What is the evidence that sound trbew4 fopl b51-avels as a wave?

What is the evidence that sound is a form . ug(qe4zh;wi of energy?

Children sometimes play with a homemadgqum ,dn ,..wxe “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cupw. qgud,. ,nmx, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or )6sbzo br ;vw ihg+ ill4x(2t*oty,g6 wavetv;gi+(o, )l h*oywb ib26gx4tzs6r l length to change?

What evidence can you give that the speed of sound in air does not depend si. e42o:0 .srphzecb2qnw)sb agnificantly on frequencysp:e.h2e q co0 )4anzbbws. 2r?

The voice of a person iv o-uv2v1gysrq-w8 )who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a r7wqp;(:tiv yl ckd 6q/.mwd,poom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amp3pz2l d p9kvd2litude of sounds in various frequen d23kldz9p 2vpcy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced p+o8 t+)dphp+j/ wkhgz f e3)fcloser together as you move up the fingerboard toward th+)f+f8epgjh)k/ 3+t ph d pzwoe bridge?

A noisy truck approaches you from behiec6kj,p.n w,b nd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — yoj,cb6nk .p,weu hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfei.fx wqsy* .ag0c3:e wrence in space,” whereas beats can be said to be due f.3:*weagyix.wqs0 cto “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowerbn co+q+ i; fj04tqr1r..cadhw9 twc9s 1ye8jed, would the points D and C (where destructive and constructive interference occur) move farther apart or clq9dw1cy. i. + eorq918j0 4hwjc+s;a bfnrtct oser together?

Traditional methods of protectie7ax 0fv:mtg( ng the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it 7fex 0vgtm(:a 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 showkx66b :,n z n6usid6+hcxwwu24uyqk :n in Fig. 12–31. Each wave can be thought of as a superposition of two souwqu26ub wz6:k66skx yucn4 i:n ,hx +dnd 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 ifki+)g p8)u vam the source and observer move in the same direction, with the same velocity? E ) 8k+pvaium)gxplain.

If a wind is blowing, will this alter the frequez0y9 +mdzdwfae1m1a n5tty4 3x rh9 wt4k*(u zncy of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity ctzf 10m 3u (hyyn519w+ae44* tdwdmzx rta k9zhanged?

Figure 12–32 shows various positions of a child in motion on a swing.t.g;- d (c vnkzia5ib7 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 o7itkn5 ci( z.bg -;avdf the whistle? Explain your reasoning.

  A hiker determines the length of wx9;4f.+qayktuitv1d h l2*na lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the edt*.; 1u9q 2va ltywik4fhx+n cho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just u: z t6rx4,uvh zyfme+gc174r below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in s uhf6z+ v:r ez4m4ycu7t1, xrgeawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 owg,sc om ;rh4n9b* 9a$^{\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 ox m4(/b(fmzpz f tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (z4xpm ( mfzb/(a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when 5 *)vrj qy 8(iisccq re+t;pu:striking the water below is heard 3.5 s q )y q;:i+vire 5 rutjc(p8s*clater. How high is the cliff?    m

  A person, with his ear to the ground, sees aind l**exumb1 .qbs*(a kx+br:z iz1 / huge stone strike the concrete pavement. A moment latbz:dmiqubk*1ar.l/ 1 sb* in+x( zxe*er 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? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one ma0al0 ufuj(9ilfl 1u2ile of distance by the “5-second rule” for estimating the distance (lla 0uiul9faj2u0f 1from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity omk*vdm7u3z30wbk c* d f 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 q96oj:n)+mvyveh e:k sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultb1 ue:gl+ve y 1c(v*bqaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensiteg*:yl1euvv qb+ 1bc(ies, not dB’s.]    dB

