What is the evidence th +-oery6 z8er/gsr uq5at sound travels as a wave?

What is the evidence that sound is a form ofr)o-i36 gptxc energy?

Children sometimes play with a homemade “telephone” by attaching a string to1;oqpcb*f7 wi:5-wu 7l ayx uf 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 how thuf oyuqfc-*wa5wbp;xli17 :7e sound wave travels from one cup to the other.

When a sound wave passes from air into watev 7f0qnvlp7llk5.g k ; 3y/wsnr, do you expect the frequency or wavelength to change?/;07yp v.5 vkg7f3klnls qnwl

What evidence can you give that the sv0kv/rkcd pbs; v86 3 l(b.bfkpeed of sound in air does not depend significapb/kskvb(8 d rkc3;.bv fl60 vntly on frequency?

The voice of a person who has inhaled 3oot so0/h;0f4srjg xhelium sounds very high-pitched. Why?

How will the air temperature in *xnvdfqe/ojzklv:33 k rc -,f34 xro2a room affect the pitch of organ pipes?

Explain how a tube might be usedygvc0p)x 3j, djabv ut7w)l +3 as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a ux lpy jw3v+)abgdv,30 jc)7tcar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up+ ran9f-9 6(hkbrloil the fingerboard tow-binfl9h( a6 orrk9l+ard the bridge?

A noisy truck approaches you from behind a bu xk.(s6l.z ddeilding. 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 the high-frequency noise. Explain. [Hint: z dd s6e.k.xl(See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferencfk .,-usnnqxu+9u2u 1qj d 1nke in space,” whereas beats can be said to be due to “interference 11u s9 un-kx.nunf q2j,dq+ukin time.” Explain.

In Fig. 12–16, if the frequency of th7rfe)+fsi r 5be speakers were lowered, would the points D and C (where destructive and er5)+ 7sr bfifconstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the heari ;gocvo y8 c+p/o3)zd0p.gf xing 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 could adding more noise reduce the sound lz3f+. po ic08/) yxvpgodc;ogevels reaching the ears?

Consider the two waves shown in Figr7lcpi/fu (e5qtm t,+. 12–31. Each wave can be thought of as a superposition of two sound wemc+r/ tf7,tqlu( i5 paves with 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 the source and obserbd 7fg (d;uzz7ver move in the same direction, with the same velocity? Exp; z(fddbu7 7zglain.

If a wind is blowing, will this alter g +vcuty4c)v8the frequency of the sound heard by a person at rest with respect to the source? Is the wave4cyv)t cgv u+8length or velocity changed?

Figure 12–32 shows various posittn ,jx,o p6/w4ey01pg jmgaz, ions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear tjgj0gen4,pz, a x1m ,6y/wpt ohe highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by q:hiex uv , v-av*0s3itng .ol, g(*iglistening for the echo of her shout reflecte*o hvx3gg:t.sa (, -u,0g i*qivlinved by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearswt7s(z; veo9d the echo of the sound reflected from the oce9oz ste7(w vd;an floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng3c+ zll c twp//.b2fhbths 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 scho8h 4oa;oam/q-l.qy oihou;)q ol 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 8q;yq loa-.i h)/uha4ooo;qm (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The 5anvxbut8 d *7splash it makes when striking the water below is heard t*8a xdb5vnu7 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees at7 tijey4folt96axf4/rwy + 4 huge stone strike the concrete pavement. A mom4o 79atftw64 rty lyfj 4i/+exent later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by . q0oxe- mmu9whc 8n4xyesf 7u3)ow7qthe “5-second rule” for estimating the distance from a li7qouh847qseyfex-w. x)3nmw uc 0m9 oghtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a h7tv4si /j,wjr h3v)s sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound who.f da l8kr(ww5se intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouve1 7gc h/6qubsly at a certain place, what will be the sound levvgb1h e6q/uc 7el if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a c s;o ,pvj2p1t)dgx:b oertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this persondg 2,tjv1b; p)o os:xp experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is t4 8puk /vu evx1h1x5osaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise41t 1k uvuv5xh/8ex po for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norml mpdijv4x cxduk: mv.+ 0;9x7al conversation. Use Table :ukx.x d 0v+l7jmm ivc;9dp4x12–2. 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 eardrucn ;nrsy3994vts4d u em 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 250 W, while the more modest amplifier B isrpq /l:ffxf3h+-r o6u d :lj*j rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 mo3r-jxl lrd* fp/u+j f :q6f:h 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 m 8q qw9vp4fs* f s;/1:zrdptclmcd*p; eter registered 130 dB when placed 2.8 m in front of a loudspeaker on ppcqt :v/c89ds dl s;mfzfwrp1 ;q**4 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 q,ewr/tbar q.zn + v2 )c8d8:aih8lfsa difference in sound level of 2.0 dB. What is the ratio ,w +:qf82di a raln/rsc8qz)t ev8h b.of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound waven7 w+e r.mf dvzadd:+69qh. ny is tripled, (a) by what factor will the intensity increase? Increase by v hfnydqd+.w.m+re a dn7z96 :a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one h3 dzku8b0o)n hig p6w(as twice the frequency of t )u0pk8z6o(n3gb iw hdhe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that(-rfmnr 1y37rlrstt 0r ; d/((vm0.pky bv ono corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 H f.0tr o;b 0rknsmnd/((r- r3 yvrylto (m1v7pz?    dB

