What is the evidence t) c03zaoxu1av maxc7)q v bt85-2jze*qyv0 tphat sound travels as a wave?

What is the evidence6 kjn8o2 ptg*8im8wuv suz3:.hqd7ff that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attace )d :qq d6ip1-aw4 tvnx.ytd-hing a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup dweynt :)qi1dt4.6- q-vadp x(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, 8 4sedzm5. ,mwto5gm bdo you expect the frequency or wavelength m5m 4m.gzetdb,w8os5to change?

What evidence can you give that the kq*khq3jgx-59 99b zzo dc.fzhag 8r 2speed of sound in air does not depend significant9krjg h dqaf9 2kqz.-x89bhg3*5oczz ly on frequency?

The voice of a person who has inhaled her f/4lvs;ubcv g1jes(l 2l u cku,e,66lium sounds very high-pitched. Why?

How will the air temperaturel r)0 eu j:hzyc(,ko+t in a room affect the pitch of organ pipes?

Explain how a tube mi-pwta .,e (u ak1r(b1 )re jmud8c(unlght be used as a filter to reduce the amplitude of sounds in v ( ap1wlt1u() bdae. e8-u,ru cm(jnkrarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (F-5vgc5t :opexzgwsr0*1 : + mmqftec0ig. 12–30) spaced closer together as you move up the fingerboard toward0gc::gqso-05vzmxr 1m t*tpec+ wf5e the bridge?

A noisy truck approaches you from behind a building. Initially you heaaagw54k o7 4o9sqim5m1 b4bxk r it but ca4a 7kb15om 4bqsok xg59m4iawnnot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space. djkl45p.w5w rss3q4i 0a mql,” whereas beats can be said to be due to “interference in time.” Ei4s pl q5ra3 .l4q.jdksw50mwxplain.

In Fig. 12–16, if the frequency of the speak yqia6qlp 2eo dv )r7d//pmvvu+1n1t-ers were lowered, would the points D and C (where destructive and constructive interference occur) move farther u2+pm/1i)6vvy/o rn1-qq7pe dl datvapart or closer together?

Traditional methods of protecting the hearing of people who work in areas wim1gdr( dhhi1s w yz0s:;-3yifth very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noissrhi i 0;ywz1y-ddhf(s:1m3 ge reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each v nrngo3 zuocmfxn,., +,*)4.j qfiqpwave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which onf q 3 )4no jnprumzc,g..o,v*xif+q,f the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shif r :xt 8l55o.7.kzfeh(drsn:b cm-hfft if the source and observer move in the same direction, witk dlh5n 5rxf. ehr z-:tsm bf7f.:8co(h the same velocity? Explain.

If a wind is blowing, will this alter the1rq3m 7 ec,ph ar+l90dr tvok wxe3+(b frequency of the sound heard by a person at rest with 3 chatxvkqd3rbr+ ,ow9p e0m17 r(+le respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child inho1tv-qm tgf8d /m,0h2 zt- l0 q-ylzz 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 whig- tt1-0,-yfloh2dqzml/qz hmv8 0 ztstle? Explain your reasoning.

  A hiker determines the length of a lake by listening forvqrho1km m:v l;8k1k6 the echo of her shout reflected by a cliff at the far end of the lakvo m8lkqr ;:6hkmvk 11e. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship juew yyh-)i(hc- *i r.g 5ths9gost 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 seawater is 1560 m/s (Table 12–1) and does not vary srigig5 h -y(h.y *-9cwe )htsoignificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng ni ovj7.ci i)i g;3g0gq,x-uyths in 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 ju.x dejq,o+4:qhgf r9d3i 2ezo xzz:)xst above a school of tuna on a foggy day. Without warning, an engine backfire occurs oq.)j h d42i:qzeg3fx+rzo,9z xd:xe 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 splasg);5bs kt )zxu*i*t jhh it makes when striking the water below is heard 3.5 s later. Howt z buh*x5j*i )ks)t;g high is the cliff?    m

