eihones 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 wav, u 0i 5hbft:e2puvwh4cb *+iles shown in Fig. 12–31. Each wave 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), ar: 2t*0,ih p+uvwhul bc45 fbiee the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in jvn 1i7,)nn6 kw/t vpythe same direction, with th6yp1vnk7)jv /in ,tw ne same velocity? Explain.

If a wind is blowing, will this alter the frequency obydchy/; se/ez x4 s9-f the sound heard by a person at rest with resp 4 e s-bx/;hcey9/sdzyect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitv w4jzp ye)+qdps352yor i p) 4zy2we jp+vdys35qs blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines th p2/ioop s:(;l.cyio de length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of ;p il. s(o2cop/ :oydithe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thez. ki0bb4w*ko echo of the sound reflected from the ocean floor directly below 2.5 s later..4bzo*iw bk k0 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 wavelenb; ab ;:ti h8 zkda5tt11gsk5ogths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a s af4hv1nm ,jgu o/6/4xyalo9wwl g,-j chool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a)gy1of -aj4m9olj u/ ,,g/a nhxl4v6ww by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makv n gbez;ci a4l31,du4es when striking the water below is heard 3.5 s later.zg3lu;vb 1ican 4,4de How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pav gix+)m u20t3xu9l vexement. A moment later two sounds are heard from thtm 93 euxl)u0vgx+ ix2e impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-seconddo*jj4d1n 5iy06p u(a:y fhhr rule” for estimating the distan4 jo10 pyh5*( fhjury6i:adndce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a 8c7n x5-d2lsd2b,glllv0 mq gsound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity if,jiw:p 3 (pkns $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of kv vre,bn n y7ea-*82t5oyhu*aox 2 kvsd/.7 s95 dB when fired simultaneously at a certain place, what will be the sound leve,enysuva ey 5*2s7 nht*o/8vr d2x-kv.o7bakl if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an xl,0e4f ;+6 bkoxdrgtairplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this perf + ;6gd0ox4lt ebk,xrson 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 l.ifbvih /xis4e1-p 1of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devp/l1eh-1 i4sxi bf vi.ice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conv8t0mex t aqc*htpk, 8i j;m5t-ersation. c*p5h x8 0km,qta eijt;t t-m8Use Table 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 it1sm ra.yk3 g :m.r7fi 0qbx(qs $5 \times10^{ -5} m^2$ (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 25c2zg7 cus.gn+0 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in t g+2cz.u7cs gnurn 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 regist;p;d1mz9f0mt* n c 2x*ghbyyfh8zq3 bered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ;qp8zf ybc2b;*zmdf19g 0y t* 3xn hhm
(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 typicj n18ud-e nan8 1p/ihoally 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 Sectio-dn8 8jhn1i 1 noe/paun 11–9.]$\approx$   

  If the amplitude of +7n sl1iigir, m4txp9 2c: vpha sound wave is tripled, (a) by what factor will the intensity incsnh 4ipii,7+ t1v: gx2mlcrp9rease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement am oraz.*x7:dv 2nv)bw dplitudes, but one has twice the frequency of the other. Whvzdob7v)2rdwn :* xa.at is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound w 6kojd,gz h6n,ave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mmhdog6,k, 6jzn at 300 Hz?    dB

  A 6000-Hz tone must have what sound levelf1u7+488q fknwt y1z4xds b1 txkc ayn570l gm to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sed5k8 snb0f717acuf+1xyy twq18kmt4l gn x z4e Fig. 12–6.)    dB