  A 6000-Hz tone must have what sound leveld9ky0;ued bo4 to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig0uddeok;y 4b9. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whed.9 9ba(ooiu:fd hp z7n the sound level is 30 dB? (See Fig. 12–6.ia: op.9 f9zbu7d(ohd)

  Your auditory system can accommodate a huge range of souu;m :h( hsfr .h: 1dau6j8yulchq3p nrsb+/,vnd levels. What is the ratio of higf (j1 6rvh:snq/.:a ul3+hsdmh b8yh puru,;chest 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 oxg;kx804g e jg9/-iyebwraj 9y*2jsy f 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mus*;egb g x0ejyyxakwi9sj -y /8 jg294rt the string be placed?    N

  An organ pipe is 112 cm long. Whattevl 3(h+cs po 27 h2+grqy5ds moc4jk59j j.o are the fundamental and first three audible overtones if tq(7.do+chrhk2+otvcj5m jy 4 l s32o 5eg9sj phe 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 w. m gdw)oobo;c m(6.ft4scmaw 9+te:bould you expect from blowing across the top of an empty soda bottle that m6g d4 :m+cao.w(tem.s9bcobwo); ftis 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range om()w)wiavom)si 6vikne* j;lt 43 8jv f human hearing (20 Hz to 20 kHz), what would be the range of the lenge3v(w8 4* w nsalvt;6k)ii m)ojj)mivths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freq f4eqcp2i0fxe;o/d 8v-o rvg) uency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of o;)po2g0cie-e4dv o rq/ xff8vnly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lc1 2ioj c7s:ulong and is tuned to play E above middle C (3ocjs 1 7:ui2cl30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (2x 7df76bxd;p e62 Hz) when xf6;7x pb 7ddethe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 208e g+f6he )son $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of ta+hs dx7vzak *e-iqq4ho6 d9a 08owx )he flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz? )aa9xde8 z i* qs-dxow4okqa h70+6vh   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, and 616 Hz, but not anfjr(l r.:6m ft any other frequencies in between. (a) Shmf r6r(j fln:.ow 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 loid 5pylm uludfki7p*.ya-*/5ng is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz k lm7y lipd .di5puy-a*/fu*5 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 y w8dc9y 9(u jnc-kx,wdnu-)w$^{\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 aus67 biqn qgccfu0i4 w:5nh -p/u/ser;dible range for a 2.14-m-long organ p6hqif05:gwe bs4c/p /ucq7 n-ui rns;ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cx06b1chtnry0 cm j9t rz w3(dc 4v+j9mm long. It is open to the outside and is y964crj3 dxv bhwt 1c jr 00m(mzc+9ntclosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust c-1uk;u txgq.xt c/ .a4fuh: ptwo strings, one of which is sounding 440 Hz. How far off in frequ c.t.xu: -;a/ ukqtchf41 pugxency is the other string? ±    Hz

