What is the evidence that b*h)bm ll ,c/t.p4aen xf*zvs5h/+p h sound travels as a wave?

What is the evidence that sound is a form of /w jem5q )mmrkm*9yk6energy?

Children sometimes play with a homemade “tele*bs, mf1m1ilgynb f,7)h cl(ar1 y;rm phone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fi (ayn*17bc frmir,lmb)ml 11;, syfhg g. 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 expectf)); uhc8pr0 y:gdrab the frequency or wavelength to ch)ghr0:dy ;frc ub)pa8ange?

What evidence can you give that the s- )fb)or2eyld- dai m+peed of sound in air does not depend significantly on fbi) om-) -dl2yarfd+e requency?

The voice of a person who has inhaled helium sounds very highck*usp*o 5s3c uj3*if-pitched. Why?

How will the air temperatgbyxi or/ :v,7miwq w1fa9.)aure in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds i8ktxaa5yv2kv (z z4v.n vv2taz k 5vay8 z(4.xkvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer t6 m6* u ;d;zqyt. b.zafg6pvfrogether as you move up the f.;qg. bf dz* mrf;vy 6uz6ap6tingerboard toward the bridge?

A noisy truck approaches you from behind a buildingd-yl2ir mfg: -jfy- z+. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–1ffz:idm-j r2 -+-ylg y5 on diffraction.]

Standing waves can be said to be due to 0v6l( bk /wict4 ; )csfehsuw2“interference in space,” whereas beats can be said to be due to “interference in time.” w2; weuk)c/t0(s46fc i vhs lbExplain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulz11-gwxx/ s uxd the points D and C (where destructive and constructive interference occur) move farther apart or clo1gsux/1xz- xwser together?

Traditional methods of protecting the hearing of people who work in areas witho;qgqk(33r4g bb5ag5/xqp ta very high noise levels have consisted mainly of effortsg 5xga /qqt3;p b35qg rk4bao( to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each ko7w in-qc7owp,u17x wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fok ci7no71-xq u pww,7ig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direckya-x:5q fm yls+ k6/ition, with the same velocity? 6a k:m-yfslk/i5yxq+ Explain.

If a wind is blowing, will this alter the frequency of thewvtn5ad 1//eq tvt6r( 87oui d sound heard by a person at rest with respect t8 d6eot5watv u/7d tvrniq/1 (o the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monit(c-zj9.**y3fxf dfvmmmc+ y oor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning. *y9* mfo3zv-c(jdmcx m.+ yff

  A hiker determines the length of a lake by listening for thqm iv4 oa0jgj5 m3vt;5e 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 length of the lakamt534iovq5 j ;g v0jme. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below th2jcaml-lfkf:e7h 6t : e 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? Assuecf 2:6a j7f-thkl:lmme the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20fdfle6j.i9-v iprz 17 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy u (16w csqpim2day. 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 (a) by tu 6s(2piwm1q che fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The roh-ji ,klpj-1j jv *5splash it makes when striking the water below is heard-v,i hp-j*k5j ojjl1r 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strikep6 8ughxvfp.+6ciw*jb-dn u: the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in thei +d p*6wv8uxfgn6bjchp .-:u 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 of di(+v*rna1 e lzfd i-kx5stance by the “5-second rule” for estima(vzi kf1elrad5x- *n +ting the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t (;p-b0qau o5g;s 4qz6m0dj9iz vgydvhe 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 soundz p(+:7bbq zu 28o: t4pxohgzm whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sim9 y sbksor (3 xe,krw gxl9k*ds.h*p7-ultaneously at a cershkkd* rw7bsk3lo-,x. (pg9e r9 sx*y tain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certap4g6sdi* nml01wkno x786kn z( sb3u iin distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Ad( i*n7b6kk0s831ismodluwn pzgn x 64d intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBi+r0rc e(d y (d86c.r++gxaemq1qai p, whereas for a CD player it is 95 dB. What is the ratio of intensities of the si0++gdmxc6ay.e8i( r ad r(q+1qp ce rignal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person sg:;hc* d hhm3thocuxuk67t 27peaking in normal conversation. Use Table 12–2. Assume the sound spread 7;u :kox2uch htm6g d3*hhct7s 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 eardrum whose ar rqzrnhrp+j0 +x 5.zsx )epbqd4:;q,kea 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 more modest amplifixj( y1kk0kq.q er B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conqqkyk k.0 jx(1nected 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 5zczbkmv27 i6b1 i-vitm li;,dB when placed 2.8 m in front of a loudspeaker on the stageb,6;l mit1ivbc7i vi -z25m zk.
(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 diffewtb6q c vh -2nc( sede*b 8ybv-n5e5-drence in sound level of 2.0 dB. What is the ratio of y(- 6enbvbcdqs8v -e2edwn-*5bh t 5 cthe 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 will the in9 .kvke7w-7* fxlrls6b aex1mtensity increase? Increal.evk ar-*wkl 6e77xf1sx 9mbse by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampl9 uynov -5w1aoitudes, but one has twice the frequency of the other. What is the ratio of their intensitievu9- 5 nooa1yws?   

