What is the evidence that sound travelkze59 rw8aknup r:,4ky *iju9s as a wave?

What is the evidence that so mf eq*xy88*ogund is a form of energy?

Children sometimes play with a homemade “tek-)7tuzdf;p bu5h uf:/qfzg (lephone” 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). Explain clearly howt:f )p/dq-5z g;u(uzb7hkff u the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wavgi2)ntu+vh1wt g6rq8 i+ dw8 helengt+w+th q8t 1iw2 i nvdh8ugrg6)h to change?

What evidence can you give that the speed of *d kyb*k:x+f ry wu+2a:):c wbz)ipq xsound in air does not depend significantly on frwibyxy+ :u+ :r:b k2 *qd)p)f x*cwzakequency?

The voice of a person whug0uy3 xgef 9al;8sq.o has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch0gjku saq 0ki* ly1;su0pj7-eh yl5c 1 of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of wfj-ecu qd a+50(b lr9sounds in various fre50e +du qrfbw(a-cl9j quency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as7ph4 e4 p 6q00g aj sgj25zik*ioku*bm you move up the fingerboard towa0q*6*osum 4pz 0j4k5g gpeh7 j2ik biard the bridge?

A noisy truck approaches you from behind a buildg x luvx4j7(i:ing. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of th:livuxjg7 4x(e high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas z bw7 7jru3/jie.o;47js nxopbeats can be said to be due to “interference in time.” Explain.box r n3 o7z74e/j;wjisp7 .ju

In Fig. 12–16, if the frequ 7sjp jze) bib*m(un*9ency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or close )(z7j*9 bjmunipb s*er together?

Traditional methods of protecting the hearic7k6 41ywi dkdng of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How cok7 4cd1 ik6dywuld adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tj1qqa9 i7bmxg+k rd8 i*t2o8 vhought of as a superposition of two sound waves with1 + 8m 8qtokqgdxvb9 j7ri*a2i slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if thegg5l4qkc2/ ny source and observer move in the same direction, withycn4k q g/gl25 the same velocity? Explain.

If a wind is blowing, will this alqi ll/h5 kpec4l2 )2yyqgyd/)ter the frequency of the sound heard by a person at rest with respect to the source? Ishy dl /5yqp)2qe ykg/i2ll4c) the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swm6 mb: .x f*0yj aj/rnieox86aing. A monitor is blowing a whistlejn:*x .6 0y ai86bxa m/mjrefo 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 the length of a lake by m af4 oqrv8j2)8xl2tq listening for the echo of her shout reflected by a cliff at the fx q2lf8 vt2)m4 j8qoraar 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 side y50r- (o(x (bzkrrxto of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sr xyozr5x-(r 0( ko(btound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengyqy.ma3i9m 8+p t -ohhths 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 adq6yekx/+wlxslqr9a+, x5 7 tj7ni8 + lrao0above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–3xo +xa8tnq/7e w 7 9jkql +i yaa,+dl6lrrs5x03). 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 a lmww7r6 0ojmpnr.-a: cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the rw.-l67op 0n:a mjwrmcliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pai aks2xc5 33jobc pj76d*i(czvement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far awayp6iz j23k*ac35 xcd(jb si 7co did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by tbx:7k2qn ev)vhe “5-second rule” for estimating the distance from a lightnin)xqn 7 k2ev:vbg strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paiirzldr;7. n8 fn 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 intensiinb lk zo rh.lt0;z*s) z0l9o7ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslyp2d1)vmpe .ue)pb ki * at a certain place, what will be the*pd) ibk1 mep). e2uvp sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an d3xftcz:d,s6 6q4ln4 bg+yc sairplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wo4 ,: ly4fc6c qx6 d3sbsdt+ngzuld this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nom o6gm8mu(0c uise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signalm 6 m(0ucmog8u and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in;apjc 3fk26w cg;tjisk1 04rb normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphegs rj14jb3fa ck6ik w0;2 tcp;re 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 strik) 0a6dtoqoo4 ses an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 25cf0lr4.x-/( ky)le lxzf9 q bk0 W, while the more modest amplifier B is rated at 40 W. (l yz/kxer 4) l(fx.lk0 cfqb-9a) Estimate the sound 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 ve4 rq:wig7o / ;au:ecfront of a loudspeake74ogrc: :eiqwu a/;ev r 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 level of 2.0 dB. Wha3rvi)+t s l 4zghhh:::3aapbit is the ratio of the amplitudes of two sounds whose levels a)i srai :3bht4zv3h:g:l h+pdiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave x8u ta3cib9, dis tripled, (a) by what factor will the intensity increase? Increase bd83ba txui,c9y a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tw9;p g;f-3 lfsbsx,daeb.6 ,rke 1fyjp ice the frequency of the other. What is the,,9 bs3epp;fb-r kja1f6;d l.sx eyfg ratio of their intensities?   