What are the lowest and nhateqy+)/8r r6cbx; highest frequencies that an ear can detect when the sound level erb/6rthxn )+a q8y;c is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of 2 oad7uta a7eg00g5mp sound levels. What is the ratio of highest to lowest intepa gm0eg5 t07uod2aa 7nsity 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 fundame/n,k.vvdm+y y ntal frequency of 440 Hz. The length of the vibrating por/. y dynvm+k,vtion 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 larb3twkig hfr (qsz v +6(7*mbx.)po9ong. What are the fundamental and first three audible overtones if the pi((z oxk 7gbhm aw*r.vbt6qp+)sir 9f3 pe 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 from blowing *sl(x,l 1o -zrj/yfqhacross the top of an empty soda bottle that is 18 cm deep, if you assumed oszh qf*jrxy-(/ ,ll1it 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 withs(6 ,n4ctyp yy open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the 4p(6t,ysycnyrange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency f82xcjjk , hblwaw7bi ly8 -;8of 540 Hz as its third harmonic. What will be its fundamental frequencc b7wjlk hyxf88,i2;-ajwb 8 ly if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.77)hqcrg i32lm1/yxi dr (ijl6 3 m long and is tuned to play E above middle C (3 riy1r i)(g6lqdcl73x/jh2im30 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 emitta*a69 ddg .chqo5zk9s middle C (262 Hz) when the tempea9 do c*tgqa5zh.d k96rature 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 20 zcs,a aqn.x,u6q y 2no ;rmk:g p*b/t0$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpieb fpmgjf8o73)61*w8rxnl dtb ce of the flute in Example 12–10 should the hole be that must be uncovered to play D aboxf d*7fwnrbj6 omgl 8p 138bt)ve 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 rescau2:)h h5 x6h7xq 7ancd9 vpionate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a cl7ahi5x ):vnau7hq 9c pc26 hdxosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m longn.ze4lbl:q wj:4 -gh e is open at both ends. It resonates at two successive harmon4n l: he4ge j-q:l.bzwics of frequencies 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 /gpop+2im3 zp $^{\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-long *g osdl/fr997 bxz ga-organ pipe at x s79d gl9z/* obfgra-20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelyt trwd:-iw; 5h 2.5 cm long. It is open to the outside and is closed at the other end by the eardr t-;5i:rdwwht um. 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 of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one zf2agf arn-ui 6dx 22.beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. Hx 2raaf6f2- in.2 dzugow far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and m:fg;z h3xwi,$C^＃$ (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) opk2m;k ,lx,cq zt3az7rg7 d/6n5 vaejnerates at an unknown frequency. If neither whistle can be heard by humans when playxm drkc2/neat3z75na 6;l,, kj g7qzved 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 fork and 9,j- prz4 srvn8 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasr,rjn z4 svp8-oning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The/q1s3 *1zomqqz , g4ihv af c-j0qrv+m tension in one string is t z + *-aq0qfh4i/mq1ojgzcvr3qvm1s,hen decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical 8lgbu/ 1ci,yiflutes each try to play middle C (262 Hz), but/i,i1y8lcgu b one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuningym qi 9l+8b3sn.2wgjf forks, A, B, and C. Fork B has a frequency 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 C are sounded togetherqlbg2 j9s8i+f.3wy mn ?$f_A$ =    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 fgato*3 qw7 c0x6m.2sgxs5tf yf4l.t zrom one speaker and 3.50 m from the other. 5 styocm4t *xt. g wl7.0afq sf23gz6x
(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 xae*;e 80ragxvibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one i*xx0;eaga8r es 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 4y hc4osm33 jkvvgx40m and 2.76 m in air. How many beats per second will be heard? (Assume T x m vo3s44kcjvy304 gh= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequga(i uemko;s /,qa*: xency of a certain fire engine’s siren is 1550 Hz when at resta;xsg:qem(kou *a, /i . What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you det6tau40pt u 83uqquvv2ect if a fire engine whose siren emits t6vu0va8tq324uq upu at 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 sourp9oi/r5sne6+vq,*u5 veuwv ga6 b0 s dce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exacts* 6u 9s0/5avg duvnov6ib,+pq 5 rewely 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 equippeybc u;ibq)yb vv;g(( 3d with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency3iv (bv y(b;bqg );ycu of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and bp:30a ka14*+khckxs6 oyadereceives them returned from an object moving directly away from it at 25 m/1 hpao*6 kkac:sbyka d+e34x0 s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sped;w(cal 9d4ezed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What (z dc a4;e9ldwfrequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movisyx. n(ta6 zob2/8l*cx4 zmgn*jto 2y ng flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railc* n6nx.2 zlj tao om2xs(*yzb8y4g/t way 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 spea 2ukafmt* +hr* (yc+xeds. Suppose the device emits sound at 3.5 MHz, (* *+ratcm x2+khf ayuand the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavi49hi 1cwq)isl d,xvja. 4jh (es 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. Wsgp* *8esd cxe,oid99r k 7jp*hen the wind velocity is 12 m/s from the north, what fr7sijc*d*x8s, *ee9kd r9p opgequency 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 objec npvp1qmf3 ,g1t moving on 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 Mach 2.3 where the speed of sou8e,z:v dj p1jcqo6k ri6p1uy1nd is 310 m/s (a) What is t6ejvjp6 1i uyq:rc1,1 8ozdk phe 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 atmosphered1l-w d,hm 9rr of a planet where the speed of sound is only ar1dwd-r9h lm,bout 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 strikesfpa6f;**q d 62,vt iaig+tq m ;fmr4vc the ocean. Determine the shock wave angle itq+*mt6;4m t q;*ardvap6vic if,gf2f produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle l.*jvb * juj;+yncgj7u*b ;su2 ud9bpa:k ;kc$/theta$ 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 g-ewq )x/fv 5schacfdgtz7e h087,( ehround flying faster than the speed of sound. By the time you hear the sonic boom, the pf7h0dg-h 7/e5e ce , vs(c hwazq)fx8tlane 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 devicen- l ydyjt)(; +ouew;g s+pem3 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 il -ysyd go(u+w+)etp;3;m nej s 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in +hp(ll cs+a6d the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has al9krw(xb; 7bt display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bot7btxkw ;l9 r(bh ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thres;1 hjh8ejlxq8 3xm0j m7j +vvtn.zt, phold of human hearing (0 dB). What will xtq .mjv01j7evh; mxln 8,3+8jjpt zhbe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound)stjlefy,1f/ are heard simultanjy /,1)l fefsteously?    dB

