What is the evidence that sound travels as a wauji wpk*x9c91 ve?

What is the evidence that s.)hh2wnus wec 4ap*4 tound is a form of energy?

Children sometimes play with a homemade “telepho3kp mzquqq* epu8e1 .,ne” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how th8 .1eq* uzp e3k,upmqqe sound wave travels from one cup to the other.

When a sound wave passes fwla6 kj:(6fhs(j a 1ok4z fiz+rom air into water, do you expect the frequency or wavelengtk+ k(j z:haiws lz4f1(6 o6jfah to change?

What evidence can you give that the speed of s- . a-vprhg6v aa0dxf8ound in air does not depend significantly on fg 806-hdvax -a.pfrav requency?

The voice of a person who has inhaled helium sounds very high-pitched. Why? nt)cn )/ x(z0f0r+ .hrpfltxq

How will the air temperature in a room affect the pitch of organ pipes9)qdliy0 aov,?

Explain how a tube might be used as a filter to reduce the amplitude of soundu8zlh qvc )r q;q02xb;s in various frequency ranges. (An example xq 8q zc;hb20u)qv;lris a car muffler.)

Why are the frets on a guitar (Fig. 12–30) sp27*s dtv raku li)f/.vaced closer together as you move up k2dv.*u7 / raftis)vlthe fingerboard toward the bridge?

A noisy truck approaches you from behind a building. : j, p+0vpxceuz;v0hj2d . gphqx85rrInitially you hear it but cannot see it. When it emerges and you do see it, its sound g:c+r v5phx8zrhdj,pp.2e jvu ;0qx0 is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “in-afwlk ga 217z:ub*q mterference in space,” whereas beats can be said to be due to “g2a bq:l f a-*kmu71wzinterference in time.” Explain.

In Fig. 12–16, if the frequency xtt+ p qx0-+*v 3bwcdgof the speakers were lowered, would the points Dd-tc+v gbw 3+q0*tpxx and C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peox0t ma kib79tg6hjj5:ple 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 amb9 7kmti5h j:0tja6x gbient 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 shown in 5n71qgllq-r.gc8mp +rg/ly zFig. 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-rl7z+1cpl.ly/q8 gg rgmq 5 n 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 s+c jjl9p** sztfhd:tgj 98b v3ame direction, with the same velocis*jpj3jvt*f8h d99b :tl + zcgty? Explain.

If a wind is blowing, will this alter the frequency of the sound7xs e6q+o lwwkkmb)c aiy: 7.l8o )em( heard by a person at rest with respe wleiaq)bk+e6mo7)78: wlyx cs .(om kct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitougqa (hqgy 6p uk (phe+tjr q),1l(*7jr 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 k6p+hqyqt)p*ggju ((q1,l j hr(u7ae for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shou 9ilg8(gbu/at 27ppqwt reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengil p(7g8a9tgb/ w2qup th of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thbg .okvikxmj a7r,+pjg,ig(.cb( u +0e echo of the sound reflected from thegcmg ,ugi(bi,(.jr0 x +.bj 7a kp+okv ocean 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 wavelengths iaig,-mn:wf65gy ipfu f9euyca 6 -;(a n air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school o( )bv a5dc-hpvf tuna on a foggy day. Without warn-5hacv)bdv (ping, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The 3 q-iwuw ,n+50vb:nkgus t5yisplash it makes when striking the water below is heard 3.5 s later. How high is the nv5yb-u : s0i,3qnw+it u5gkwcliff?    m

  A person, with his ear to the gr 7j5xx,sn* e9n(hm zwcound, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? Scmw,7*9 5sxhn nzjex(ee Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent errora7m5sg; .-l/ qpy vdx2byiz,a made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike q;sgl y x,25may-pdzia7b/.v if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t -zhaw+03labe he 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 whose intensimjzvuxz;91 k +b 1:bmzj33p8 /htgymcty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firedh3i 1+wpp2;wu csnc (i simultaneously at a certain place, what will be the sound level if only o pn(u+w ;pih3wsc1i2cne is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frjjm93 h; -kpeqom 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? [Hint: Add inte3k9m -jj qehp;nsities, not dB’s.]    dB

