What is the evidencew29xo 8m- 2m3uv kzgsd that sound travels as a wave?

What is the evidence that sound is a form of energus 4zt8 gb-t*sy?

Children sometimes play with a homemade “telephonvvi5ce2l: * dt*l.lqk e” by attaching a string to the bottoms of two paper cups. When the string is stretched and a cel dlv*.5i 2*q ct:kvlhild speaks into one cup, 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 freqj mi )wlr /b9n:n*g bfi.oxt).uency or wavelengthn mb.9 biw.)ofxjirl/tng* :) to change?

What evidence can you give that the speed of sound in air does not depmqzqyum9/j;ca)f,4x2ldw, w m :xe1 vend significantly on m m1ef:4/uvd2 wq,cwj y q),mxl;x 9zafrequency?

The voice of a person who has inhae,6 e)sm/ri2x g-fg(w7 jlu dyled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pis+m x os, ml8/y 4seph7kk,h)mtch of organ pipes?

Explain how a tube might be used as a filter to redu45 08zgl bsnlsr-jmt46aa q 0mce the amplitude of sounds in various fr gzn45ml smqaarb l06t4-s8j 0equency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetherzcm,1m 6x1hc k,- :ldy jlngn3 as you move up the fingerboarnm1mx 6,j c lzhl1d:gy,3-kncd toward the bridge?

A noisy truck approaches you from bgcbp e2 dt0i08ehind 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-fret0 cdi pbe820gquency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferencjpdrhi7yby*x 1 3xme*b7, seuk 395pa e in space,” whereas beats can be said to be due to “interference in* u3ky9 ar7hj3,5d1pm* xeb7pb ey ixs time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouccl7y 0be)f vgm6g;7j cle2g8dc m4o*ld the points D and C (where destructiv gc7 m;v472gc) el8cy6m*eb0fdogjlce and constructive interference occur) move farther apart or closer together?

Traditional methods of prote a98i6tid53dcgrb ufdk or)4 )cting 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 ugitd ocfkb)3i8 6r ad)9rd45electronically, 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 thougns.uuzuj2 vkr;; s6 mya3xw; 8ht of as a superposition of two 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? E.r;ys zk8x vum6u3asjn;u2; wxplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer xj9sr( -:/zlxcbhu8wmove in the same direction, with the same velocitx:9/rjz -8uxlhbcw( s y? Explain.

If a wind is blowing, will this alter the frequency of1vqx jkjk0u,0 the sound heard by a person atj1 kq,0jk0uvx rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mo:as n 4rn(/-59jzey wege;w0epkms 0ltion 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 ten(nz :5wr;mj9 e paey-0e0w/ ss 4lgkhe sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the n94q mfwnep+djc7n ahmujx022 (6e u* echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengthh92f *eenn0 7 4ucmjq6a+nud2mwpj(x of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hesa2w jj8t0ykit(/; a tars 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 seawater is 1560 m/s (Table 12–1) and does not vary significant ; 20tsat/(wyjaik 8jtly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths 5a7 d )me2 ki*x,i2oylih5 tekin air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting i:nswfqti 0 aps p 7zq21.q(*ijust above a school of tuna on a foggy day. Without warnia. ii72p(tq: *f qnz0siqs 1pwng, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strik(ima; iik,ytapvq 4a6,*)xv;d9irw bing the water bemakr,9t vvawxq)(,* iid i; b ay;4i6plow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grsysg r/o ups*fai-/)8 ound, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travegsr/f*u)8 pis- /yaso ls 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 mile f8e-+ -7m edp owt:,k/tgbvckof distance by the “5-second rule” for estimating the distance from a lightning, pgbtckow-k+ vfe78/-dmet: strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 12l+ta kaf3x x v.ti4,xr90p8ql0 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose i+ izt*p26zec/(s j t x*vfnel1 /prd(kntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers p g g*qw-4yvs+yroduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the s-4 gysqwgv y*+ound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with wg zz3ej, yb49vw5,tkfour equally noisy jet engines is experiencing a sound level bordering okgwz j5,bwz4y3, ev9 tn 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-to-noisewskivsaqw pv5w05(f6 4jfd:3 ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal k5vadvj pw4i:wq0(5sf3w6f sand the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a . 15:u)7zjuhszf ruykperson speaking in normal conversation. Use Table 12–2. Assume the sound spreadsfu7rj1)h.u s :zuzky5 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 strdpd-30w46+yv1 ibfjjcz 2u zl ikes 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 Wt2.tgs1m(gm r+*ea nx, while the more modest amplifier B is rated at 40 W. (a) tgrme.+s*xtn2g(1m a Estimate 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, aoxxv)u/t f v.tcjn75 c7z/ lp5 dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the st7tjzp7f lu x /5ot.v)5n/xc vcage.
(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. What:qd-hgjv *z( m 1d7d5zir:rep is the raq -( jd ir1 e5p:*ddz7rmv:gzhtio 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 what factor will39w: pycw69c knk yj6l the intensity increase? Increase by a fac9kjk w w 96c:cyl63pnytor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have ekm*m (t.7 7,kewuspo* k 3sqedqual displacement amplitudes, but one has twice the frequency of the other. What uedosm *q7*.pwes,7 k(k3t km is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in aaz hq y,)9ttl/ir that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hza,yq9 z/)thtl?    dB