  A person standing a n1nu )86snk/k ciqtda7*;w zmcertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering7aznu /kk8ns nwic1 )t;dmq *6 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 s0ba six/w6bid;g4dh+,a4 ;aa pexm6o ignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Wha;d gx eaoa,a/i64i4 d whba+b0;s x6mpt 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 sound from a person speaking in normal con)bow bfk5d +p/versation. Use Tw/b)+ opk 5dbfable 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 strikes an eardrux6./2( mpcm bnmpo8z cm 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 rav2by /b w7ewr,6,lzv uted at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at e, z bu lryvw7v,bw/62a 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 front of a3: rjoq8:gp 3)juq myx loudspeaker on orq)g:3 p8jx:ymu3 jq 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 dpulsug(n)b-(l5 .h4gewtqcblu 3 j;3 ifference in sound level of 2.0 dB. What is thegtle4c- qj(u533 lwnp (slh . bb;)guu ratio of the amplitudes 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 wh*q 1)- ef24keal xbkcwf:j*yrp+l ath xac4 5)at factor will the intensity increase? Increase qcf)k l4tew 4 +p x)aya* b-rkcj1ea2*hl:x f5by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frequg*. .w9x t,e1 fu2k.z aqyqzfpency of the other. What is the9xk,2q .zfge.ay .u*tzwpq f1 ratio of their intensities?   

  What would be the sousiok)3* ,i/m2as8d cke lr-kcnd level (in dB) of a sound wave in air that corresponds to a displacement amplit3sc,/i*-a 8kl) oirksec m2kdude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudjlb g77y nom6 3:lts89fzz m-j as a 100-Hz tone that has a 50-dB sound level? (See -8ms zjlflo9 n73:jbg tmy67z Fig. 12–6.)    dB

What are the lowest and highest frequ8o0f,iq7md:f-w rq xtencies that an ear can detect when the sound l7x-t :o,8rfq wifq0dm evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can. )6d-s-v;ly f/u ghou nwofl ag5t)t3 accommodate a huge range of sound levels. What is the ratig-d /6 tg s.lalu h))ofvf tow3;u5n-yo 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 fundamental frequency of 440 Hz. Thefx94jsxnf)4gig s*)p length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under)jpx f 49gxsg4*nfis) what tension must the string be placed?    N