  A cassette player is said to havlw ;aoxj xn.,4e 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 noiwo. j4n a;,lxxse for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norms2wusrvwk .bq z2m;(/5tdvy; (n5wjj al conversation. U2 k/ wqsbjrtdvsm.j;uv w5yz(; w2n5(se Table 12–2. 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 str7rw/t m)9e. h jqau(h1 l)vbkgikes 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 l95uos /q j2mcthe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expectj/umo52q9 lc s 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 registr 9cyu/w4g-c ev+:xz cered 130 dB when placed 2.8 m in front of a loudspeaker on ccz-4uy cgx/9wev:r+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 lht q 6y- 8r7sdy3l3wdqevel of 2.0 dB. What is the ratio of the a3hrdq wy-ldq8s6 7t 3ymplitudes of two sounds 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 t iod+b*nt5tw 94eu2fg he intensity increase? Incr 4t9 bi+uw52dg*ontefease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one u )hgvj:9gf3 ykw1ht 8has twice the frequency of the other. Wha 1 vt3gyw:h)k hf98gujt is the ratio of their intensities?   

  What would be the sound lglc6idvh1r8u ,2;5 hdo x4 rljevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of 8oih5j rrdh l2c; ,dxglv6u14vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as azpmgt 90l3y m ;r67qzy 100-Hz tone that lq 3yg pmyzt976zr;m0 has a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highes bnhv7 )ag 87fxjmahbj+d1.(mt frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–81 7bhhgj +bxn.d 7av mfma(j)6.)

  Your auditory system1 xly m:jnl*r( can accommodate a huge range of sound levels. What is the r(j 1ln*lmr x:yatio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundab)/rdg9.:1/;cyj pt wwpp jxsmental frequency of 440 Hz. The length of the vibrating portion is 32 cm, andt9pjscxg; ).j/p 1:ywdp /wrb 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 audibgjq 0fuyuv7xvwj10b*48:u dzle overto1:7fuz*gu 0 jv4xvu 0bjqdwy8nes 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 frequ: hknw;cu.i-dh sq 76 k37sfnzency would you expect from blowing across the top of an empty soda bottle that is 6 ukfq7:hh3w.; zs dnki-7snc 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 opeg cm6n/7e z2ye-w6fz kn-tube pipes spanning the range of human hearing (20 Hz to 20 kHz)yfe26 /czwzgn e6km 7-, 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 frequenc 8:/yazo sr6rfd7n ydf,/k i6sy of 540 Hz as its third harmonic. What will be its fundamental frequency if i6 ffas8,7dsryk/:n/ziydo r6t is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar striv6;2jr enz yjjpi1/d)ft5 t(png is 0.73 m long and is tuned to play E above middle C (33 p r2j(/pjjn 5izt1e vydft;6)0 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 o:g4vgebz/an. sok 3-dkz/ts , rgan pipe that emits middle C (262 Hz) when4avk/-kd3 /bz , oestsggnz:. the 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 ap abeq9c 3oe:r f0.s+et 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 thmbnpoi oozx9/2r6n)9b4/m1w s7 jr ehe hole be that must be uncovered to play D above / pmexswo7 r4 noo692jzh9ri n1mb/)b 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 pipe can resonate at v1 a7f efv7ozo091tfi 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (e 0zfoi7va1f1f7 t9voa) 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 iglpqkb6o2a:5+ /b5g up5sf+xwn /oqsu g7x / cs open at both ends. It resonates at two successive harmonipaobu u5:xsbl/kx+ +g g fqposn/c25g /67q5wcs of frequencies 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 uxbtyr+ 7i8t m-ue-6s$^{\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 a8o qa)j ne53krww7r 4sre present within the audible range for a 2.14-m-long organ pipe a38w7kn )wr q5j o4sraet 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2laelth5 9 wrtk*4 v-.r.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ea9wt-*rle5l4.ht kr avr 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 two stringz)mi(llf-v+x )moi.xe1 6eefs, one of which is sounding 440 Hz. How far off in frequency is the other str)ie)x(v-mle . xmo1ffi6+el zing? ±    Hz