  The sound level 12.0 m from a loudspeaker, pla urz-g) .vl -rv1bh*uaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equ1. )zlu-rvbvr g- hu*aally in all directions?    W

  A stereo amplifier is rated at 150 W output cw/ ca9 bp3,rodeek +5at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? owdbe3/9p+c eark , c5   dB

  Workers around jet aircraft typically wear protective devices over their ears. k2/rsyse8a f1a/w * bqm g0to.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 qo 8gys wa*fs2r/bmae/. t10kairplane engine?    W

  In audio and communications systeeg wostzcj5((- 9wdz- ms, 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 violin is tuned to a frequencyg5yc;r 7 5,ap xpw3ej yy g;ue6za5kj( 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 fun+cl hhc a1e;dj6kp9l,damental frequency of 440 Hz and a l 9hp,1kcl jdea6h;c+ 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 ).uz7gy -fc d4 wvgtrg;9)jnuvibration above a vertical open tube filled with water (Fig. 7.utg 9; cfvg4jn gr)y )wdzu-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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is )x 7omum pjvj8;at;hr 4ed3 .anear 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 (in its fundamental mode) t;r8)edpoau3am 4x jvh . ;mj7with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fi7 lzlm0sfok7-8gm;i ull 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 tdc(0yt):+gc v2zgl05a p uc xr+,xoq tone in the 500–1000-Hz range coming from two sources. The sound is 0uxct:0l ,cxyrv+ cgg25z)+dpoqta(loudest at points equidistant 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 stationary. sidxp, 9s7 *pt23 x1yfk y3ughzff a,,b9qda3 The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approache,9 f3y73ap kf*1sbifdpq 3x, ,s9g d 2tayzhxus. What is the speed of the moving train?   m/s

  The frequency of a stea u-; jhviu k- d:(0ipq6gl3tda29xacym train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz-:iu3pd t;qha id9kg u6(-2jc0 vxlya. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars juz.ja5 w.qhcn7 st by listening to the difference in pitch of the engine noiz.a5 h w7cqj.nse 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, sound m.bdgseqj0d5/8bjgy: 3t* uwing together, produce a beat frequency of 11 Hz. The shorteyg 85bb/wdgm*j0eu .sqt dj:3r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stt 8a4k/xtc6iyss: ,m yationary 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 ost tsky8:mx c/6a,4iybserver when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/p(a48( urieaav6;k yhs what beat frequency would you expect if 5.50-MHz ultrasound waves were directi4y (av68hp;rauae ( ked along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 mkzvw3lg 0jv0b: d;f2k/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave d 0:kbk fz203 lgvw;jvof 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 h*2eq+es upx2q1 ufc7frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 mscpqe12 exfq*u7 + u2hs long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from on0+ wr;a5pso*9c jbj mwe 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 +wpar9*mo;b0 5cjsjw be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and 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 presencel7n( *m3q y0q*qg trrp of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a l*nplg 7( rqqq3r*0m ytiving 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, called “singing rods,” invol4c/9qgpxpp*h z g)j )oves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with t)h jco4 p/p z*)qgxgp9he other hand. With a 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 thd(71 anw*xwnpeu e) 5u-swk( qreshold of hearing for the human ear at a frequency of about 1000 Hz new(ad nu71(q*x ew5 w) -kpusis $I_0$ = $1 \times10^{12 } W / m^2$ 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 ofs6yd*0f b(w xn the ground hears the sonic boom 1.5 min after the plane pas6b0f(* x fwdysses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbokg( ux8 39fx k/jh/rgsat 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