What is the evidence that sound travels +kie 3j4 4 luwtomu3p/as a wave?

What is the evidence that sound is a f 4 81ybq2 -)cvbyqbimaorm of energy?

Children sometimes play wit-m*lhqtj54zoq-d mp ia8 0bp.h a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard p qm4tho- .b 0jq mi8ad*lp-z5at 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 ih.pq.wr64.udp hj 7 tlnto water, do you expect the frequency or wavelength to chan 6h.p t4jw.prqh7l.d uge?

What evidence can you give that the speed of sound in ai 6g/:vzegsb-m r does not depend significantly b-g/vg 6esm z:on frequency?

The voice of a person who has inhaled helium sounds very fv+-.cz3afe f6ab o7 thigh-pitched. Why?

How will the air temperature in a room affect the pitch of o06maj,e iis 4t4.xnbz-)cs qlrgan pipes?

Explain how a tube might be used as a filter to reduce xdym r877q ;-l:twg jlthe amplitude of sounds in va- 8 dwxj lyqlg7r:7m;trious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3lw fq.j qleb*+7op/cm2nazx-o 8yi4xg1c 30 n0) spaced closer together as you move up thqf8cnamlqoiw17/ycj. 40 o3*-x2 gblp nzx + ee fingerboard toward the bridge?

A noisy truck approaches you fro9nkd ghn- ,xfid0c9 +ym behind a building. 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: See Section 11–15 on diffra,0dkcidn y fg9-hxn+9ction.]

Standing waves can be said to be dumu 8b);gm-af3u *yidz ,h(zase to “interference in space,” whereas beats can be said to be due to “interferenc)z yg;hu -sbfa(du 3,*am zmi8e in time.” Explain.

In Fig. 12–16, if the agg,eai; -*g,qcu8:c y09f++zjmmzkqer fz, frequency of the speakers were lowered, would the points D and C (where destructive and constructive interfaf-; f qya,emruj0ec m9g ,gz zk8g+zi,:q* +cerence occur) move farther apart or closer together?

Traditional methods of protecting the wbro7x2h1j 4g hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Insb1rwhx27 ogj 4tead, 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 :e*ya*ox/ a7 wgc-gwoshown 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)g:agxe-y/ caow 7 *ow* or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directiontug 0x:u rt ;,s84wgft, with the sames4u8w0:r fg tu t,t;gx velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hexni0ns/gg, 2 wgp +jf.ard by a person at rest with respect to the source? Is the wavelength + xnjp/g,ns2. gwg0fior velocity changed?

Figure 12–32 shows vay.oz)tqi0x m1a-ot /mrious positions 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 0/ai z-x) yoqtm1.tmothe child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake pj4ms) y4t (,wfcbj sd14b;ru by listening for the echo of her shout reflected by a cliff at the farmfucsb4wt;d4p rjj,)4s (y1b 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 watejh9)a3pmk je6czft )2rline. 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? akmj p3f) h9ej2ztc)6Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in a w0aer/4fh8-bebf q 5sir 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 q 9.c3xk-e kmcdrifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How muchk 9c -e.3kmcqx 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 cliff. The splash it makes :k:87 0sw fj3 hszezskwhen striking the water below is heard 3.5 s later. How high is 8kj:zek zh:w3f0 ss7sthe cliff?    m

  A person, with his ear to the ground, sees a zllc4* jlklhb7g +4;zhuge stone strike the concrete pavement. A moment later two soun l+lb;z*k 7llg4j hz4cds 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 the “5-seco1nplfp v :b.a +fcsz +z p/*fn1w7tig2nd rule” for estimating the distan17+i+vt l pn.bz2fpn:1fzcs pga*/w fce 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 aox2w8me k y9 svc,)t i+d-7x5ygo,yx a-*g fxht 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+ h wyzgx/z:h2 a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce7g*xiv2 b9 onw8 3k:oib a+xzm a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add igv8 mb xb2kz:+aoio9 *i3w7xn ntensities, not dB’s.]    dB

  A person standing a certain distance from an airplanehde: d 5g:u qikh1c*y9 with 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 ::k*hiyc eu g d19hq5dall but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a b6xg1ifk3. :+l zztoz signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio f xog:ztb+31.6zzkl iof intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from 0xb5 d/+d1ihqtkxdo7 a person speaking in normal conversation. Use Table 12–2. Assume x/dqdx+oid t1k75bh 0 the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose areatebkak wpuqr2 ajxhlc 435;6 lz 11s0abe,x.6 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, whiiwt gv+apa )+20n 7wjgle the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudsvg7+2pi)atnw w+aj g0 peaker 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 registerj4f nu.er/m ,t1jbyr0ed 130 dB when placed 2.8 m in front of a loudspeaker o1,fejjyur 0 /t 4mnrb.n 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 1dtq0p;; y n4pqdz 2wzof 2.0 dB. What is the ratio of the amplitudes of two soundsq1y 0pz;p42dwznd qt; whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensm5y5q* ud(yq ;t*4wycuh je :jity increase? Increase by a qm5equ 4tuyjyd;chj y*w:* (5factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplic)dqg g/)/ -0csccje jtudes, but one has twice the frequency of the other. What is the ratio of their intensities?c)cg0 sg/q-jec /j)cd   

