What is the evidence that sound travels as a waveq+/d0vhp 9v:pqcni/kx *l 4tq ?

What is the evidence that sound ww/41zwove 0rnsy )9lis a form of energy?

Children sometimes play with a homemade “telephone” by attachin ,lu vl5+yobr2g a string to the bottoms of two paper cups. When the strvllu b,+r25 oying is stretched and a child speaks into one cup, the sound can be heard 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 from air into water, do you expect the frequensv1q8hly14 e wcy or wavelewq4s 1 1vhyel8ngth to change?

What evidence can you give that thv7ez(aq)ugx 3 e speed of sound in air does not depend significaz(7qxg3a e)vu ntly on frequency?

The voice of a person who has inhaled helium sounds very high0 eqsh *qoa 5vapobg/ify ;+60g5uu+d-pitched. Why?

How will the air temperature in a room affectngr6 0hn4; e4 fgij c jv3*bc8n3(xjuc/ qv8mh the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the -mewrau(+pif 2/yz.q1s adn3yb b3)pgv(h.k amplitude of sounds in various frequer1ak()3bmd+.a us ez3p2in-/(g .vqwyyphb fncy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you wuepq;1r*2svy5:s : dz1 r e- ub8fqkkmove up t:y uuw*rk- fvbks28rqd1q5:s ;1eez phe fingerboard toward the bridge?

A noisy truck approaches yo es8,k4d 6wfsbi:wc+c u from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brightekw6f+b8dc4ssew : i,cr” — 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,” cj9-5y a2s mnvwhereas beats can be said to be due to “interference in time.” Explain2v-scamyj9 n5 .

In Fig. 12–16, if the frequency of the spe; qkkfl2bs*x1*rgjmp, c o4 .nakers were lowered, would the points D and C (where destructive and constructive interferenb.jlr2k*m* pfcoq1n4;,kxsg ce occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoplz1; 553mtb gheuwmc(m e 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 z(1h55cwme;3bm g tumnoise. 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 )(i1l7 jsl3xit6 kh wishown 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) lw61li3 hjkxis 7ti(), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obo g:onzt,mli5b o:h*3server move in the same direction, with th,5:otgb im:lnz3 ho o*e same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sou 2fqfm+rgp) w4o6d3i lolmu.;nd heard by a person at rest with respect to the6iffpr4 ;wo3om q+ )d.lulgm2 source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor vm zt /m:wm-.wqpn0z3is 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 reaspw nw/.-mz0zvm t3:q moning.

  A hiker determines the length of a lake bysx/:3 fw r tzdo*f )nycb;t hc8d14o6h 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 leng6ynsdbc:cr1xf ; * d t3oohz) hfwt8/4th of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below ts:w)m26iv h2yslm)1zm6 pw7qifhbc 6 he waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the spee2y )liq2pm 6fwh1)6 sbih67mc v: swmzd of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavepi4:t;nhrsbe 642oyg lengths 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 school of tunfkrv7sa2:q0z prc l./a on a foggy day. Without warrz.v: 0klacs/r2pf q7ning, an engine backfire occurs on another 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 top of an v1xh585*au2me8 eae*b b5n: sftrb t cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the n8he*rb58een : u bvtxt*s551 2abamfcliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete01- kmt o7clhg pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete -1ohtk0cl7mg, 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 2f5niqf1t m6berror made over one mile of distance by the “5-second rule” ftffb25q1 n mi6or estimating 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 pain level of 120 dB9 5fsdcyf vs ,k19jfm/ -mw2ah?    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 intwro3pk.x sxx edd.)c q384r)uensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired(: 0 tosemvjmf65hraibmo+ 60z)u5rt simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Abt6o(:jo0)6+ze mifs a5u5h mr tmrv0dd intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with *dyx/:zis6(y pv mvu*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/ysv6p*vx i:m y(u*dz all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 jd42k r6+grei dB, whereas for a CD player it is 95 dB. rek i2dg+j46 rWhat 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 f4) qjcm 4p)(ig4n mmbzrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly)gb( pmq44j4)znmi cm 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 a288aaoil7 rkl+g 6w s lqzg8ii*+n7 darea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is ratvm+12yldx 15y32nawlvh4jgved at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the soundd 4v21glxl2ahvm+ny3j 51yv w level 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 registered 130 dB when placed 2.8 m in front oqqpesx l ,6(n:f a louqsqx6 nep,: (ldspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound l sh2;i pb.qe+level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?+iblsq e2p.; h [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what facmr1qhbpdp ;(/ tor will the intensity increr;1 pqp/hm d(base? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the rq0ie* nlhp77 frequency of the other. What is the ra*en 7lp7qih0rtio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that 2/l4rlop/jxm corresponds to a displacement amplitudmor //4j2l lpxe of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level t3 wipx2 x 6*gmud96zm9fuh)vqo seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fizif2m q63x*mh)v 99wuguxpd 6g. 12–6.)    dB

What are the lowest and highest frequencies dqhl4r0:ja c4t ie5q9 that an ear can detect when the sound level is 30 dl 5t4 r 0j:hiec49aqdqB? (See Fig. 12–6.)