  What is the beat frequency if middle C (262 Hz) o;+li dmff9mzt,lt*6 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 opecf1k(fv5rp 8 qrates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neitkv8q1f( cf5rp her whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s w r3g.)i lwb ,tbxljhb5(y; ,jrhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency o,r;lhb b biry x(.jg5)j3,tw lf the string? Explain your reasoning.    Hz

  Two violin strings are tuned to t +hjcn9k-0o pkhe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings o9 0k- pc+hnkjare played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical taxk- )n -eso3flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at o kn--s ea)t3x25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz5r 3f bah.lchf+.0bq0m srw t2; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togetherqw. 0r+ b5 3a0m2rtsl.fhbhcf , 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 from one speak fy.cii/gmr ;( 17uo2gglz4coer and 3.50 m from the other. 2yoru;i71o. gg4cm(f gcl/iz
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but it5e/ 217ren oi,jxlr47.a svj 2nbgfxu j8x7 a piano tuner hearnfg2lr7 2ni,b u ev7j.xeoi 5j4sxxaj1 7/8t rs three 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 wavelengths 2.64 m and 2.76 m in air. How man l,brs4lkh0m5ku: k;ly beats per second will be heard? (Assumlklk0ksb; h 4 ml5r,:ue T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certainifl:gdbyi:i, j),6e k3tis3 p fire engine’s siren is 1550 Hz when at restiei ij::bdl3,t3fgik s y),p6. 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 frequ067z.oqbbmtize 61q0mqq 9gd ency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/stm eqdb16m. qqz oz6b7g0i0q9
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source r5u2 ,*wmpta*jr3 lfnd bj0. eis moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Arenj0wa* b.pmdj rr3t*el,5u f2 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 th; +mz 39uyftkml y53rwe 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 frequencr9mykm5u yztwl f 3+;3y the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves ,qg)rfqg4 yzq.ok/h4 at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is t4qg.yz f/) ,qgro qk4hhe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sp9 8bsw*tteb ,seed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency ds8ewt*b,sb t9 oes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expvcv nq0 p)7n4geriments, a tuba was played on a moving flat train car at a fr nnv 7)40pvcgqequency 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 speed of 10 m/s ?   Hz

  A Doppler flow meter 5hs:(d hyf;wk2j8:pm 5- mtqweq-zbwuses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human t;2b8 -jhe:qhs(yq 5m5zp:wfdkt w- mwissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi)) umhk 0orh*lz aq/1ung ultrasonic 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. Whe gz ue7c*i kira.26gmvq4se3 ivo k,45n the wind velocity is 12 m/s from the north, what frequency will observers hear 4r5ga ivu4 7ko g,* vmie.3s6z2qe ckiwho are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed;i+t r ftxd)n- at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 wha+-u1o,mm0 jee3 nokqere the speed of sound is 310 m/s (a) What is the angle the uoo q m+01,eknm-3 eajshock 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 90ag ws; mh8ila,ln3 bthin atmosphere of a planet where the speed of sound is only about 35 m/s s8,ai 3l 9;mnglhbw a0
(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. / s:bhi(fs) ,.3crwsvzdiyldo:-/ok Determine the shock wave angle it produces )-z: s,iyl/i b.o3dkrcvhw d/:(sfos
(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 mqp a0xnnb9+v0 ,n cd3$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane nopfk n fzg*jl0,l 9 5i3tb)8u zb(tw,exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic botb,z ,lfu oblkf0 ti3pw5 (g9 8nz*)njom, the plane 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 20w 0bmf5pw va jy74bo:c(9 75*nslwokl,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 the minimum ol7lmns 40wca 5f*wp7 95(j bkw y:bovtime between pulses (in fresh water)?    s