  An organ pipe is 112 cm f g f/q;wj5k5vlong. What are the fundamental and first three audible overtonef /k;5jg vfqw5s 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 frequencyf;uz*yl*. xhy would you expect from blowing across the top of an empty soda bottle that is 18 l*f h uzyyx*;.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 r30 ;si meq;od/zwckz8pn)k c 2ange of human hearing (20 Hz to 20 kHz), what would be thez;s23okdc 8 wm/z)0 ; cepinkq range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wh9*fm ;k oykvpq4z1b(rat will be its fundamental frequency if it is fingered at a length o 4;p*mrbzvoq 1f(9ykkf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abo r* hc/s2ciq dk jmw:(b8qy-5hve middle C (33c sqr*wim b5q2/ dh:8-h(kcj y0 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 ozn2 *-sgw s g,pf0 vecyv86r24-dm bhvrgan pipe that emits middle C (262 Hz) when the temperature is 21 2,-fv-sm d g 4z v8cn*6yhwg2s0evpbr$^{\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 atjq +.h. 0gddfc y;d1buj9y/ oe 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpikyz zl7ara /b;b) q4*uece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 *7al)r b z;4q uzybak/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 recmcv6v 4 x*: 1 zg-of48 ddwvqkv:9+,wvkrbtssonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe.vwxvkc8:v w-zvb c 94o4d+gtd r*6q1v:sfm,k ----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 endse g* rrq:cvyk.;zpv 8t8fq6n9. It resonates at two successive harmonics of frequencies 275 Hz and:6yk;rqfz* p 8qter8g. 9vc vn 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 f xn, u ts2+w0c m7gte+1ye)dd$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for asn),) gy tgxq1g0ow p4 2.14-m-long organ pipegwy) tnq1xsp40,o) gg at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 f9t3t iyc-h*r cm long. It is open to the outside and is closed at the other end by the eardrum. Esti 3cyft-9r*hitmate 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 every 2.0 s when trying to adjust two stri pc f+b)ay51zgok .il)ngs, one of wzfba+olgkc1) p5y). ihich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if opwo fhdd( ./s27mp7wmiddle 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, while another (brand X) oper v)m uv*dnz+jl2 m+m y,-(q1p-oo2i* fnviwh dates at an unknown frequency. If neither whistle can be heard by humans when played separately, bo 2v2vo+(n)qvm *-wdn*dh u jm f+ili,zm-py1ut 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 when sounded with a 350-Hz tuning fork uvl6, bk)b1wfand 9 beats/s when sounded with a 355-Hz tuning fork. Whaw6 1 k,ublvf)bt is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2 pm- b2y2w;(fbksl(g m t:e+jqx6,bco94 Hz. The tension in one string is then decreased by 2.0%. What will ktmm jb22 (bg:-x;lopb+ efcsywq(,6 be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes d.orcm67p)wvi m3sh7each try to play middle C (262 Hz), but one is at 5.0°C and the other7dmimv.)37orph wc6 s at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B,/ifx)edw : 5)t32rxh,jhoyu f and C. Fork 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 frequenwj3tdru2yf)e, fi )hohx 5:/x cy 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 3.002*l2 q6rqmqz. y3 7emtmm6wtd m from one speaker and 3.50 m from the 6ezm 2wym7mr2qd* mt.q 3lq 6tother.
(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 0vji no8kgg .q hfn* i93xu04pat 132 Hz, but a piano tuner hears three bep8* fk4j3xo90v0gqh u .iginn ats 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.kf49crc :x(fu 0ijs49 o vuuw6 How many beats per second will be heard? (Asswu ucu9 cifkf ojs(4:4v 960xrume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engin4wtc svn3rac(js 4 t(+u1ju j*e’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/swj csrscv ua*(4t jj3un(1t 4+
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engvb+ ftr1jx )gwbfdzwe8*.-h 7 ine whose siren emits at 155f8rwh fb. -zbw*1+jgt)d 7vex0 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 t 2 jfo(w 0+of2rg:yvmmoving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they0r2v mo j+fgfy2( :otw close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. ;j 4vzu:m 9kc1yq68kbwje6ekWhen one is at rest and the other is moving6 mkjkc q894kjyz1ebu:ve 6;w 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 ultrasoni -drxf2lr:+nx l gc16uc sound waves at 50.0 kHz and receives them returned fromlclrxdun-:f 26r+1 g x an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward am*8nlt8 jbn h2 wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wav8hb8 mn lt2*jne?    $ \times10^{4}$ Hz

  In one of the original Ducx9iyg z65gw/bpt+r t+ k h)6oppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same toneutb/6)wykx9h r t6gpcg++iz 5 while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose-i 1d.4xx* r +iynoxutrip f5: the device emiy*i1i dr-ti:u fr4x5x xno+p.ts 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 ultrasonic waves ohozdrx- (lttno2. :/o8r mn/dop)5i / e;ppuaf 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 kj7a(7kiz / o;+vbnu nthe wind velocity is 12 m/s from the north, what frequency v n;7kan+/ zkbiou 7j(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 speed att cm 6nt c(-0l6hao9a/vi+e a yi165 mrpme:tm 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) What is s m;4exhy,b z7x7mn5bmr ++ htthe angle the shock wave make5hemnh;s,yb+r m t7b7x+m4zxs 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 thfh n -wy562cipin atmosphere of a planet where the speed of sound is only aboup-6if2y c5 nwht 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 wavq0:tt/dz ui *kxq/8cq2 : ykgqe angle iz/i k q*cq t0dq2/ygu::qxk8t t 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 b3 yv8kw+v*k pbs-p8t$/theta$ 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 grou(xie2 mo3oll0vf3 wo, nd flying faster than0( om3v3o,feoil x2 wl the speed of sound. By the time you hear 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 that sends 20,000bifxj p2 1g xv +x:skggrx;l,)*ji4w6-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,p4 :gxl; k i,*xvxbfj) rj+gs6i21gwx what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in th h2js *vl 78se6-ddqvw.o ;be ;slc0tde human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistsk 3t+dumc8e 0 ytp5xm9 of many plastic pipes of various lengths, whict8ym+5x 3e c9u pkmd0th 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 thresh ztlwc(v3l9:2bqa y(bz4 mu u+old of human hearing (0 ml(+bc 2vb39yu4zwt u(a:z lq dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hea(udx1a(jr,hm*a qi m. rd sxam j,*( (.im 1hdurqaimultaneously?    dB