  Your auditory systemggtjt )8ebx,0 can accommodate a huge range of sound levels. What is the ratio ofgtbg)jt8x0 ,e 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 frequency of 440 Hz. T+c9vdt 0eha6 ts8* cqghe length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tec t+s9v*hcg 8a6qdte0nsion must the string be placed?    N

  An organ pipe is 112 cm lo9/v 2 gj9mqpwcng. What are the fundamental and first three audible overtones if the pipe isjgv 9qm2wp c9/
(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 frequealxl9 w v2jtuo5ggz(25x; iu ;ncy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it ww oz;jl2;gv5xugi( ul 5t2a9x as 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 o. es8m j.jyiy7pen-tube pipes spanning the range of huma.jy.e7m8ij ysn hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. W7wsyg hg ng39(hat will3yg ws9g 7hg(n be its fundamental frequency 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 above midd x9:7bjnskbl- tz9d hfsu8 c6/le C (330 Hz: sjb79u h8dl9nfs t/k-b xc6z).
(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) uvib +kd t;8;n+xqx 6lwhen the temperature nx;tb+xq8d;vl6 iu+kis 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 2g/j: lr/m m)3ffp-wkz0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example -ge(rz(mesc8cuiyy, )k0eopqa5 a 1* 12–10 should the hole be that must be uncovered to play D above middl*cri eop(yu-ze (meya)8s qgca0,5k1e C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, ylo)vs6bwidtlc6cw;*i 2 +4 hand 616 Hz, but not at any othh ci6 4+owyv ictd6wls*b2; )ler frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m lq2ap:b oyk5 :uong is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. ouq:k2ba 5yp: 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 d 2w.k9vbts/ldx5(au $^{\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 fo/inczl4s9/ed ua68kr r a 2.14-m-long organ pipe at 20z 6a/n94i /8cksrul ed $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately *nx *l:p vc,byi .vx(dkn 4;mx2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the a;mx*vn(xi*b v4 pk: lnx.,dycudible 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 eveqrq 9bi j9zn *ok.r)d0ry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How n)jq*z09bokr9rd.qi far off in frequency is the other string? ±    Hz

  What is the beat frequency if m ug,lnb-/fa5f l1 hicha5(jq/iddle 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 s 9izzhgij7ymu+,9x-)3igi f) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill wfh i)9sgxuzmz+i9 g i -iyj37,hine 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 00mos ;for gl*)h1 hpc57s4ty fn. hrnfork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency ofchprnf 5lr0nt )omf1. y70;*hshgo s4 the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same f8*e9wa xvk t/x p:p-a rli5y5irrq93jrequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when thippxar*5 tk 3v8 i:9 y-/rj xr59eaqlwe two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard i n)2:tn9*+bmhha ( w yw-a.3fmkh 0+ ronvsqxkf two identical flutes each try to play middle C (262 Hz), but one is at 5.0w-:ht b.3(rf n0kkym2+q 9 nnxah)mhos*aw+v°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz;y5k(/5k f gokkubgs +4 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 kfbg 4/+55kg( kksyuofrequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speake9otu5 0disrr +r and 3.50 m from the other. 0do+rt siu9 5r
(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 suppbz)-i26l5 mqlnoz)cr brw7;aosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz7bloaqz c))i-r6zrm 5 b2;w ln, 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 2.64gxp2(7u* 8 k rcx,mafy m and 2.76 m in air. How many beats per second will be heard? (Assumgyx82acmkfu(7 ,p*x re T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rej6gfls2p r 7hz paruy c7qw05k8*j- d;st. What frequency do you de6p *l ujyrq;2zjpgs07 7wc8fkhard -5tect 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 frequechl d5 aj zka8j:31zm4ncy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of :a lja1hdk 48jzm z5c332 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at gdq;c 9ig,50q3o :kcsbhn3xj 15 m/s versus you mo kh5gcc93 ; n:qs,o0 dgjxqb3iving 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 fre yohb 382;mjssvs5jq( li/9i pquency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at ;bqs2lmvijjos5 3 (syp /8i9hrest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them vle(t 6 yaz71-dkz :jpreturned from an objezp7y : e1(-dvlzaktj6ct moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an uq, ch12j;+qiho wjz8tf 7wpg2ltrasonic sound wave with frq2+w8,2fjiowh qcgh7pjz1; t equency 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 moving flbhwz84+q* ypw+y,;,r txemtvat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in +*qtztymw r , e;vb8+hx4,w ypthe 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. Suppks 6k9 q;lm, .ddpiai+ose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is floid,il. daps;+ 9mqk6kwing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fd evt cmis3 lhy6:cw1sd81 ;i6requency $2.25 \times10^{ 6}$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 soundhz bd hj* xmyn:a0g6) /ok/+oi of frequency 570 Hz. When the wind velocity is 12 m/s 0kzio jgyhmb/6:xo/*hn a)d+from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2xe3fq21hdz: uic;me 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 Macx ,rhef4f1l7 ih 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the air7f e1l4i,rx fhplane’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 thimm + cl9hyp-diq.h/)rn atmosphere of a planet where the speed of sound is onl/h)9cm d+ip. rl-hymqy 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 travelingep0(cavm40q2zngqu 3)) dtt) nt)zl g 8500 m/s strikes the ocean. Determine the shock wave angle it produce3 v4mz l20 agzp() 0 tqnnqe))dgc)tuts
(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 xg jzr-+*znfhje +(w 2$/theta$ 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 (zxwtfx 7y4fbgb( qn yn2/q/+.5wtuvabove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–3+q5wtbw7xuy.(n 2 (g/qvz/ 4 fnfx ybt4. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward f:64 yz*tw)p sj .vlyhfrom the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (: p.t4 )szl yvf*jwyh6in fresh water)?    s

