What is the evidence that sound travels as a wan vt4 :zus 7 u;viq4)njzpvi6.ve?

What is the evidence that sound is a form of edgpbgda* y.1;nergy?

Children sometimes play with a homemade “tk3 o gofawy1djho: .a: pd4e4-elephone” 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 the sound wapo j4ya-od1f.: ko4ew :3gdhave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fr y83 h+q/qxg2ov ;hjxtspu ,)aequency or waveghvhap qsq)8x oy/ x+j3; u2t,length to change?

What evidence can you give that the speed of sound in air does not depe*a4kxx*dp ewsj 6 b;o)nd significantly on frequency wkjx*od*)64 ebsaxp;?

The voice of a person who has inhale(/:)isvemzr ge y,jl(dzd3a i8e(+ted helium sounds very high-pitched. Why?

How will the air temperatgh-u sdbafy msqw 3 +7,96hh7e-k cz:fure in a room affect the pitch of organ pipes?

Explain how a tube migh1j1mm 5v n+8-shid ub g(zm5qut be used as a filter to reduce the amplitude of sounds in various frequency ranges. (Anjz5-s +51g dv8nm(i umq bum1h example is a car muffler.)

Why are the frets on a p,cqx i f eb/-(rc2+wzguitar (Fig. 12–30) spaced closer together as you move up the fingerboard towaxrpiqc/-c ,e fzbw +(2rd the bridge?

A noisy truck approaches you from beh+mu1q kt73xf-q0bz l wind 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. [Hiuq 1 -37fwzkt0qlmx b+nt: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacn hrfx9 6cwnirvs.c +n6 py2 z;ut)(0ze,” whereas beats can) hr6nc9rz2c vznw0p ;n6ft.(x+sy iu be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points Dk nsg9up.5,xw and C (where destructive and constructive interference occur) move farther apart or closu,9w snp.5kxger together?

Traditional methods of protecting the hearing of people who work vt8 rx8a2m6p da0m3j min areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the amd 2aa v86 mr8mp0mjtx3bient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as fmcb+mj a+9ed r,gi7d 6-;ed ra superposition of two sound wavmj 7rgfed c +6i;r e+bda,9dm-es 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 s0gu*f2 muyujc o o2e79hift if the source and observer move in the same direction, with the same velf *u02 j yogc2oe7umu9ocity? Explain.

If a wind is blowing, will this alter the frequency of td8yk+n zzap;2h5n4 ss he sound heard by a person at rest with respecns5zhzayp;n2 +s8d4k t to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moti u joxbz(4g-.gon on a swing. A monitor is blowing (x ou-jg b.g4za 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? Explain your reasoning.

  A hiker determines the length of a lak* .e9zn r91wp fg( arkffaes65e by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estiew9r . a1 a69fnrf ks*egpf(5zmate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shigq8 +h/ 2golxu4qnxw5i .tj, xp just below the waterline. He hears the echo of the sound reflected from gui2/hql .+gjon 5 xx8x4twq, the 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 in air aqdb97sqi 1 56 +rh.3bdn*xob qjrxl;kt 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 of tuna on a foggy day.hf;(guv,l k jkyunx8p5;lz,3 Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the bau (, 3vu8y l;p kjx5knf,lh;zgckfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Thep6;;j2wfag+d3xm:d hr(-qm 1ic kuur splash it makes when striking the water below is heard 3.5 s later. How high is the cliff? (dumpr+am jf-:cu 2iwg ;dqk;rh631x    m

