What is the evidence that sound travelsn:kmti+7bgc sn s 317o zg+2thgzb+2u as a wave?

What is the evidence that sounn -gef 9 b3;zvz 83-qaeo6stold is a form of energy?

Children sometimes play with a homemade “telephone” by attaching ai,f2 fnqry*cc:q qb-e sa(+dj jt -x) zi/i0p, 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 otherxtzf (:qc*)an/i02- qe- y, ijqcbs fj+,i drp cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave pas0k.; 5 rb:gp:wk qc:mk rur:yyses from air into water, do you expect the frequency or wavelength to changeqkr kk:0c:yp:b.u: w;mgrry5?

What evidence can you give th2u:z qax1wf v.7cry-fw ,/uq3eq m .aeat the speed of sound in air does not depend significantly on frer/., u31wxuwav c qq 2z7-.eqmfye:afquency?

The voice of a person who has inhaled helium sounds e 5i2ewa3xh 50v gi6n4mvvy3 kvery high-pitched. Why?

How will the air temperature ig* 1b5xf ,yfnun a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundn- wst26b v0gus in various frequenn-2w ubs6 gtv0cy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacedxj*6il , .f,mo1 pybn ihfh32u closer together as you move up the fingerboard toward the bm. 2fx ju*yb3i6hnl,1hio ,fp ridge?

A noisy truck approaches yo crujh, 7im71gj+ud o/n3)glj u from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise gudjor/ncji)7+3mg ,7jul 1h . Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “intjtlz3s i-um*. erference in space,” whereas beats can be said to be due to “interference in t l* m.utsiz3j-ime.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweoyp2kd ;ldjr 3b; ppbc. riqf.9l h89;red, would the points D and C (where destructive and constructive interference occur) mo;k 8frb9.lq dhcy9rbp. d2p;jo l i;3pve farther apart or closer together?

Traditional methods of protecting the hearing of peopi w;*eb)xd:nj4d jfdx r6u5*g nz1hk1le who work in areas with very high noise lez1 ij ewrgnukb41d*x;fdx)*6jd5h : nvels 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 shown in Fig. 12–31. Each wave can be thought of as a supioc8.tjm evn(hn ikhg 0h * 1k:7 bfkpb/48m5qerposition of o4t/qe 18nbi.7*(:n 8k kgib f jcvpmhk0h5h mtwo sound waves 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 sourdl3fq76 qo r+w+gbu0c )jnm p.ce and observer move in the same direction, with the same velocitnwmq)+ c60dgq+o rpblfu 7.3j y? Explain.

If a wind is blowing, will this alter the frequency of the sound heard byb6r qkvs/4 rd: a person at rest with respect to the source? Is the wavelength or velocity changed?vd6rqbk rs 4/:

Figure 12–32 shows various positions hh06t9xt 7h jeof 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? Explain your 709hje htx6ht reasoning.

  A hiker determines the length of a lake by listening fnxpl +a dq3 v/aw5sd.:or the echo of her shout reflected by a cliff d3l sap/vd+5xawn:q .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 n433ylb wm:hsmp fe53side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor direcw5f3mpn e 34s3y :hmlbtly 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 aty z*2yvnm34b d 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 boak:x5tx94 kvv st is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig9:xs 5xv4kkvt . 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 awk.mv5y zx37srt/k5wwx j562 qy v6r w cliff. The splash it makes when striking the .w6 k x3 vwvqw yzjywm7k/xtr56525 rswater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike theu q-qfbsg26edv)j0v- concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and theybjvsu6evq2 -0qfg)-d 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 oneh,f o 0o+ccdj3tv,1zs mile of distance by the “5-second rule” for estimating the distance from a lightning strike if tc,oszv 3, t+odcfhj10he temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity i7 vp4bcjaa g.gn4 63f+kqm5 gof a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a h9zqjqv /6 orkumz/ 5f co-//nsound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a -zl cgb+3heh 8cr71cgsound level of 95 dB when fired simultaneously at a certain place, what will be the soun3bh cz8-cerlhc 1 gg+7d level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from al or023 x bgeo,yky-7on airplane with four equally noisy jet engin l7r 3o-xkobg oy0,ye2es 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 intensities, not dB’s.]    dB

