What is the evidence that sound travels as a wbrw+ /gupr42t ave?

What is the evidence that sou1:oq0zhcd 7hd8k- cplnd is a form of energy?

Children sometimes play with a homemadeg8 9b d4*opwxb “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, thd4*b owg 9b8xpe sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passek:0:wl l 9wb6vsc3kmas from air into water, do you expect the frequency or wavelength to change?sb:cma :69ww llk 0kv3

What evidence can you give that the speed of sounc) n ;vv x .aox8*.iqzj1clzo9d in air does not depend significantly on frequency?c cv9jl;ox . qz)1avxoi8*n.z

The voice of a person who has s, +hfxc2ml)cinhaled helium sounds very high-pitched. Why?

How will the air temperature in a room aff y0myh(. m kc5qnl neud5.y18sect the pitch of organ pipes?

Explain how a tube might be used as a filter to r1r. yv5nx 8nthez*. r xc* zom+;gx7cz0yk3h zeduce the amplitude of sounds in varikhzg.x5r.+v7y mte10x ynhcr*z8 ;3xz n* z ocous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar gec(.ntvm4 ,k(Fig. 12–30) spaced closer together as you move up kv4,. cme(gtn the fingerboard toward the bridge?

A noisy truck approaches you fro/mb 5 3q4ed q3awblo6tm 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 noiseol/3b 3atwdqm65q b4e. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats c2 ui.yw+,.q wqq ilva4n8/xnm an be said to be due to “interference in time.” Explainl/.n imux 8qwvy iq.+n2,wq4a.

In Fig. 12–16, if the frequency of the speakers were lowered, woulox lrtsz47ic, 1kbz81h sg ;d1d the points D and C (where destructive and constructive interference occur) move farther zbd gz1i 4718s,hc lstk;ox1 rapart or closer together?

Traditional methods of protecting the hearingr ocv zj*/gkv hzq93u2.35 hed of people who work in areas with very hig. z2h3ecz / q5r9u3 jkhvdo*vgh 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 levels reaching the ears?

Consider the two waves shownfc)nbhl 78v( w in Fig. 12–31. Each wave can be thought of as a superposition of two sound wavn (v7 h)wlfc8bes 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 observer move in the same diret,4vdggs2)f yg4zqqut7 +/emction, with the same velo vyt44sq+2umtgfqd),g/ ge7z city? Explain.

If a wind is blowing, will this alter the frequency of the sound heard ena9:(spjp+s *lzbm7 -upj6r by a person at rest with respe*l+ ( -zpajunrm6p: b7 sj9sepct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positionr(d-n/qp,7rpe5ctw y ;l 2rn ms 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 the highest frequency for the sound of the whistle? Expl(-t,n7r edrny 5clr ;2qm/p pwain your reasoning.

  A hiker determines the length of a lake by listening w efa 8,jbrgci::pw3, for the echo of her shout reflected by 3w wp:br,cagei, j:f 8a 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 hq*4ok1eah2 vgxapn3u4 -hv r -is 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 thisxah- q1oa2 k3 hrp4e *g4vvnu- 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 wavelengths in aiid-j vw.h 84l )vs9tncr 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 schoo+*ro stye4:y mhp *go6l 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 rhy4*e *:oy tp+m6ogsheard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash i lm7scd hasf2,c tt(./t makes when striking the water below is heard 3.5 s later. How high t2s(7thclfac ./dsm ,is the cliff?    m

  A person, with his ear to the ground, sees 8cnkhk z68 l4opr33ew3hgos mnqc( 67a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the oh 4oz73le366n w 8q(k g3ohr 8mkcncpsther 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 yy)t 1bb i(x*pmile of distance by the “5-second rule” fo* )bytyxp(1bi r estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? gza( hy t3def22iac4)   W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level w -x(ai w96gdlt*ngmmzg(s+ -of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whi,+ rz-p/dnj xen fired simultaneously at a certain place, what will be the sound level ifripx -/d ,+jnz only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frov4nz1 sw6j6im2tln/ lm an airplane 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 all but one engine? [Hint1/lls v664 mz2nwtijn: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas3jy67w hm*yb mb:qre40zvj ; t for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devi:*y h e ;jymbvz0j6t3m4qr7bwce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pervwc4ar6c,3(3k , +vhk 2ytbl8lzv bqfson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unifolvcwkbz 3kv+3fyt,qa28bv 4,hlc (r6 rmly 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 striljmwcg ns wf(4k8 43 7:g(tmickes 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 250 W, while thepw0r( ir8b** j0wzhcq;f+(u eux+npg more modest amplifier B is rated at 40 W. (a) Estimate t+ ecwxq (ruwbpu 00fgn i(+rh* p*zj8;he 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 re)q2 n j/gz0 1-wqmxvev 27qvumgistered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. v wvuvxg12m2 qm)z n7/0-j qeq
(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 i.u5d* )mkdgk)rung 5an sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose lru5 nk)gm)*gak5d.udevels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wzyz nk:..x./zxg8sei ill the intensityk.. n8z xz:/ie.xs ygz increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal d-0-/) v zuqsd xwk/uwzcc6 m7displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitidkq /xm-70wz d /uccvu6) -wszes?   