  A person, with his ear to the ground, s:k12o yg8*qn1 xmkcd1k 3cw dvees 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 concretondx1mq38d k* 1g2c wc:vky k1e, 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 )f/fw:w )zilr distance by the “5-second rule” for estimating the distance from a lightning strike if thrwl ifz:)/f )we 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?h)nhz.0kpj1vs ba4v 4* nk4wv    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 so4ccz, *mtynj +d4x;* oib5iiy und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simuld3g;vgja7q 0+jlejs*1h :ap vtaneously at a certain placsj;da:ve3 g avl0gq7 1 +hpj*je, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certainxpxe .7a mm2z*2 zrcn0 distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all *7p0c2mz xxrmze n2a. but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said tv5a tf4p 3md9ro have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95tv3 am rfp9d45 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of so)n 7a+ml zb rsjaqw177und from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphean7bl w)7+q msj17razre 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 slr 6x0l.508l4qly8+ktgvgf 4zk nvj o -ojdi-trikes 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 the mor5fw* 7goqkmy-s77 z tje modest amplifier B is rated at 40 W. (a) Estimay w5m tj7kfszoq g-7*7te the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frv ze:if lra7t: *:pi3sont of a loudspeaker on the stage:ta :e7rf:z3psi* ilv.
(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 diffephg ))yh6 uyx d3h)e3;wfl4rc9pit,c rence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9i ) 4 )3y)phcwxl;u6f,rhet dp3hcyg 9.]$\approx$   

  If the amplitude of a soun5:gghjj/razye: nv ;c:,s i .k*hp kv31n/wjkd wave is tripled, (a) by what factor will the intensig:/1/i 5kckvrnz jv.3*ej ny,h: kg;s:phajw ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ame5(e2zyz( ,ejfqjra l 5dp)2bplitudes, but one has twice the frequency of the other. What(l(e aj)2z , j55yzprf2beqde is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound w zuaht5/:pfv:kem/7e.kvj n , ave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300v/nz5k7p , v.j ahkf:me:tu e/ Hz?    dB

  A 6000-Hz tone must have what sound level to seq;+vki6 azd, qxuo1y (em as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.;+vuki zy qd,1x6(aq o)    dB

What are the lowest and highest frequencies that an ear can detec,flssk9;rdr1.(mwe rhda 4 -dt when the sound level is 30 dB? (See Fig. 1d; ,-1a(r fwdsm h9k4er drsl.2–6.)