  Approximately how many octaves are there in the human audible rangqyg1p-doco2a2l-i0*lc wj 4 oe? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.gg p:,jx- ps+0owt:asp2;las It consists of many plastic pipes of various lengths, which are open on botlj x,aa2pp: gwostg0:-+ ps;sh 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 y (fjs0s8p0-2 w)sydfziur9;pnh dd( threshold of human hearing (0 dB). What will be the sound level of 1000 -sydd02 wnisr y)ps8(;h9 0 fzu(fdjpsuch mosquitoes?    dB

  What is the resultant souze8;ozf1:9bn cro m qp,,jay - v+a;zfnd level when an 82-dB sound and an 87-dB sound are heard simu9-,e:z1ay fo b8 z +afcjz;pvmon;r,q ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, p /skjj88su t-xlaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates e-8 ts/kjs8 uxjqually in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz.q 8dm.)m8yq+n1r0tyfr ac /op The power output drops by 10 dB at 15 kHz. Wha1rp0f yom.cm+qyt dq)/n 8ar8t is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicalmna o )b,9tc70 qjx*8sbj/nuz ly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercencu9t* zs8q),nx0/j abjb7om pted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicic2lhc4/l v4(psbufh aw0x8 8 ations systems, 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 f-7m rewwqe .1m qam+z53i.m(uu 8hmssrequency 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 upsod+n*q8 .u frequency of 440 Hz and a mass per unit length of uson 8.p+ dq*u$6.1 \times10^{-4 }$ 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 inv n l-c.tud*h1to vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distancd*utv 1l.hnc -e from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at 5bo6b lmgd66wone end lw6b65dg6om band also 75 cm long. How much 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 +trr*t )l qv6zfull 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 t)fz-p+wlts;2j2w kq 7l;ul o the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. Wh;tl2sl;2 jwz -+o)qtlfk7wpu at is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles.g6xv 2 h+i/k).fl-v3jorhke f One train is stationary. The conductor on the stationr) hvvg/ifx kfe6o. -3h2kjl +ary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538e; ws*jf,g k p:r*,aeq Hz. After it pq*psf a,,r; gw:jeke*asses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thebu jm.tgin012 difference in pitch of the engine noise between approaching and receding cbtg1n.0u m ji2ars. 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, producjx.w b*23i egee a beat frequency of 11 Hz. The shorter one is 2.4 jbg*e2ex3w.i0 m long. How long is the other?    m

Two loudspeakers are at:hm u3tndu cgv;+cu3 og31x 6e opposite ends of a railroad car as it moves past a statiootgc c31h3mv g3:6un+ex u du;nary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 mvryw( znlw, z1,qg m5,/s what beat frequency would you expect if 5.50-MHz ultrasound wv, mn ,zyz5w1,(wlgqr aves were directed 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 m/s while the moth is0fsxf0-erg) p flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is th r0f-0gp)f xese 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 asx v-0 pgb qlr6--;opda;tun,l it approaches a moth. The pulses are applg;ptoxb la,rn-d q- pv;-u06roximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals ftaj-en6ne54nqov7y/x)a r1 s rom one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to cr1 jq naexo /4-7an5r)te6nvyseate deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can bx84 6q2ls ol.cehxd/te compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the prest c.hlqe l2od 64s/x8xsure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, crb7voxqnm7cdo)* eskl-; * 6qrc3v:mix- vk:alled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the k-x v vnv:3rmlbm cd :ix67c**o7q;-qorske)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 the wu ik7a2ap)s5human ear at a frequency of about 1000 upw 7i2)5ka asHz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic )l.ig9jj )lz,lrmjd2(+ ,3pifa ohxiboom 1.5 min after the plane passes directly overhead. What is tzdh i 9l g2)lx3r,,flaii+jo)j m.jp(he plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa/yrw:fl7 qo jxw6vcf . c+o6k4izz-rn5w3m. s t 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