  A 6000-Hz tone must have what sound levl 0- ms(mlwyv. qx4vq9el to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)4qm- s.v(0 mlyvwql 9x    dB

What are the lowest and highest frequencies that an ear can detectw zdo2z/sj8h p4aq85 r when the sound level is 30 dB? (s4zz/ h2jqpd858wo ar See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whheowuz:rldxy71a-dr6 /; r e-at is the ratio of highest to lowest intensr /od 76e-rywe;a -zhx urld1:ity 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 fu-nx q/ix+ b*zpoe su)5ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm,-*xuqe/ib5ps o xn+)z and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenoya:4mtojyt-h/9 c4jc1*ci e- xi er0tal and first three audible overtones ifm9 -jio 4tecc thy-r4i:/ayoc j* x01e 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 fri(z qsyhki)pom 8oxa 3r8wna0j 1zn29.t k t87om blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed a ti1x8z8hty mn2o9as.nz ( jwk)rp 708oqik3it 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 rang 46spgk/ zx6gie of human hearing (20 Hz to 20 kHz), 46sgip /6k gxzwhat would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as it. hwpfhr :( xubv-++hgn)of-bs third harmonic. What will be its funw+-r):hpbx h.h+g- vu(bffo ndamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar 9jh1 k-bvmb y) 5 zzw-bozumn1wytq r0-96t6vstring is 0.73 m long and is tuned to play E above middle C (330 Hz). v yqyjnzzhmwtr9mw9 6-u6v 10t --ko)b1z5bb
(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 emit; -xo iv7qo*ojs middle C (262 Hz) when ixo -qoo j;7v*the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune az m 1pcn:osk)+t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute ip vwcuzi(6s50n Example 12–10 should the hole be that must be uncovered to play D above middle C azwc 56u v(ips0t 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 him l88orxlmae9-tl p c;-k3l;bv b30can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betwe;hvl mlll-eak -;ix8o08 bb c93rmp3ten. (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 resonates at two succ) wcd-xtf-h th+ ffo-1essive harmonics of frequencies 275 Hz and 330 Hhfffcohdw-)t 1+ xt--z. 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 dxm5zns63 fu c.7ap k.$^{\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 a 2.14-8zsj ;:ucdkg+ f1:6pf n2;ci 5iuetf om-long organ piud g6us;nf85j+iet p :fk1fc ;co2z: ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 qpkjux)b f)f2 t;h.efaq2-)acm 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 relationship of your answer to the informatabtq);a.))kpq2fju -fh fex 2ion 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 5xxdf, .bp hc/strings, one of which is sounding 440 Hz. How far off in frequxcdb,5f /p xh.ency is the other string? ±    Hz