  Your auditory system can accommodate a huge range of skp1 vp m+gq8mkn6m +5es 9t8xrd ski**ound levels. What is the ratio of highest to lowest t mk6p vx+q5re898idp +1mg*mks*n skintensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length ( 20pwxsechi -2j.ivlof the vibrating portion is 32 cm, and it has a mass of x (iwvesjhc - 2p.l0i20.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thrmpy sni zs*.a2g6)1g eee audible overtognz)2sa. *i6mye sg1pnes 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 efv.)2(wukki blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tu)v keiw(.kf u2be?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes nb t0v17phcs(cqrlp6,x wt -. spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengqx( wr .6cltp ,hvcbn7pt-s 01ths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string haytjg wy--+qxl52 4 zvks a frequency of 540 Hz as its third harmonic. What will be i 4wtkg -yjzv 5-y2+xqlts fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mid q ;l2vb+rb6 o0 /*yvzwqks,sxdle C (330 Hz). ysw +brqkb /0 vz6;2sv*,oqlx
(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) (d/vkma0k5mqi rb38,f m rds(when the tempeki 5fsq, r d((v/m0bda mkm38rrature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 204b5s,:b ar hsy $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece rixp e7b+uftu1)6v z2o+xnu -of the flute in Example 12–10 should the hole be that must be uncovered to play D abvzue+bufxpi 7 2nou- xt6)1r +ove 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 264 Hz, 440 Hz, and 616 Hz, butrk jt6p fm)bbhd -)-)b not at any other frequencies in k)b- rdp- f6)hmb)jbtbetween. (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 res ,pzkz2itw, .konates at two successive harmonics of frequencies 2,t2kz zpki.,w 75 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 xt6 ui ejrj (mfe 50g+u7)nmw8$^{\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 petxx-,ri un( d;nl:-eresent within the audible range for a 2.14-m-long organ pipe at 20 :xx-l,nr (;etu-ndi e$^{\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 the1/rl x4mfeu.ukpgh7 9dtme :: outside and is clot.g/xud7: r lh1e:em49mf u pksed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat evecg xv 6ya)405qpv px.ury 2.0 s when trying to adjust two strings, one of which is sounding 46c vaxq)yx5.p v ug40p40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if x si-*mxq 1)0oi hbf7q8uiea1 middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whiwh1p n(0g,dsx7 ojnyear9 l 9)le another (brand X) operates at an unknown frequency. If neither whistle can be )0o d(e w, 9ahlp x7rngj9nsy1heard 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 producerj-spwad0; cv,7t; 0q8l qgmb s 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tu78v; 0l0 spatbc;,jwdg- qm qrning 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 tensionu km c;i:.a )7rhiujd3 in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playe.jhi i3;ku a:mdc)7urd together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flu9ut mw+o3sxo6r4 r, 9ird(wgctes each try to play middle C (263r m6sx(gow ,9dct wrui9ro4+2 Hz), but 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. Forkmynx1r1osk i. .si r9x t.*y1tb,zl3 r B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C1trymlb r .srkx,x.*n 1oi9z 1t.is3 y? 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 perbp a 0-pi4qrt:/dlj /b dx,0ndson stands 3.00 m from one speaker and 3.50 m fromp,/i:x d0n04qj dd-trlabb p/ the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano .lk ve53,n.5plbs uksi0 lp/p tuner hears three beats every 2.0 s when they are played together. (a) If one is vibra3ppivll ,ksb0 .5s.kln/p5 euting 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.yn3ffv - ) k2 vy3n8rjw.gttk( How many beats per second will be nyjg.fkwv832ry (t-kv f)nt3 heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’oz3h:c5z.ri rqg 4* zcs siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s.*ozrzgh5: q4c3 czri
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency* dnzbskpnd6 oug/d/:(k 7v.o do you detect if a fire engine whose siren emits at 1550 vso (n:d.d/kpz/6 ko7gbndu*Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving yvv.kx;hi.x/2r3 r ).rnqjyh toward you at 15 m/s versus you moving toward it at 15 m/s Are ) .xh xqk.j vrn.rv;y/ih23rythe two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped p gkgo4x;x4f /with the same single frequency horn. When one is at res4g xpkfxgo; /4t and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultr/y d i i-w:+bimavaat,no/ v2(asonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivedo ta2ia, iw/+ivbanv-:y/ d (m sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall 1zc./g )+ t6 jbnx*d(vqo ,4obd/aeedioj x z-at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound1gz* )o,dqezeb6(dnodcvo+4/ x/ .x ab jitj- wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playbe-46bb z )p)fc1pfrt ed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a spe)bt-c p4zfer bf1 b)p6ed of 10 m/s ?   Hz

  A Doppler flow meter u8rwi2l:iqgwk8q .w1 dses ultrasound waves to measure blood-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 frequency if blood is flowing in large leg arteries at 2 cm/s d kwrdiq 8i:2w.gq18w lirectly away from the sound source?   Hz

  The Doppler effect u 1 l4rfsovui)9iqr6l. sing 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. Wh c4vb:wdico;7+e rs-ken the wind velocity is 12 m/s from the north, what fr-:wr+4 ;iobse vkcdc 7equency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its )bkq5) t2 7n*9 qokw ygqlms-bspeed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whamhrj : kjqb3:vhr0 wrd-j1*y h;1lf+o t is the angle th y+ j;kbj1-rdjqv0*:w of3mlh:1r rhhe shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the evtdh7 tcnw+ -q/ 0myro.35rp speed of sound is-ro+ c7 n/ 0v.dtywhrep5qtm3 only 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 xl/sm5 syg ,(aocean. Determine the shock wave angle ims /yal, gx5(st produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle b98 zs8qcjhpk+whwr;ud/ 1f) jrfjfr- 3 /yw2$/theta$ 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 exactly 1.5 km above the grounlhus+m18w b8v d flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal usv8 +wmbl 18hdistance 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 sen(, m e+83 4y gudxrv-nlc exf0mqj.s3yds 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 the minimum time between pulses (3 xe.qyre3c vn u0f +4m(y-x,mgsljd8in fresh water)?    s