  What would be the sound level (in dB)u+k cwahv5a), : thlk73u:ggf of a sound wave in air that corresponds to a displacement amplitude of vibrating uk+3:lvgak u: ,t7h wh)acg5fair molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must haveiak3 /kjrf,:ev o4w 2y b)v/wz what sound level to seem as loud as a 100-Hz tone that has , /aeobk3yw4 v:)v/wi2r jfkza 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear ct1 g *qgwl0;bnan detect when the sound level it g lgn*10bwq;s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a exaa x: m*gwl:n8 *ee6huge range of sound levels. What is the ratio of highest to lowest intensitl8a :n*: xgee6*x awmey 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. The length of txl4fg r ty625jhe vibrating portion is 32 cm, and it has a mass of 0.35f jlr46yxtg 25 g. Under what tension must the string be placed?    N

  An organ pipe is 112 ) ryhymmj9 a-6cm long. What are the fundamental and first three audible overtones if th9y) -jhmmr 6aye 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 from blowing across thqgo,75 -d cowfe top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube?odq-7gf5wo c,    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 sf x *dbsz1z*kit91h-pipes spanning the range of human hearing (20 Hz to 209 *zktdb1z*hfs s-xi1 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 4ncvb,i/f. ht 540 Hz as its third harmonic. What will be it4 tic./v, nfhbs 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 abos, vkh+*l3qw3m/cf -om um0nptr2y3 rve middle C (330 r*u vmqw3k t33yl+m r 0p/2,fsmn -hcoHz).
(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 (mr- p9o3vh ;q1apq;s dt1rl0i262 Hz) when the tempa;910r-1o td v rpslmqpi3; qherature 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 20k -h8.(e(a isum v 8g2:fervvv0s -hdv5sa0ky $^{\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 1,u(l z 3kk(r rbj1z)tr2–10 should the hole be that must be uncovered to play D above middle C at,r)b(jkrzr1t u 3(lkz 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 resonate0wmzd5juh-p *j rdx, + at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Showuh r,- dj+zx05w dmjp* 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 long iskb/s bcbxtv)..h55e m1 yc2iy open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wctbc)y/ .ek1mbbis5 5 xhv.y2hat 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 wr dofak3;n-et *qx+g 8/*upw$^{\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 5k f)awd; 8wdy-v m;fsrange for a 2.14-m-long organ pipe8a;wyvw)df ;mf5 -dks at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. Iee9t(ory,v+ m x;g we)qc 4ju8t 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 gr );,weeu x r yq+o8cmetg9(j4vaph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 ,)id3n9eo(fox:go 0rtp4ej7ul7syk j:r+ nb s when trying to adjust two strings, one of which is sounding y3gu4t o7nd9 rr+b 7 nx:jl:k)jope f,0i(os e440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequn ct3jrf0e+u6ency 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, whgym dn/nfvs z4b*)-i2:uz wu7ile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans /d byfiszg 4nmu n27 zw-:*v)uwhen played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hzgme 65hr:w,zk tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the swe r,h mgz65k:tring? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz:b3y2p1k 5jhkdxqp5owt v9p 9. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together9k235: hv pw qpx1po tk5d9ybj? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two ideg8 4bav0os-zy ntical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25oba4vs 0gy8-z.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B ht+2r l.3x)ogfov+k2rqw eu e+as 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 .2)3fe+lo 2outr ke+ vqgwx+rand 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 standsa.9tlv5vax) ir 07dyu 3.00 m from one speaker and 3.50)y9xvltivara0u.7d 5 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 132 Hz, but aa1p ;gfxags wn/ v)4m7 piano tuner hears three beats every 2.0 s when they are played toget14fxap)7gmnasvwg/ ;her. (a) If one 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 wavelengtvi)0txkf j ,:iuy+e5 nhs 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 2+n)iuti0: y , 5exfkvj0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certpz+x5ewj m,)iain fire engine’s siren is 1550 Hz when at rest. What 5+w)imxpe ,z jfrequency 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 frequ yvq(u6kjl9d 5ency do you detect if a fire engine whose siren emitqd lvjy (9k56us 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/6,:byl1 fa/gv htfy d source is moving toward you at 15 m/s versus you movin1fvh:6b ag/tf,y yd l/g 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 horn. When o1fmms1 o1sqd7gj vrvs*: h5q6ne is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequ6v:sfvr 1* 1 jsh71 qmgo5qmsdency 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 q.o1 q**i(80w nso/wy2,vjsny gkvuis/ryx8 .0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sou1 v/is8ywjqkn2*/ wqrg*ns 0iou y s8,v.oxy(nd frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flie 8f6:wtc pg9rw. ryn+ys, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? 6rfycpw+gr tw y.:89n   $ \times10^{4}$ Hz