  What would be the sound level (in dBbiz:8g+s)tb;;so f s r) of a sound wave in air that corresponds to a di8g;s+tbzi fb: ;s sro)splacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lep4 hj (-qdrr uembhr,o(- v.pg)t i1t2*kwl7 oud as a 100-Hz tone that has a 50-dB souu(q- (gel1r t hwhed4r-7p .2orvp )*i,bjmtknd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tha lunklzl;83n5wwg6 t 9t an ear can detect when the sound level is9;t6wgn3 zll 5k8lwnu 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is t ;cnx 5hor setzv).+o5he ratio of highest to lowest 5;vnco+xe.hto 5)rs zintensity 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 53 i 6t;w)clhaosh5m tof 440 Hz. The length of the vibrating portion is ihatm5h t3;c6o )5 wsl32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three a7xli.a/- 9dw1lm aqzl udible overton/dl-.za1q9xlam7 liw es if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across pwqs/:z +-0 xhmrs; wsmt7:fyck b1.xthe top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed ; m z +/xbpft 7 qyw1.rs:c:mx0shw-kstube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe o7 )oi8y5zwxjm rgan with open-tube pipes spanning the range of human hearing (20 Hz to 20o5x)w8yi7zj m 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 frelpn 5e 59oql.kquency of 540 Hz as its third harmonic. What will be its fundamental frequenclon5kl p.59qe y if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strin;m3ge.6thz l;; mbgh 8vuwhoat y.4-)/ pboq gg is 0.73 m long and is tuned to play E above middle C (33o h gmgwp4mtu .lazo6;bbe;8y)3g-.v h/qh ;t0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz)/p bj:w/ag-u s when th//:-awb usj pge 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 ajmkbz4,xl31l t 20 $^{\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 12–1q9lhql /vd)9 )euj))eon )v mz0 should the hole be that must be uncovered to play D above middle C at 2)/)qvvhj)llqe)onz 9 9ue) m d94 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 reson4 95 nty3efqdgate at 264 Hz, 440 Hz, and 616 Hz, but not at any oe t3qdf4n g9y5ther 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 long is open at both ends. It resona5610 qgmbv yprtes at two successive harmonics of frequencies 275 Hz and 330 Hz.y v1mp6b5 q0rg 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 lw88jevnacu -ft +*rwaco: 5,$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-looqn 1e:0.v dplng organ p0np e1. :qvldoipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to,.+gia4t7apacd. pj hho yy. 7dau/e5 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 relationshicya+. 7j d at,i5/ dheayghp.u4a.p7op 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 two strin7sg 5aagab/k5z+ s0lpgs, one of which is sounk sag5b+pzl57a/g 0sa ding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle (i.q *qe:bc3/p3l6 umdw gfxpC (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 operateffx4 y;n3tepys x-2h cc,i ln 9(*az.oj.nr6bs at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separait6,s* zfyx(.h39 jcexnn- 2 lrbp.yoa cfn ;4tely, 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 whls-s96o:3xgq b addn4 en sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explaiqn 3als6go4dsd 9bx:-n your reasoning.    Hz

  Two violin strings are tuned t2zqq . 8qzmnk-o the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%.qz .zkqqm- n82 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 pltjdhnh359540 ayvj d(b;t zim5tv(m.9vo menay middle C (262 Hz), but one is at 5.0°C and the other at 2539ni5zhvvam( 4v j b. jmt(0my 95dn;ehd to5t.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a 4:cpx f7kfc u2jaa3fkuy r,+1frequency 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 a2 k7ycxr4+p: j,u k31 fuacffare 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 person stands 3.00 m from one speakerh*m aw6ix*bzu; vu 7x. and 3.50 m from the other. uam .*z7hx*6b iu;wxv
(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 vibratinxl;foa3 u3u ,b 5azqkxqb c01(g at 132 Hz, but a piano tuner hears threqxuxflu ; 35ak q0,ac(obz1 3be beats every 2.0 s when they 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 wav1,wgfywzhcp(2 5 zn gj.t2al5wt1t p0elengths 2.64 m and 2.76 m in air. How many beats per second will be h nt021 (jhf,lwg5 z5 aw.pc twygp1tz2eard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ofz+s) v12wow jbfvjq4( a certain fire engine’s siren is 1550 Hz when at rest.vvfzow2s 4j1b)q+w (j What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yo0c)cw 6xddgh,:tb f5 mu detect if a fire engine whose siren emits at 1550 Hz moves at a speexc 6hd:5g dw0 tfm)b,cd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towaejt) j .p *550ejcpehwrd you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are tp5) t*j50jhje ee.cwp hey 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 fw9: 7 4xuhfu ;ymb5dnfrequency 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 emu7m:du4 nfxwb9 y h;5fit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives thht7ff o5b(h;xdbxq15 em returned from an object moving directly a5;h5 b(hdox fxt b1qf7way from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spevjm5,l)1 qfsuwvvox03a) x( ned of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectnvvl vj5w)a3o0x,m )1s fxqu(ed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fl/ g.,nld gxrp/e,l37oa1*,c mvc)dqawmj u 4bat 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 frequency was heard if the train car approached the station at a s3gnlae1,j r7qd,d/p/ v 4ul cw* )gx.mom,abc peed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blooda66 mt+xj o2ko-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequenmt626ajo x+ kocy if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wav(d(i(w( zjfvv es of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of fg)1 (f t:cjrqvxxy4a9;cj)tv:hpxu: requency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are locatcjt( x)9: xjfc aphv1: y:x4qur;gv t)ed, 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 20 ( y5(woh gxtijx;.-om - x;/ bpdd2bhh$^{\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 w tzqx)b xd(59there the speed of sound is 310 m/s (a) What is the angle the shock wave makes wit)tb(x9d 5z txqh 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 ss0 oa .vz 0m:zyaw4. +rb.qn 7yjatsp-ound is j7w-ma.yyzbqpo: ass4+t.va.z0n r0only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine tgu5 xqcaxl0 pl+v)6)uhe shock wave angle it +6x ua l0pu)qxlv)gc5produces
(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 6vhgbb.vmp2qh9*k ;hj8at/x $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhea,cin0;.o mvtack)q -5wer (cgd and 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 plan cqwckc50vom-iert)gn ;a., (e has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-H5ha psl hd q9vno liy)/1+2o1kz 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, what is the minimu s5p n kod1h2laqil9)yo/v+1hm time between pulses (in fresh water)?    s