  What is the beat frequency ifwckz2h+5eh d)5: yly y 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 operat4x h(r: vq8htqes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are h48hq:(vqxr tplayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundeds: :;i.) eommhka wplpwiv,0;u 4k.pf with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationasp a,ow e .:hwivim lu km.p:k04pf;;)l frequency of the string? Explain your reasoning.    Hz

  Two violin strings a8 y,d gxfv(wt*qe*so:re tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard whee8 **s(xwgv,q:d to yfn the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to eh*7mq d9nocz-9djt -play middle C (262 Hz), but one is at --h9z*dj 9qdt o mn7ec5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. 3/(*l ysyalvsu h54lm 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 frequency is 4 Hz. What are the possible frequencilvu4h3a(*yl/ yl5 ssmes of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m fop4hf,y1 fpqqlf3v6zozfc(ux v : q0i17n5y - rom one speaker and 3h 1fyufvqlf o4:yi-zzvo7,(0nf 3p1x5qpc6 q .50 m from 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 Hu:x3vq oe6qxqq9 7m)v 0 j/:vqa.lpryz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mus70qpe39ym.qqx v jqvlo:au:) /x qv 6rt 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. qu7oru1pq59 gioey(4 How many beats per second will be he7p 9 uiou1o 54eyqr(qgard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engin epci y44.2z evg+w7bie’s siren is 1550 Hz when at rest. What fbic. 2+ wgz47ivee4 yprequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire en8x) 9k9k 5flo2y xki, fqop6magine whose siren emits at 1550 Hz moves at a s,iao qklx589xo26fk f)mk9p ypeed 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 toward you at io /c;-oh9e an15 m/s versus you moving toward it at 15 m/s Are the two /ia hco9-; onefrequencies 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 the same single f1 ltpf*c (f fh-rqt/a:ypxq f/v-fu7 )requency horn. When one is at rest and the other is moving toward the first at 15/rv:1/ f7fh(-qlfft ) tfcp- *qyxupa 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 ultu4b3 lyh8f u*m+u*pozrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 2o* 8zyl* u+pf3h4u bmu5 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s Asr( ijv0wqb.2s1uv 7js it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wavejruvbs 2vs.j (7iq 10w?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played zib5lb/c 2 *q w-*xjdmon a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same jmwi/ b*ql* dx5c-2z btone 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. Suppd 4sipg1yt86+x.pgm11w yp diose 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 iftp1y1i+dpg s.d84x y1g w6imp blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using hby fb8*k7 ff0np2q ktq2j-4j7jqm x7 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 wind v1g z6tx /imrk-elocity is 12 m/s from the north, what frequency will observers hear who are located, at rim6x rg-t/k1zest,
(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 movkdv9h(an u;/-x hov 0hing on land 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 (a) y5,cy vdm y-wyz uv2z16,v:wiWhat is the angle the shovvw1,v 6y5yu-m 2dwz,yi :zyc ck 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 atmosph.gd3rt9kj 1 kzere of a planet where the speed of sound is only about 35 m/1 k9gjrt 3k.dzs
(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 travelinuoy7*bd9j;1rxj : i nmg 8500 m/s strikes the ocean. Determine the shock wave angle it produce *ro9mjd1: nxi yu7j;bs
(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 /o65; )nw0ttfbe xd wp$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a p m3q y/gm0pvaf - 1l)zsg( /kq5ldo4lalane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dispa lmf3v-lgd14s /5(q0lmka /yq)gzotance 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 20,000-Hz sound pulseo 94qlddu2.h kks2ug,li9y,gm.f. ihs downward from the bottom of the boat, ahq,,us24 fl2.9d.k g k.d9gyiiohml und then detects 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 t i4 q awx zm.-9q5bzcdfrzs861here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It t + n+y ;j739kteimtenconsists of many plastic pipes of various lengths, whichje+tten it 9ky 7n+3;m 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 msy(n) +(i y; rc1**baudhhnk jakes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquityn**au +iy)hcnh(r1d(b;j sk oes?    dB