  A person, with his ear to the ground, sees a huge * )e(vebu9n jrstone strike the concrete pavement. A moment later two sounds are heard from the impact: one tbnjr v(e* eu9)ravels 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 ..pet z0g*yl w crla2ew 1yk9+of distance by the “5-second rule” for estimating the distance from a lightning strike if the temper 1weglwz.9ely2t k+yrc 0p*. aature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of 6ci9-jyxyshuh4 g 3q*b2 blo2a 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 sound whos .5lgru6mgwc )e intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously eaf1zy8 tn6:j1nb,q4xx e7i9jy f 4 qlat a certain place, what will be the sound level if only one is exploded? [Hint: Add intenybty 4q4xa,in81ee 1:ljjqx6 znf7f9sities, not dB’s.]    dB

  A person standing a certain distance from an yf.i.g eo1np- airplane with four equally noisy jet engines is experiencing a soun o .eypf-in1g.d 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 az:-l r qajz(dh2e9c,brlxl,-u p +4t n signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each de zbe l,n:xar p+4u 2-lrjt(d9 qclzh,-vice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nor*;uf 4 yif)nhrbp v3 +7styn4wmal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the 7u hyn+fbf)p*n t;wvyi3 44srmouth. $\approx$    $ \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 eardrum0 y+ n(;hlamnn1vk6 dz whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the ,sa ycjtc z5:)more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3cca s:), jt5yz.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 mejm9c 0dt,y9 vtter registered 130 dB when placed 2.8 m in front of a loudspeaker onm, 90 tdvjc9yt 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 i1x:p 1fk0o5qza0g, 4on)srs vjp g8xwn sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [aojwzok x5 nv:01pp,0r1s8xf4 qsg )g Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by z/ u/ z ezlo4awzp4h47w2uno+what factor will the intensity increase? Increa2z+o/u zp wz4/weao47 lzhun4se by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but on /vqx( camz8u(e has twice the frequency of the other. What is the c x8q v((u/amzratio of their intensities?   

  What would be the sound lfid8n ot, w(.xbk (we/evel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.1wk bd, eiw.t o(nf(/x83 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound ledgea:u 63d0*u xwk wf-vel to seem as loud as a 100-Hz tone that hauxk wadegu- f0w63* d:s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detec ymhzy7ab:9 *ub,yp 4rt when the sound le49h7myzyry* b:bpu, avel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accomq/ heb 5f*i8g0xgg3ureb l 4s-modate a huge range of sound levels. What is the ratio of highest to lowest intensitlireu*-eb b3/ 5 ggq48shgfx0 y 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 frequenct skl 57hdp6w:y of 440 Hz. The length of the vibrating portion is 32 cm,t lsp k6d57wh: 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 fundamental and fplpt phq6 6 gwo 02,hkk(+kwmtq02 vt8irst three audible overtones ifq2wwk6p( 2lvtpph,kg0mo8+k0t6q t h 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 ) hednh-q9ap)q46x t0l d8oz+o.si ybfrom blowing across the top of an empty )qnd4+.qbe)dxt yo s6 pi-a h0hlzo9 8soda 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 organt1u1t1 f lpdm kqx k6qv6h20q, with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths ofv,f6hp md q01tk6lq 1q xt2ku1 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 harvj,wm5.( u7gdp: w qq mimi(y5monic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origj7q5 gi5 u :dyqwi(pmv(wm ,m.inal length?   Hz