  Approximately how many octaveas,vq --1*ylr xl iq/bs are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe 09ku1 t;m1*x p+smgxz4kis.dv as9 zusymphony. It consists of many plastic pipes of various lengths, which are open on both endski;s 1 s xz1txdmu9+gzv4p09.umas*k .
(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 threshu4 zm 5 6n x0(li8o+t2mloulmhold of human l4+2mu5to i80 oxmlm6uh( zlnhearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound l*ddm)6 zzfssz/gwd*4uxnj: +evel when an 82-dB sound and an 87-dB sound are heard sis4gxn uz dz+dmf*z:s)*d w6j/multaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i*zj8ue 7+nb+guocpe) s 105 dB. What is tcu7 e ne) +j*u+pzgb8ohe acoustic 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 powehj,qyz ;axs:(9 zuau6r output drops by 10 dB at 15 kHz. What is the power output in wattsy :a6hujs qa;uz,x9(z at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices /.qyeg. / :cmj hdn em,1b9wanover their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and thq9cm.e nhw .mdge,b /:/anj1yat the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sysfhce0vrv7 ; (5e.j kmotems, 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 tunedr 2rhgiyd +,y62-u1tupiok - h 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 j+ryyya+ -j 3bzp4vdhnkz ;a5:0 if dj2;:l ct32 cm long between fixed points with a fundamental frequency of 440 Hi:4jj+nd l:r-5av c tad j; 3+0ykz;yyzbph2 fz 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 vibr1-xr9wrdpqm i v c77:oation above a vertical open tube filled with water (Fig. 12–35). The xd7 rropwqim c:v-91 7water 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 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 ofy *v)c lqne5uqqc.j 4+ 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 ()lqey .n+5*vcq juq4cin its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r 6poux1;+e:za t/ubd vesonate 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-Hzl dtz3of-4fu. range coming from two sources. The sound is loudest at pointsof4dtzu3 l.f - 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 the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cm-y-i 5i7k*t6ue+2clhl z jo i, xag5wonductor on the staoijak- e,5icgtl+mz2*h5uxw i y67- ltionary 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 trax.r17t-nqf uhs w+ 2dt3 v7pe fvgw(+din whistle as it approaches you is 538 Hz. After it passes you, its frequency w37t2ptvu+r g(n s7evh 1fdqxd w.f+-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 listening to the v/cq p2e3dsz*hgj ( e0difference in pitch of the engine noise b2 cee*gsvz (d3qjh/0p etween 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, 2mt 0juul9.nd7d mt 6asounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other? 20 uma7ut9t.d l6dn jm   m

Two loudspeakers are at opposite en,*on+b z)o olq jqo+z7 -x8tbf9a xvs-ds of a railroad car 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) heooblo)qqa-z-,sbt89 n+zxxvj*+ o f7 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 igr+ jk8 mrwk,ap3r*w-n the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wave rw3 -wka8+r*rmpg j,ks 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 suhvpd3rd3wpzacj2ii./t7 z 4j2:2jspeed 6.5 m/s while the moth is flying toward 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 bat2 4ht2j .rp/ 7ui:v3p2s3dzzidcja wj after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency soy ki( ,/eb+bo8vnt2uh und pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat soouk/b8 y,vt2ihn(b e + 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 Alpinbz( * ;x)ehwmjrn9 fu4e village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and whicuren4z* bw9)(fx; h mjh 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 stao/q 7d p,3thn*pw mt38d.zrypnding waves, which can cause acoustic “dead spots” at the locations of the pressure nodp8 dnmp zo/y, q*r.tdptwh337 es. 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 51 andi bc tol0:ek8/ma long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” o 5l 0i81ekn c:btm/daor 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 humk( + u:d q,-whvoq,isian ear at a frequency of abouti,iku,dh w (qvqs-o+: 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 Mach 2.0. An observer on the gjtk9:0 igj;be cg(ay2round hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planjta9cj2b( gg yki0;e: e’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is e equm xf+.)4l15 $^{\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