  A cassette player is said to have a signal-0i:r v) dzac400kfvqd*. dekito-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 backg0f ai0e*iddvc)r q0:kvk4zd .round noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal converswn 062 f ibrnruo675vf2)l3o43g ohbr 1gc dzlation. Use Table 12–2. Assume the sound spo4u7l)fwovbl63 rbdgr2g1 inn6z 253 fh0 ocrreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an earhufc g1tk0rj(+sj5 d+drum 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 tuy.rdm-ctfbw9 ju, 40he more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a lou 4tdjmwuy .-9r,u fb0cdspeaker 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 dBbw fq *du5 lzu1.th zc;6,eant*a9f-i when placed 2.8 m in front of a loudspeaker on-9qaf e ;utlnc,5zh.i d6 wa1*fu*zbt the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. z5m*0qt 3q q fy;as;hxWhat is the ratio of the amplitudqq5*z qf;t3ys;a m x0hes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soundm4vlyo75vv9 m vs (oq4 wave is tripled, (a) by what factor will the intensity increase? Increase byvoqymos vv9m7l54 v(4 a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equ*t31q1s mi5njhap) omal displacement amplitudes, but one has twice the frequency of the other. What is the spta3ni1oh*jm 5q1 )mratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that 6rkdi7dz(4: exm(1dd:xprqc corresponds to a displacement amplitude of vibrating air moleculesp( xq:d(: ed7 cdxdir1mk64zr of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to bces .bks)iia1( d1, tseem as loud as a 100-Hz tone that has b c,(ekat.s) isi11d ba 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whd):cz l.b*b4zh4a5q; ij 9fcf. qdwojen the sounda:5b 4j fb 9zdcw..qh 4 i;c*q)jzlfdo level is 30 dB? (See Fig. 12–6.)

  Your auditory system5rl*jqye*/muj+.bom o,; psyp3n 8hz can accommodate a huge range of sound levels. What is the ratio of highest to 3;osur *+ppm .qo h*jnzmey58, lyb/jlowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengt,cojl,3;fzdb9 i4t(ok /qy tfh of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Undei9 4/jbtt(dfk,;oc, flozy q3r what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are theuby2 zirj pd7mt .zn 9::mhs4( fundamental and first three audible overtomy:zs94r7hm uzbndj.2:( i tp nes if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across thet3c4dddwa4 i u:87 rud top of an emptut8didr dd ua4c7 :43wy 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 open-tube pipes spanning the range of l85w.um vn5m jhuman hearing (20 Hz to 20 kHz), what would be the ra5mv .wju m85nlnge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequencajlfe+tv tc0 5,1r 7kby of 540 Hz as its third harmonic. What will be its fundamental ftk 5+t07lba1,ej v rcfrequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lo (kd*4 /ofmitx 9rfg+ang and is tuned to play E above middle C (330 Hz). d+m9ktgr*f4 f(x /oia
(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 :zfg);ybzs , a*5v 4ujoc-:r qe ilfh:of an open organ pipe that emits middle C (262 Hz) when theo qcsf: ;jab4izhg)v fr-,:zl :5*euy temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 ;ncma p 1k2xe;$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of tnq jtm9-w2*l e faj19ohe flute in Example 12–10 should the hole be that must bl1e9qa2f t* 9m-nj woje 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 pipe can rejtri4fve-v (7 rbt:ir*:z y *esonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in bejet:vzvft *4e:* riibr-(7yr tween. (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 ope* pe(6mfykde.n at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hzy. pde6f(mke *. 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 2j) r mxb3i6lr$^{\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 withks9)buy7*/ykl vg6n kp70 cb .bkep ,rin the audible range for a 2.14-m-long organ pk y0k),ely7kv b kgu9b p6sbc*p.7rn/ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2rki q pm.tlq3 0hs.bu6c12 q0z.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 ear canal. What is the relationshi2q0 b6hq k1cuz qr s3tlp.0mi.p 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 tfpw4c.y3 ks0 fwo strings, one of wh4sf.y3fcp0 wkich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequexi b,5*.ne1voh ph62vdh9gzfncy 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 p (z x4k-p.wmh),pbyzoperates 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 frequenpw(y-bpz kp m4z),xh. cy 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 ; az6q5ozlvb1;wsvp, beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the s5;v;q,ob zls61wa zpvtring? Explain your reasoning.    Hz