  What is the beat frequency if middle C g (3k8 -q9pk:tp xc7eqi85cqtk +ku ti(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 ( d;ul,b6xrs+,k d sn-nbrand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 500sds-nrb ,+k;ludx6 ,n0 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 350seto.y- y 3x8t-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoningyt .x y-38toes.    Hz

  Two violin strings agv7n9gmze; :jre tuned to the same frequency, 294 Hz. The tension in one string is then decreased by ; :gjmzvng 97e2.0%. 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 flutes each try to play middle C j.3 ql 6 wlgnqcw hpur (+1p+e-zxgv9/(262 Hz), but one is at v.3x/+uwwe+ 6p- p9ngj1cl (qrlzg qh 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, ank8e:9*uuca 6zyc+dk. wd;bi y d C. Fork B has a frequency of 441 Hz; when cudk9k* 6dy:ba.;c +uziewy8A 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 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 persdc+*mrkw s* k5n( xql1on stands 3.00 m from one speaker and 3.50kdx(1w5* lm +r* snqkc 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*sau 8 f.oy/7+x1 -ognarid n*hqn;po, but a piano tuner hears three beats every 2.0 s when o8 1oa*up;x/h*d .ngfys-r7+q ani onthey are played together. (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 wavelengths 2.64 m and 2.7crb .m4p:ucgy s.s t,59y5viu +tw;+m pzbi*b6 m in air. How many beats per second wi5 9tpzywc5i.s4b;cum +mrbv ,bt *u p: .isgy+ll be heard? (Assume 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 re vbg7-fn-4 mcc6jh7y mst. What frequency do you detect if you move with a speed of- 7m64jnbcm7hgv-cfy 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect ifkw8 xou0 1dpkrq /vk94 a fire engine whose siren emit1vw/ku kd49 o0xqrk 8ps 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 2;n*3qr5( kpwu g .4or.avewwt000-Hz source is moving toward you at 15 m/s versus you moving3 *q5rpt vo.awekrw(;g u.nw4 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 tlvo;eetds*v + *buzv3q :(i(ohe 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 frequency of 5.5 Hz. What is the frequency the horns emit? Assums3dv; (u(tz*o vb*levq : ieo+e T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soukc*, y)k )lkzgnd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequk, g*c)lzykk )ency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ult 50:qhyw * t: i4;;ppip/vwn jc,oxqoprasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wavejxw yi0 p5;;p:: ,/pv4 wpqtoohn qc*i?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played qrl)+njq) + tocf bc-2+imim.u j 5pm.on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat fretnl)cqm r qfu5 +2mii .j+ .-bm+opc)jquency 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-flx-9zd twh /:rj8gb5m gow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound9zhwjg8 m/r t-d5: xgb source?   Hz

  The Doppler effect using ultrh18cl:+3 bqg zhl1 szxasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequenc0f(t j2(r6gp 1tfq shky 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at t1ftrp6 (h0sk g2jqf( 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 atuh9mr.1 zc7 r1-yjf /zt0eejc 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..jr; uccwm)2 szfjz 203 where the speed of sound is 310 m/s (a) What is the angle the shz m)jrw;0j. 2uf2zsccock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of socftxz;-8k m7cund is on8c 7;tm-ckfxz ly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Detx 0tvs)c/ow+iermine the shock wave angle it wt)is xoc /0+vproduces
(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-v ovs* cb3rlfza. .5$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead anoz(j4q4n 1 dzwd see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km.zzq(djo4w4 n 1 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 sends 20,000-Hz sound pulses downwax : /zm2;9t0hfhql,e- sseaqhrd from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water l/stahhz,eq 9e ; 0-fmx:sh2q)?    s