  Approximately how many octaves a3;mdig qku:q)vt 7xi4 re there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syk bb72fe vt-y(mphony. It consists of many plastic pipes of various lengths, which arfb(-ve k2y7b te 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 fr5l .+4q jh uvi,1zeyjwom a person makes a sound close to the threshold of human hearing (0 dB). What will be the15 4u+wej l.y,h qijvz sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound aref7 a flmms9),r heard simultaa ,mm)fr 7fls9neously?    dB

  The sound level 12.0e + ;y,c8u/qazu0 vbwg m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speakerv8ua0/c, ;+bgy qewuz, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power 6ftmqt*g1ee1q-oif 2 output drops by 10 dB at 15 kHz. What is the power output in watttio- f6 1qe2 1ftq*gmes at 15 kHz?    dB

  Workers around jet aircraft typical oh406g yvi4swwx) kt;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.xo)hk wg0stiv4;yw6 4 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 communication.vox2:sugrh*zc upb.w ps.9,qz 2yq0s 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 frep,r, h u34ibfjvc kv4*quency 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 fundam4un:u:kq x8l uental frequency of 440lu xk:8:nu 4qu 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 tube filled with waes8(udju9rknf e(60 fx ee8-dp+k l*uter (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 distance from thed90fk6(eelpxs feuuk+8*r -uenj 8 (d 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 g*7e* . z0fqawzzxlixle .+.dstring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mll.*gxiea.ef*q w0z7 .z+ dz xode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t+da+d ;avgi1j)nwz4 xo 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 v/)kyn s36ipftone 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 moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than v6n yk/sf3p)ithe other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the wks,eqt 9lswo 2a7d 6w113iiu stationary train hears a 3.0-wl 1e7d,2oq1ut3kww96ais s iHz 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; n3/q gwuber. you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? q;3wn . b/greu   m/s

  At a race track, you can estimate thw,jmrtr 8 jx 0ceo:2j(e speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sou8 xtoj2,jr (c:w0mrejnd of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce bfv4v:3 o;w teiv f6d*a beat frequency of 11 Hz. The swtb4o63: v f*ive vfd;horter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mp ejho3g kdnz7*e:.1x oves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passedz13xep*n: 7 go.hkj de him, at C?

  If the velocity of blood flow in the aortapk29q 0;2fkv5yi*w 5nbvk xvw is normally about 0.32 m/s what beat frequency would you expec*b52 q0x2 5v pkywiv;f9knvkwt if 5.50-MHz ultrasound waves 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 is flying tow5p9*i fhnew-e ard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave refewh np5i-9fe* lects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it appr1 *m* r)xqdkwa4flw.c oaches 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 t f m lq)c*1wad4xrk*w.he next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from on5 y2un ,:suobme 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 muyn, :b uso5m2ust 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 of :e3houfg c3rh3- m;lk 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. Cal;r c-m3g3hol3 e:ukfh culate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing ) *9y2mxk qbu*sd vs2nrods,” involves a long, slender aluminum bs v**ysqm2dx2 )u n9krod 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-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 hr9v(u s+ fx3asuman ear at a frequency of abou(ufs+a3 v9sx rt 1000 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 atfxy*,* *hg flq Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhefhyqgl* *xf *,ad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1w7d-0a-c zw/gzbv: zp xk1 m 9m-udli25 $^{\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