  What would be the sound level (in dB) of a sound wave in air that correspo.yxf x.(s):gd7f.td hfuvd 2x nds to a displacement amplitude of vibrating air molecules of 0.13 mm . ) sdfd yvx g(xthud.f2x7:.fat 300 Hz?    dB

  A 6000-Hz tone must hav ns;rs(4lbk16dhff g: ) im4xq( ze(kve what sound level to seem as loud as a 100-Hz tone that has a 50-dB soun(ebl; 6f4xq(g : hm)frd1snk vs4z(ikd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the so haj:4a cacy uz 6y,90zyh-(svund level is 30 dB? (See Fig. 12–6.ca(0h :ahzuzc y4 ayj,yv-9 s6)

  Your auditory system can accommodate a huge range of sound levid8m9a4fmqu2 fs/y5 be(y6k pa,tzb4els. What is the ratio of highest b2f,9e4 it /d pmq5yya 4u68bfm(zkas 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 funj8s hzfc10gfl 94,q ebdamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the cg,blfjz91 q8 f0hse4string be placed?    N

  An organ pipe is 11282ssugi 8q)v y cm long. What are the fundamental and first three audible overtones q8vu82ygssi)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 fru cqo8yw.w-9ec02w61 oofnq jom blowing across the top of an empqu80ww2efcnyoq -9o6 1j cow.ty soda bottle that is 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+cksttd) / u8u open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengt t+tuuk8dc/s )hs of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as xox9hrbi6ycswp3j / 5(d a8n1 its third harmonic. What will be its s8r5xc 1di 6h3(yx npwo/9bjafundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string iss0.gp3g z3b+at8 pesq 0.73 m long and is tuned to play E above middle C 03.e8zq+apssg 3t pgb(330 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 hcw32ih(;8lnp j5r fu(262 Hz) when the hcf8rph; 2ui3nj( 5lwtemperature 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 a fma43r8 okscv ft0,*ct 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 12–10 should theo 0gow a2x p6 6/6lkbbk(-rzgq,w aj6a hole be that must bbow2b/6a qar066kk -pj,z o waglgx(6 e uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pisoan is4u z,ql5567hg pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other freques6nqsoz h7 5i,5l4agu ncies 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 1.8ltf)8qr (w19ckhw x z-0 m long is open at both ends. It resonates at two successive harmonics of freque-zrl tw8q (xch9)w1kfncies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 mstwbufq /z0doq p144*5 * vks$^{\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 a;bty/f 6+ rw ta3u/q9y ;u- *(vswtijsff5lqu udible range for a 2.14-m-long organ astqyqf-u us* tfu(v;t/bl/;635ifjyw 9r+wpipe 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 x(kuid :p0p2copen 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 kcpxid 2: pu0(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 adjuly0u7/sxka7x:k2 u ye z/rb 7kst two strings, one of which is sounding 440 Hz. How far off in frequrax77k/yl e/0 syuzu k7: k2bxency is the other string? ±    Hz

  What is the beat frequen0hl9kua3 z5r lb/6o gicy 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 operatp s79pux3ck (kes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occuucpkk(3s7x p 9rs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wir 4 bzy.coq aiik5gk.v(.uc9.th a 350-Hz tuning fork and 9 beats/s when sounded with aiz qgrvkc c.5y(au. .k.4boi9 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensio 0f,ztgvgtl g3*1jpr3n in one string is theflgt,tgpgv0 j*313rz n decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play midgc;y 6*p+rseu+w da0/o 5fbvmdle C (262 Hz), bcmv/56wy++ ugdfo;e bp ar0s* ut one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; kr;xx/im4 efugy)::f when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are so r y:4;):k efgfiuxm/xunded 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 person stands 3.00 m frp u5qpm h+;auuy2 qs: bv,e-j5om one speaker and 3.50 m from the othev5q:;p mb jse hq5-2u +a,uupyr.
(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 arelgqh 19cl5h7n supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the freque 1h97 5llhgncqncy 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 2.649be .i (ikb av+m)tzj2 m and 2.76 m in air. How many beats per second will vjtb )ikba9zi m +(.e2be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is hsol-xmrkai0a 605z4 1550 Hz when at rest. What frequency dla o m5kh6ix a4r0-s0zo you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect i;8ef,ki:z cow;z7d/ .qb3v6 l- km9 ottbqefvf a fire engine whose siren emits at 1550 Hz moves at a speed of;8b.bekd ieqql9mvf fk :,wot zzt36 7-o;/cv 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifgufl:3xmbs2uj1 , bb 3t in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly3,bl3b2m fbu:xgsu 1 j 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 sitik x g 5d6fw(knr-24pngle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s t 5kgx knpwdi42 (6trf-he driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receikteipmi+.3 lp , )e*voves them returned from an obit, *poi+epm .)3kl evject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, thel rq,/qd f.r7t bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thefrtr7qd .lq/, reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler 0v5m,r q)jl: rhaan f*experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played ma5*jlr ) q,afrhnv :0the 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 ultraso/g(lxpe()) ; lozq oq-bgnr j5und waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is tak)e()/zq 5n goxobg-;pll r(j qen 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 ulh nac hrt.s 0p9orcry0- /is--z1rjc,trasonic 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 frequency 570 Hz. When the wind velocity is 1 vbd3pwoln6(yh6r6r:;fn8 nf 2 m/s from the north, what frequency will observers hear 6or8l(6rb6v ;3d:ynf nnpw fhwho 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 landmkg ghd pu5x.z4wpr8(h x+ k:, 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 sk5cbu 9l8q.a 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motio9 c8aq .ls5bkun?    $^{\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 thief 5:ycd joh+v.ifiegqn0u6 r*9( )odn atmosphere of a planet where the speed of sound is only about 35 m/:r(* ) g+hc9endvf.6ijqy f eouio0 d5s
(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 rogm 5a0)x 8qaf.d ;nvthe shock wave angle it na;0m xdog8rf av.5 )qproduces
(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 .h1.wo gu,o/gk9mk0nr t1ujd $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a tuy.e jv*8l .qplane 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 tra*yve..qu t8j lveled 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 sendnql:: j1-jon t vakp;-pzb1u9s 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, what is n- opv 19tlb-::k;jn1qa zujp the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves mhno(m*abh,; are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called v/ z2 zrt8b-eh,;a:hes i fjn1a sewer pipe symphony. It consists of many plastic pipes of varsf- nhh;/ev1 izbrz jte,a :82ious 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 makes a sounb t 97 b7h(xx(n1nrwjed close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such me hbrb(7(9j nxw tn71xosquitoes?    dB