  Approximately how many octaves are there in thm 3s3gqznc2056e ahute human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It con69 wo2zcxcxix, xmi*am1f b+;fu;/ l xsists of many plastic pipes of variouwcfc ;m xl /+xmoxa;xf6 uxib19*i ,z2s lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makekn qo u(i-foc10p6zxb.c+u v 4os (go/s a sound close to the threshold of human hearing (0 dB). What w6k 4 gp+.(o(sn-v ozf1uqoiu cxc/o0bill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level wheb :) ,pr 9sl7nzc:ow nsabd;f; *rzzv-n an 82-dB sound and an 87-dB sound are heard simuvn7 r,scb*z; l)rs:f-oz :9a;dpbn z wltaneously?    dB

  The sound level 12.0 m sfpz +61hahwwp5p j59from a loudspeaker, placed in the open, is 105 dB. What is the acoustic powepws9h1fahw +zj5p6 p 5r output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 15 5gz0yk*6fowy s ;*a)x*lgay / b+zlzp0 W output at 1000 Hz. The power output drops by 10 dB *f*y5)b6x kly;yg*sa+z aozgwlzp0 /at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraftx)bu p qo(o p,2hn)0wtl/b;anhw8 *mh 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 ear has ah)n hub* ;wh,wo0lp)(p/n om2xabq 8t n 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 communications system44(:ysvdbfsqo fymq171,scs s, 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 isxut3wvxmt)4i9j 5 p5w 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 lu q7ib25f7 r6d+idmued points with a fundamental frequency of 4406 2udbid u5lq7f+7rmi 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 tubey csg 9z6(uc 7+dox 5debzpl47 filled with water (Fig. 12–35). The water level is allowed to de bcz l5dx 7(7+d64zsu9pgoy crop 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 near a tube that isuf,0nh4 h/wtw 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)unw0f h ,/wth4 with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tv ,qy2/n 0yvy*lq 1mlvo resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure vuwo; (nns e.bm:j7 f(m,z *ttakur:(tone in 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 m(.mutztj f;7:beno*k vw(aur,m (:nsoves 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 tra 3nv8(kb qitp t,.1wwjin is stationary. The conductor on the stationary train hears a 3.0-Hz bb8 .kiv,qtj3twn1p ( weat 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 5381 9zp iji(/p :j*icne+v8hk ) w/ybayw Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the tri:w9k(8i + 1z/wpvhbejy iyja/n*)pc ain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenii2 y; snofx740c; csdlng to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How f;yn di4720l;ssfxo ccast is it going?    m/s

  Two open organ pipes, sounding together, p*gzo 6vtz4c :oroduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Ho ot:z6zc4ov *gw long is the other?    m

Two loudspeakers are at opposite ends of a railroad sf c/wyr4)/g+2g.4e;pr rw 5o pcys zvcar as it moves past a stationary observer2gf rz5 vcp/4;.ww)gyc/rr 4sy+ pes o 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 flowh8j/)l5wpl(t- nlz g x in 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 that thh pzg)txw-ljn 8 5(ll/e waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at spoaa17a fq1oq.p y3v0e ;3 xsldeed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat y3 qv10ap.oofa ; x1lasd3e7qemits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freque+;e c/ss 2mswuncy 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 bef /m2s;u sw+escore the next chirp is emitted?    m

The “alpenhorn” (Fig. 1g8/aomy (ljj)j j 1 sf3mrxq122–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is calj/31x)rmgojym2 j8q a j1(fs lled 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 bypfbz l 7enkj,)*9ub. i6wbow+ the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roo)oj piw 9k7+wuel*zbb .f6nb,m.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” u wbd55) cy7pbvs3. aminvolves 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 rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-lcs53ubv5.ya 7wdp)mb ong 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 t;f1 z5 p4d0/qsorhcwahreshold of hearing for the human ear at a frequency of about 1000 Hzd5/w 1s a 0hocfprqz;4 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 bpxp8: 4 z0gvqhears the sonic boom 1.5 min after the plane passes dir pqz 0b84pxg:vectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1c b9:4c:u1ptdpz2 bpb5 $^{\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