  In one of the original Doppler experimenwdzyww. 5 2,gqts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second iden2 yzw g5wwd.,qtical 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 ultrasound iw8qy/z 2xzja5ur6:iwaves to measure blood-flow speeds. Suppose the device emitsqux5r/ j: ai iw8zy26z sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofluf1 el:1.w0n5qdbgr 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 fr-99w3o 5 cuj/7athr iqgrd sp/equency 570 Hz. When the wind velocity is 12 m/s ir ao/t 3d5wj -s997qpg /rchufrom 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 la)8 t u1 ubwrzk2/*xusz+pg4uond 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 theo a bqgn)1r:1a speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion)b a: rnqo1g1a?    $^{\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 w/ cdy g5e+d s,sfwuterb8p,/4here the speed of sound is only about g,5sef+ eu,y4pt8cw/s/b rdd35 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 r7 ex*7j-4xu/b vfjn n;.r mxpwave angle im;nu7x j7xp.r *rn4vx/f- ebjt 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 3wfp opb:9r uh/exb/0 $/theta$ 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 e1+(6i ske mbu5nd2, nusbp6za xactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a (sun p2, bs +1minb 6u5z6akedhorizontal 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 that (aeo(4cfbae/ sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, whf(/cb( e4a eoaat is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?29qetz qog1sj801g zv5mje) l $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of c wi.g7e4j a oi;t)ho+u h6jz8many plastic pipes of various lengths, c)j hih gai.4 +zoew6t8uoj7;which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person mat5xhfs(t se 9-kes a sound close to the threshold of human hearingfs5e(hx9stt- (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundr*l7 i, l)oj2tvaqgu uawmo6q 2;u9 u,ycc;*l and an 87-dB sound are heard simultaneouslyau,2 lcg quuomw2 oilqa*u;) 9c*vr 76tjy;,l?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,1j /dku1/sfy+wsc -dynii fc5v m1g23 is 105 dB. What is the acoustic power output ( idic/s1gn v3y1ds/21+ 5yffmc-kwujW) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W e0 2mk-0qsajlq1dk c1v;jp k9 output at 1000 Hz. The power output drops by 10m0k qe- 1 dsapk0kj9jqcv ;l21 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft 6pe7 c*l,fhfe6*9n+i xrp v:pjg r8ee typically 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 ear676v+:g l8 e*xpinerfe9erpjfc *, ph has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatub6(d6 5 de*tfq 8rfrjions 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 violinjbaiun2 +70 k4ct (zpf is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fix*cnip(v7 vs9 zed points with a fundamental frequency 9snv*p i(v cz7of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open t+cafr )0wuq5u ube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above)uqr w a5u0fc+ 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 near a tube that is opefkj/nry/3 l *zn 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) with the *r 3 zj/fkynl/third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one8lzferd,,ym nh 9: u6e full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range drwqv28x; v3rcoming from two sources. The sound is loudest at points eqv ; 2xw3rr8dvquidistant 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. : ju,byt7tgd6 One train is stationary. The conductor on the stationg:ty j,td 6ub7ary 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 apg8k0p d+ca2train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant dcgk0+pp28 aa velocity)?    m/s

  At a race track, you can estimate the speed of uhh/ka:- fv asn4/9 wccars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Supps9/n vk aac:4hwuf -h/ose 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 toh4zs cvm(pp-m,t4261 02kv kp sugsjx gether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lon-zhspuvs4, c4( 62v s pmxj2k0pkgt 1mg is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastpzr-xzpln/ fk(whvb1y zfv .3** 9/ tr 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 b3-b hz/fx*r9( vfw zvyknt l/rpzp*1 .y 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 imh 1+ iuy4brit63pcw962vc so h)fzp;n the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume +y b 2ohf63cswchp;4v )6zmpi1uir9t 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 is flying tolu,h.d(2g soxward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of t(,g x.2uhod lshe wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freque +(3og0*4ziu/0jddgf mr 8 ng7mcmfv uncy sound pulses as it approaches 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 detected by the bat so that the echo from one chirp returns before the next3 80mmnfuov*g (c4dj /g +f0ui7rgdzm chirp is emitted?    m

The “alpenhorn” (Fig. 12–3pne;zn.:tjx 38) was once used to send signals from one Alpine village to another. Since lower frequej:znn .t3px;ency 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 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 presence:n ow;.h(lfjx hll 68q2v*vk/8nqkwy of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Cons. h8ly(v 2l/wkl on xk8*whv:nq;qfj6 ider 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, called “singing rods,” involves a long,od1ni-8+ tb qfmqjb 9(r+q v0q slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit dmo+nrt qq098iq qj(vb-f+b1 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 s kh-k2y vcewr1/29ekear at a frequency of about 1000ck22s 9h -eweykk/vr1 Hz 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 obsehnw: 2 1g. acs6d8oubyrver on the ground hears the sonic boom s2h6.g od8 1ya nu:bwc1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa1h5) ql 0lumjet 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