  An unfingered guitar string isog2tt*y r21js2ez*+ mn okr.e 0.73 m long and is tuned to play E above middle C or2y2s* t.mor ezt+j*ge k1 2n(330 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 oft o5jy dns 6o+xe;vme y*3b.v. an open organ pipe that emits middle C (262 Hz) when the temperaturmb .xvnve5 oye+t*ys.j63 do;e 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 7vh(c3h xc p.hp5c) hr:rmf-/vs ov 3rqs t0i.at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 sho/k0xg n5.u uu0jgr +53* 9ktyf5hsej dsdyfd,uld the hole be that must dgx5 ,+ su3nk k.u0sfjhtd0u5fy9jgd/yr5 e* be 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 resonate at 264 Hz, k73d(cx lqv(ys jwmz, .j 9ie 5l(a/va440 Hz, and 616 Hz, but not at any other frequencies in between. (a) She 9 3 a5l/,zy7 i(mvvs(jwlk( .qdjxacow 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 resonar; 92nyogmo)n/ ak1o n-0uu9h(lxfeb 1rvr p;tes at two successive harmomo2nvapb f-h0ok1ney1 ; ( r9 /xuglou nr9r;)nics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 t)+u 7p 15m/r/ca rxk eph-vxw$^{\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 20sf6v26 sg idr(ygrf 2/7gpsr .14-m-long organ sdf(/66 yfgs7pv rir20sg r2g pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appro)/qzs g77-hg by*vcddh5wy 1nximately 2.5 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 relationship of your answer to the information in the graph of Fig. 12–6? -ys5 y dg 1v)q*c7zg b7nhdhw/$f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings,j :asp7h huft/:1zfl, one of which is s: ualhf:, s/hftz17 jpounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzb(kx1u )i-)bhagu (y f) 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 aaufzne4yw )4 kf1lm ::sd8yf,t 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 played simultaneously, estimate the operating frequency of bral),s: kz48 n4:y fe ffmwu1daynd X.    kHz

  A guitar string produces 4 beazut me/cz r*v- /r+ :crccw2m d()xs*wts/s when sounded with a 350-Hz tuning fork and 9 bea2r)r cew c/zsvc*zc wr*u/tm(-+x m :dts/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in d jv7vtv u8cd)8wj,o9one string is then duo vddt,97 8vcjwv)8jecreased by 2.0%. What will 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 flutbcri6 / o5,hlves each try to play middle C (262 Hz), but one is at 5.0°C and the other r 6b co5/ilvh,at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 3oerbz9t a r06441 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 possible when A and C r9zetra0 b 36oare 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 3.0dnmn7ao97hm( 0 ,f:6rmqtb jq0 m from one speaker and 3.50 m from the oth 0nnqo7m7 hqjm6mr :,tad9bf( er.
(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 q9;gewm 8/ 2e1;tyqvubhmyj* vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when hebqyw;m1;tgy28v *9/u qjemthey are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats pej 9d8ksf 4s2omm6m*ufr second will be heard? (Assume T = 20 ud6ss 9 4jokf*fm2 m8m$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eiim4 kt2ovs ahxt9 ,m:1 c,n3tngine’s siren is 1550 Hz when at rest. What frequency do you detect if you 3a,9x t tni,v41 skh mito:2cmmove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stiw xn6x0ww w:x9l*fb/ 1vx1nxall. What frequency do you detect if a fire engine whose siren emits at 1550 Hwf w 0lw w xx1vxan1:*x/9nbx6z 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 m5( 8(sg/s ikv7ufygt source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly u7yvs8 t/km5g( gfs(ithe 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 ey:6m(g 6+ io+ xbo v7b+ogakjequipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at r+ (g g x6boja:ok +76bovme+iyest 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 ultrasonic sound b ,y6lhb+ (z;f/eod.( )6jzewavzm.iy l4dl uwaves at 50.0 kHz and receives them returned from an object moving directly away v4zuzae6b ,(lzj dly;d)e w./+( .libhyom6f from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an vcj.fu nxey d:;8 z:xd;er0wd+y t x-3ultrtedr08 c.e-:y nfxxxv3;wddy;ju + :zasonic 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 plaf2 :o d)zye7yhyed on a moving flat train car at a frequency of 75 Hz, and a second identical ty7z2oehf :)d yuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrq +j mqole(to:8euhy af9.ii/s/2za 8asound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s ditle/yq8qja/2fuii.m o8+: a(o sze9hrectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency m wr88-w, 1d uoglpoj,u:c 6bf $2.25 \times10^{ 6}$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 emitsv gea7tbkxg/*)fqm; (oy sl19 sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what ofgs1;lqmyb/g9e() akxt v*7 frequency 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 mc /14lst3gq1-n,xo y 2b zomhspeed 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 Macq q +d6o95r kxs-3for.kgq)o uh 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the aookrqsq5k .+q fu6x3o r)- gd9irplane’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 tnu1h w(7 0 if:.mmounrhe thin atmosphere of a planet where the speed of sound is only about 35 m/7 h0(ofw u1 nmin:r.mus
(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 qy)n4k2 p+l 8d+qspc tthe ocean. Determine the shock wave angle itd)qpkyc8+nq 4 pls+2t 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 xs 5z7-xpy:zd$/theta$ 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 eu/ty *eg-cbknr zj ,0.xactly 1.5 km above the ground flying faster than the speed of sound. By tk-0n jgetc.*ryub,z / he 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 sendugm/c;gp6)f kh*l-npy6.4 i1uzt m p cs 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designcy6f) .tkg *il 6m;u-1cnup/4 pz pmghed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there inyw8t 3 ug8y1i v,wgz.n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum hasx nz)4j5oy1cp a display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are o5yj) nocx41zppen 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 makmn4a sgd,df-)9k q7zx es a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes gknd49qx ,samz7fd) -?    dB