  Two violin strings are tuned to thm.ekj78mrfwir29 c 7m e same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What wil7.ij merk7mf 8 rw2m9cl be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will d8l2 , ma.,wpug0m tvidn4ip,be heard if two identical flutes each try to play middle C (262 Hz), buln,w am di 0.mut p2d4,pgvi8,t 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 frequeh*cwzx;y(750rtj k+ clo w 2aency 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 C? What beat frequencies are p(ekhaco 7crl;w*+t 0 2yzxwj5ossible 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 dq wk2j7rg) 9ez,c jafq( c(5eon8y6lju+gs: 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the oo (n d wc,fguc(j)9rql85jkaezsj 7e :g6y2q+ther.
(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 arenu1hs3e- 7mj3q7qf c jr0)cwr5z8b ps supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s wh-c j7z ep07r 3nj8fs) rh1mb3qscq5u wen 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 aq5glgsiz k2kag j/je /n-*)k5ir. How many beats per second will be heard?zlkkq k-/ g *5eja)g5gn2ji/s (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirenti ctud)6j to6/y(d* d is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 6ou d/tjt* ditd y6c()m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What w/qv3) wqe : ozgvfl(j5bqinb3+ 5w.t frequency do you detect if a fire engine whose siren emitstwb nv5j 3g.izl )fvow3qq:(w5qb/e+ at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequens v)fsvc3q93 scy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the tw3v 3sqs sv9c)fo frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the1ut 5fg kg/ ;uu*zx+ql same single frequency horn. When one is at uqxg+;5*u/z l1tug fk rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends ou-g:wbz5vh2i uw0rnv: t ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Wha25v:unwbzgv- hr :w0it is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at fhub6 r+hrg x81c +2/u(tjpcd a speed of 5 m/s As it flies, the bat emits an ultrasox1tbh uhcd2cp/( j+ +r6u fg8rnic sound 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 played on a moving fl5gge8jphn u-4+xg0fa at 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 a a+5-pen0g4uj g8x ghft a speed of 10 m/s ?   Hz

  A Doppler flow meter kp5;jkdf: .e(eydv 2-tiq8cba7 x7glq*k/nm uses ultrasound waves to measure blood-flow speeds. Suppose 7ki yk 8cx/tdeaq7-:5 g2q dl.k vfn*;bpmj( ethe device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using +5;dn(2ntxs7mmiky z,dn- wb 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. When the v85x ywqtcp9g2+bd9zwind velocity is 12 m/s from the north, what frequency will observers hear who ag+w95b zd8c9qy 2t vpxre 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 lanthy 5+6x qjua(v:suyto, +uc2d 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 2.3 where the speed of sound is 310 m/s ( qqflw:4bv l35a) What is the angle the shock wave makes with the direction of the airp:q v4wlfbq3 5llane’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 atmosphenrx5xc 4;cqc+ cd1/wdre of a planet where the speed of sound is qccx/15cwdcd4+ rnx ; 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 ocean. Determine the shock wave anglbit(f g7 y-s4oe it producessg4of (7 -tybi
(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 cs( s+oyqaz/ 3$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a 5,sn;fhh/hrt;6aw yfplane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you h/; yh5rht 6fwf,h s;anear the sonic boom, 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 th1aw8r.dv o 7tqat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detetqw avdr 17.o8cts echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audi s137vmn3.iz gv/ljp bble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cor h/asb eic -.+l0sf6cnsists of many plastic pipes of various lengths, which a.hf/cb cs0s+eil -r 6are 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 f+-yjhtu7(ud*dnuf 5 n vj mrp1od:-1e rom a person makes a sound close to the threshold of human hearing (0 dB). W 7yftpuh+1u oun (m* --j5vnrdjd ed1:hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when u eq6 +j.xs+dzan 82-dB sound and an 87-dB sound are heard simultaq+.sdx6jz ue+neously?    dB