  The sound level 12.0 p56 m8pz spsma q6c9y.9kwd 9wm from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) ofd 9zq.k6 syw 6ppmsmap w9985c the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 100 wbws7 tt 1agxi811lg90 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?t1gg17tiw bl 8x9 swa1    dB

  Workers around jet aircraft typically wear protective devices over their eq)g yrklkw7 1-d z:kj5ars. Assume that the sound level of a jet airplane engine, at a dist7q1-gr j d zwky5k:)klance 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 engine?    W

  In audio and communications systems, the gas3 ulwk e-xh,3in, $\beta$ 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 tune9*9gm 1p pabu2gxrsp3bn vib. z1v3x3d 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 wdq79c 8lo3x7bd;qd0cc zcr b/ith a fundamental frequendqc3dz r0oc;9 c7 cxq7b d/lb8cy 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 s 20(o,-axsabzbo ,b7zbm, xb vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tubeb7bx0abz-b,oxaz ,s, o( 2sbm 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 uhf2 jq 6*zvn07jor*v near a tube that is open at one end and also 75 cm long. How much tension s u *072jzq6fnrv*jv hohould be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r13n;wh0d(zgdq p -poongu +8uesonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming m, trjotsw;36aj.dz *from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. ,o6dwtjms.3a*rjt;z What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conh/i c 2x+4nvw2 katn+nductor on the stationary train hears atnik22x ++c nwha/4vn 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 tr 6ummd7cqcew )u h;q4-s,doh1 ain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 4 - hc co)71u6qudh,wd ;qme4ms86 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed 5 - 5xqmi:. e7j0cbg;nue cpgl arj79hof cars just by listening to the difference in pitch of the engine noise between a-g7r5in pjmubga:l.q;e7c9 0j5 xeh cpproaching 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, souny c1;9wsi358); gr- qf(qamffqopcis ding together, produce a beat frequency of 11 Hz. The shorqsc) cprs3 ;of8wm; g1 9qiyi (5aqff-ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroadr w7(s- t kkib(( rr;6f*rgxr utgi/*zske6v 2 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 2rekvt(2s tr rikru( ; 7x 6/f6gkrwz g*s*(i-b12 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 aorta is normallyb64qyd5wu ;ue euf79wp0gb/h about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cee5470 eduwbuf y 96w up/g;qbhlls? 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 flyazws4onll6 ia7 ,7a+ cing 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 bat aw, a7+ a4znoa6sll c7ifter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as itplp ,arw* uslwn,w-61c / xqwfq5ho-) 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 p *xo6uq-s /qrwh w lp)n,5a -,wwlf1cby the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpin n(7rpbu z6zn*4kc)9 o )9c,wzxijtwr e 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, w7cp k )9nx( 9r nu*ztib6zj)4wco,rzand it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stan)amj z3vhv4a/ding waves, which can cause a)jmzvhav3/4acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singinco;zede:( t*ug rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other han(odt*z: eu ec;d. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold yce.5 z 7wz6dhben/ (lof hearing for the human ear at a frequency of about 10005(e d7/zlyn6 b.whecz 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 groundlzqcgsxi:tw4,+ 9/xwcl5ml2o kex; 6 hears the sonic boom 1.5 min after the plane passes directly overhead. W5km2/sxgq9o wxl :cxi lt4zecl,+ w; 6hat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isfl1r tf)3 nx*d 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