  Approximately how many octaves are t9v/k46o b.bt4v a*iynkmk9qn(ui( pghere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manwg6ddb5i+t7+nf .+k hk+pmvsy p bdi7nm.h+vd6+gksw5kf +t+ plastic pipes of various 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 sound close to the threshol:3fou i:bw, /bgvayy1cep)v8d of human hearing (0 dB). What will be the sound level of 1000 /:vbpicbo ) y f1av83gy ue,w:such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8:to jfhl8w* *;v6mqs3swt0s g+ w8yv k7-dB sound are heard simultaneously? 8 t:hs*w63;m sv 8wywvojfg kl*q+ 0ts   dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i1j(6znmh1 a q:5xa:tun. paohs 105 dB. What is the acoustic power output (W) of the speaker, assuming it ra. (hn1hmaxuqz:t5 6n1a p:jaodiates equally in all directions?    W

  A stereo amplifier is rat ub/r),xcu w6hs)xr9eed at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the porehs,/ x9xc r)6u)wbuwer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices oveyl n af /u6zx1n7xw ;m(:au7bpr 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 unproxm71p( lwyn f bu:aa/xzun7;6 tected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,8q*+ dpvda0+i g ui5zy 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 isyyd 9hcz*t *s2 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 fixed points with a fundamenta:th 8s2x:tkb el frequency of 440 Hz and a mass per unit length bxh :se2tk:t8 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 wi ,fb.juroe,i;prfspj2zo,9+ r)n s6eth water (Fig. 12–35). The water level is a ,;ezp+p i fs j.r),benro29sj,rf6oullowed 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 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 thatpf)fgch1f 6-pe4 d,g m is open at one end and also 75 cm long. -cfpphg 61dmgfe, f) 4How 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 obr(kag7i9 sm6wserved to 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 to57pkbcss 0 rm*n-qd o3ne 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 s s- s*d7mcqrn5ob0 pk3ource than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whis k.b(;nf; eeasa,5augtles. One train is stationary. The conductor on the stationauae, ;gabenas. 5f (;kry train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is ;ddmpto7)p7g;;g : xs gvugo9538 Hz. After it passes ;dd:g;pg7o 7tv9 ;)mgxu spgoyou, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by liste5gi nt-d (in5(ycf -xhning to the difference in pitch of the enginnxh(igd- cf(t-5yn i5e 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 fast is it going?    m/s

  Two open organ pipes, sounding together, produce a bea a pl3nkfy-ai6xmqk :w5j-+ ;ct frequency of 11 Hz. The shorter one is:i6 xqaf-np-3kc+wk ajym 5;l 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past .:z pdyafghd gi9c(2(a stationary observer at 10c:g .y(hp(i 2adzg9df m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the ao . 7 lj(/v9u4 :oodxerpglkof0rta is normally about 0.32 m/s what beat frequency would r7 l:9/dofoxg(lo04u.k jevpyou expect 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 toward the b(0sukn)r /; flcrs+ dnat 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 reflects off the moth0s+d k r/s;u)lc r(nfn?    kHz

  A bat emits a series of high frequency sound pulses as itxu(a0d,txv ;o approaches a moth. The pulses are approximately 70.0 ms apao,dvx 0at(;xurt, 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 onej.+wrquzp n+2 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 resonaqnjr p+2u.z+w ting. 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 presen8j.lw9 e 2b ; w2r+ze9cyo n4xvwn8xbdce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.09on be2w8 r8vlex.4+n9 dc; wbjxywz2 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,” i +)ww2 -l,+wrzzzgsx5*y , lu,dfyvjrnvolves 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 toy,u2w)zw ,wrr*slfvxz-ly++jdzg ,5 “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 threshotmy:sfxjor9al62) ++8 ls6eeun* wq b ld of hearing for the human ear at a frequency of about +uqma6 s +8e2y6e) :s*ltnjfox9 br lw1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.3/:6u 11itpct8v0ca esw sc;4 g*x j wtfiyuf50. An observer on the ground hears the sonic boom 1.5 min after the plane passes directwic xu0fvi1ut psc:eac w6*f4s81 j3gt5t;y/ly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatbkn( 47cj-j8 oykixr ; is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h