  The sound level 12.0 m from a loudspeai1.xtixff pehe(gar2z (2)j ;p3 mm 55kg+k bxker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all di ka+3gmx1pp ;. ) (ixgfe(hfej52km2 tzx5br irections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops - yfxsn/d 3p+uby 10 dB at 15 kHz. What is the powu yx/ sn-pfd+3er output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective)rz+r93; b eqpzy)ci l:sr/,7s.iyxq g;wqdl 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 unprotected ear at a distance of 30 m from a jet airplane wrx e/p,q;g rizq+)i3cbry ls:zqs9l)y;d7.engine?    W

  In audio and communicat7im hbn2 tdb-2bg 5u9qb6uss0ions 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 tus*m(j d;qv, ; gcwx*soned 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 bydl 78bb4t+rg*by ;ewetween fixed points with a fundamental fdg*+t lb7 rye;48b wybrequency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verth6 x cs-7gddq+ical open tube filled with water (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 to the water level is 0q6h+7 sddc gx-.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 2.1v1n g yz x(twff7/oz;r(1s xl1lb/g1r 0 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its funztlxl1f v(r/b fwg1zgnxy7/ro1; s( 1 damental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obseraxh:v h )rtk(1ved 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 puretlqucl :)y8, q tone in the 500–1000-Hz range coming from two sources. Thetlq c)qu8y: ,l sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cox /u:ckt w; o:r)nudp5nductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed ;d/5:u )w noxpk:crtuof the moving train?   m/s

  The frequency of a steam w qhnjv+q1l 07train whistle as it approaches you is 538 Hz. After it passe7qjw +nv1 lq0hs you, 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 listening to t:0hl7 jft7yr the difference in pitch of the engine noise between approachingrt:y7 hjl0 f7t 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 beat ft u:l30b;k ik(yzc* bbrequency of 11 Hz. The shorter one is 2.40 m long. Hou :b lik (c0yk;btzb3*w long is the other?    m

Two loudspeakers are a4 p e( :bh56wyz4srhzvjbo34 xt opposite ends 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 wh :p xr44by3hs4wh zjoez56bv (en (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 aorta is normally about 0.32 m/ ;dalcfufz9eh 55hm( 2s what beat 92fuzhe f l5mdh5a; (cfrequency would you 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 whileqrn:gs5ll( ggcm ;37r 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 m(l 7rn5: lscgr g;qg3detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency - /rdu-c ,px/c uxnek8(vdzj-w0xat+ sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before xrxv0 at/8( dedn -,p-- xwuckcuzj/+the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to w )y j4v txdqgr9v(6r3send signals from one Alpine village to another. Since lower frequency soundrjv)tv3(y g6d q4xr9ws 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 which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo l51xs+s1sw,;yc w5y z5wxmhr yistening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m highwcy sxw51w;yyx zs5 h ,r1m+5s. 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 alu-m9n4gu24e,tx cn h xrminum rod held in the hn 4g9xn eux2h4crt -,mand 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 thresh,hl7 npx 6+ub8 teequ:z dq+ bpo*p5)wold of hearing for the human ear at a frequency of abq+7 lt*,+ h:bpz)dequ56w uoxpb8pe n out 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 ground hears the sonic boo;zyxy37 : iohwm 1.5 min after the plane passes directiwo3; h7zx:y yly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedblgx8:csr sn)/oat 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