  What is the resultantw04l 7fy6skmt5 s3ovt sound level when an 82-dB sound and an 87-dB sound are heard simultaneksv mlt 5w7o0f64sy3tously?    dB

  The sound level 12.0 m from a loudspeaker, placed in thwb he)lzi,-(h,;jdx2uh y p5ke open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming ,2ejlhyh i dhu),5pb-; (kzwx it radiates equally in all directions?    W

  A stereo amplifier is 844xiy*wo f nwrated at 150 W output at 1000 Hz. The power output drops by 10 d x*8wfwo4 niy4B at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typarqp7 e7i4qhege--6 cically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 4g-eae7e-h6 qi cqpr7 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, te. fu+kh+9m vwhe gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequen*c 5ro0x1zvy qcy 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 pointh -padjowcv9gkg3i sq +(20h 86yu*ubs with a fundamental frequency of 440 Hz and a mass per unit l8(k9pgushjw6bd ia+ hy uv 2-*oq 3gc0ength of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled withwzpxt.hod8 72w3uy -kku5*pc 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 thew3cyw-p5*u78 uhpkt.2o k zxd tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube tha-ve jx73zjxlu (+.ofl t is open at one end and also 75 cm long. lf 7v-x .(jx3 uojze+lHow much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r bn/sdj .t3p m114pvny34kzmkesonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from tw 8scvqjysugdci43mnw44 g0i.8 c2-jfeb+0 sc o sources. The sound is loudest at points equidistant from the two sources. To determine exactlyy mjfc -8qd4+.0j gibuwss2ge84n vc4cic3s0 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(syo/8 +.b gztw tjb-yiaqn03 conductor on the stationary train hears a 3.0-Hz beat frequency when the other tryqtjg+ az no8w/ 3ib(yb0st.-ain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whsk5 2 dya5yt.5 zqwjq 5)c/oelistle as it approaches you is 538 Hz. After it passes you, its frequency is m ytdy)5q5jw co a.5/5qkls 2zeeasured 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 tw eohc.ja 68+fd7uxa:he difference in pitch of the engine noise ba86hewojx.d:a c+ fu7 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, sounding together, produce a beat frequency of qea7 *oum9rel-(fg3 qcqs v+*11 Hz. The shorter one is 2.40 m long. Hg oc9m-q*7svr3eqa u*+ (felqow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past3sn xv4av-u.t a stationary observer at 10 m/s as shown in Fig. 12–37. If the utn.34sv a-xvspeakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abo.we:p9r+siy out 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with.ow9r eiy:sp + a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5h(xv+:zp *b .la c5 a*ad8 5d2vvfpfj5e2 ozqg 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 detecx*cfp2 vjqadz alv z 5bfhp*e2 :.d( g85vo5+ated by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulo9/wwbif r.j. ses 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 sbwwro i..jf/9 o that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was ;2; jaangq ue-5g:b uwhpr.7a 9xsa 2jonce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is 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 t earj aa-a7;s25wjuhngxup2 gb ;:9.qo F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comprom- .w xb6uay. m,dqn)brised by the presence of standing wn m.-,a dxuw)rb6yqb.aves, 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 high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slenad.y4s)s: ;hsf- ivx7nk - wofder aluminum rod held in the hand near the rod’s midpois. s :vnokxsy;4-f)fdw -h a7int. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humavo2dkty2,i3k z 3p*hnx,3zs f n ear at a frequency of abou,*ky2pf t ozvzxi332 nsd hk,3t 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. 4xf)ox4s b g,/bymcw n36mkt3An observer on the ground hears the sonic boom 1.5 min after tk,sb nfmxw43 4cbg mo) x6/y3the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 jm0hd8d* f2ql$^{\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