  What is the resultant sound level w p j /jhznbf5,xn,x73ihen an 82-dB sound and an 87-dB sound are heard simul7bz n5hxjnf,/jxp i,3 taneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What0d0 ,6mnw a2ey9x5cp(uo / cryvpg2 xy is tyacrw/9cd25 6,0popg en ymv x(2yxu0he acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W1e1e3,i hpsje output at 1000 Hz. The power output drops by pe e3hi,se 11j10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prop j(mi )g l7wd++v8eyh)uk il2tective 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 j p(dgyhlkl7iijvw)2 )e+ m +u8et airplane engine?    W

  In audio and communicat;olcc5j7 beu+ ions 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 tuned to a frequp 7jn0t4/ik;f-a v,v g*i;m:z vky dnxency 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 betweelz:kt2v+h zg; n fixed points with a fundamental frequency of 440 Hz and a mass per unit length tvzkg z2h+;:lof $6.1 \times10^{-4 }$ 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 with h6 a;sf esd/8owatera/se 6fs hod8; (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 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 thatw .z16g)7x8s4x qr fkvy iw9cc 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 fundak71igyxww)z8 qvs .cxf 64 9rcmental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate ps)uscu+nsiic 0j(( w )s:*cc 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 9 u:dl+zh,zm ;2a xldq8,jq zrin the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound le,z;9 d, +qaqzhzldu:r j mxl28vel 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 )v rl7ry s.e-uconductor on the stationary train hears a 3.0-Hz beat frequency when the other train ap-uyre.s 7vr) lproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistlj k p1pzu 8bfn 3v*c2thrqj.7-e as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train m pckjtfjnrb2p 38* uv17q -.zhoving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listen k3bi aujt/p:8ing to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved3i ab/kujt 8:p) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundio faa4a,y* 8dung together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is theuaa8 o*,dyf4 a other?    m

Two loudspeakers are at opposite ends of a rail zk6r3ai.stlhw e, l(0road car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) 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 havt,siz3a. l(kw h60rl ee passed him, at C?

  If the velocity of blood flow in the aorta is normal jj9cy+hf4 l*bwl) pq:0f)cpqly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along t 49:jwp)ll)cyfhc b j+*f0 qqphe flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while thus le b(xuov ;h5a(5 csv+m/g/e moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth mg;+u(auvxs/b 5 hl(s5eov/c?    kHz

  A bat emits a series of high frequency sound pulses as it approa(8ewmk 6kow. uches a moth. The pulses are approximately 70.0 ms apart, and each is ok(6u8.wm wk eabout 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was ony8p d3hy 2rf yk/0mv5fce 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 t/h20rdp fm f8ykvyy 35he 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 compromise01bk qq(.fqlqk xs,5p8h7x xod by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Considexhlq 0 8, qbq5. k1fxsqo(kpx7r 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, ca4 re;oa44;kgyx cq7gz lled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringie;q7 a g;coxgy 44rz4kng 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 w7u7xrf tq38 mfor the human ear at a frequency of about 10x3r7tq f8wum 700 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. 3rut5p8bnbb yqq;b,2 An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s albrt3 2b 5uqy qn;8bbp,titude?    $ \times10^{4 }$ m

  The wake of a speedboat qos2pd g(p)+ ,7kk 6 /ph7kt irjuq2bais 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