  What is the resultant sound level when an-i1ienb w.4;u/0*/w tr mnr vl q,kghv 82-dB sound and an 87-dB sound are heard si-4m1 0;*uin whbq v terr.k /g/iwv,nlmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is bb g nq04; t+,kzju:kyxdp) ;t105 dB. What is the acousticdqb;0y4+)z, t;gjxku nbk:pt power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power nzo;uf/gv(, ax 1b 7nhoutput drops by 10 dB at 15o x n;/7fhav1 gu,bn(z kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically gr : 4t+ldsh51jsos3kwear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unp:t1kd4 h 5sssl jgo3r+rotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatiovszw7,;r v kn0ns 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 frequ o+h+rh3gxy-j s/;.fis nj8 wgency 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 betwee 2+xluvoy9ug3 ycu/1gsc4 a3hn fixed points with a fundamental frequency of 440 Hz and a mass per ux l+y g hc3guycovs/u4 391au2nit 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 wate1.e z/ rseqf62n1kb ljr (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 the tube opening tq j26ee1kznl./sb fr1o 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 s;ppw0+r 0hnj ytring of mass 2.10 g is near a tube that is open at one end a0hjy+nw; p rp0nd also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resotx y)b csj)1 fude) /j3)zg fdw cb12/c0obe5dnate 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 tone in the 500–1000-Hz range coming from two sx5e;jm/ qwu f6qc3(quources. 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 minij5qm3 6u/w ;qqcxefu(mal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train ioj:acb (ut9rdo5hbx i5ke.e+dyq 2m+z1;r 1v s stationary. The conductor on the stationary k. hdj ;e+i1d orybzc59(ev5rox2tumq:+b1atrain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. nlpn3af 0in9*After it passes you, its frequency is measured as 486 H9 plan0ni*fn3 z. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you cag u likv*2ij :n+6.eep lej4fk/7pgm;n estimate the speed of cars just by listening to the difference in pitch of the engine noise between approlki uk/ ienjl7 +2 f4m.*;e pegvpg:j6aching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together,m2i34)cd a- vhsx8xa i produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Hod4 ah)acx 3s-xii28vmw long is the other?    m

Two loudspeakers are at opposite ends of a railroad car socn4 y5ib)m+xer m(fr2 89zl as it moves 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 betweex8)nf irc9+ reoz ( 2l5sybmm4n the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is nor +co9iuijo5l:l -r hk4 1(efa:u0rceemally 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 the c:j ere1h4+i a(o9 u0fl:u c o5-riklewaves 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 toward thebae+ nb61m1 cy bat at speed 5 m/s The bat emits a sound wave of 511nba yebm61+c .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 frequency sound pulses as it approach(/vx 2jhmm zwp g9d+k9es a moth. The pulses are apprm+hm92/ dz 9jkx(w pvgoximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villa9hst 72q hnbc cn1.zqp+n2me7ge to another. Since lower frequency sounds are less suscepmtn7hchzqs1+p92. bq c7 2en ntible 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 cowpd5 ve*bi 07pmpromised by the presence of standing waves, which can cause acoustic “dead spots” at the locationp5dp0 7*e wbivs 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender;dt)py 8kqvn2 (9nqd.mq *dqr aluminum rod held in the hvdq.rqn)*;d 2nm d9 8p(qky qtand 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 t:5b m p3i6pkkeb2;ovy he human ear at a frequency of abom k:oieb 6p5bvp3 ;2kyut 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 at Mal u vbm5w:9xb;ch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passx9ulb ;:mb5 vwes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat )a7zbnyr-9h 17 jjmzfis 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