  What would be the sound levcq180 - / gbdoa jp+ ws;o5ltpwsn9xx3el (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 30ps x /c+wa;go8j1txn3-l9 d0bwpsq 5o0 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as oit ;tbn-zr4.m 3kyt 1a 100-Hz tone that htozt.-3 ; 1n4itm kybras a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an m m8uuyln, ;+b .s5dbchvu)7j jhsz./ear can detect when the sound level is 30 dB? (See bcj8m hu.+;v/bhy u .ds)lmsu,7j n5zFig. 12–6.)

  Your auditory system kf )k(l4,k7 2och ibfxcan accommodate a huge range of sound levels. What is the ratio of h(i472kfkof h) bc klx,ighest 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. The2b )xsp 7vuhh*zv+4 xlg+b,xdc9i jm6 length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wh62im pvxjdb9c+h4 ,*l)xvshgz 7ux+bat tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibg.owiazi/ kdm79r/j 2km7dy(le oveyjr. a k iwm7/di/k27o(z dgm9rtones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across tzg y9 t,kctd o:w4y 62hhs:6vshe top of an empty soda boscgtw6s, 2:tdoy:hzk4 y9 v6httle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tx86 j r(z* u. lenx:yer:2gqutube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of p: .y28uereg: *(t l6qnxuzrjxipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency ou/mi x3 z43cpaf 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its oriuz ip4/3ma3xc ginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E(q7w mt*v9xnd5+b et h above middle C (3309 5*+dt7qne twbxm(vh 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 organ piprm yax)txpzhy;7)65we that emits middle C (262 Hz) when the temper)t;7)wx6m ryxhypza5 ature 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 atuo 7jj6 n;ks/g 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouumik6b2x 6 2z)nydag2 thpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C atzayuig)6 x2n2bk 2 6md 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 ceq .geto3 pqs75/sat-an resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in beeosq3/ -t qpe.ag 5ts7tween. (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 , kb(btq2fgys* yi07qtwo successive harmonics of frequencies 275 Hz a27ybbs,i* qk 0 yt(gqfnd 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 ob4lym)a4klpy -pl,xl(vxe p4(e g 8 5$^{\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 (extsm,7sn1p)pt v2ts-b wm:dc 0d( zfor a 2.14-m-long organ pipe1b( st )p-(c2dmte ds xnmtp,zv:w70s at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appqhg+og2-cp2 proximately 2.5 cm long. It is open to the outside and is closed at the -pg+2coqpg2 h other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust twox amh a;1mtw:) strings, one of which is sounding 440 Hz. How far off in frequency isa1 wmm;h x:t)a the other string? ±    Hz

  What is the beat frequlq,z9s7fti(aszkk 1 w v )s;q,u9b *euency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatemyc29+o(o gxh5x *bon s at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequxmx+n oho2*y(obg9 5cency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4u/8uis./aw trw f.n2: q0wg ou beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when s.8: /uq rus/w ngawwf02uot. iounded 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 ba(2lf-+fh+ c t(bl bktension in one string is then decrea ktb albc(h+f fb-+2(lsed 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 flutes each dvh :rg)t c6* lgy3n;otry to play middle C (262 Hz),rh ):*vydgnc3 ;tg6o l but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuninmnt.yrg/mfu):p 7n5xg forks, A, B, 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 arg)x m t7pyurnmf/: n.5e 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 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 from one spetvmg)i: , u-3zfbyh7e aker and 3.50 m ftib g37fm), e-y :zuhvrom 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 1h-osfkr/cz)5 i.1 / n4slddkt32 Hz, but a piano tuner hears three beats every 2.0 s o5 c)/f-rn z 1lkidts4d .kh/swhen 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 m8 :jm470cvpg y:kkthj in air. How many beats per sec kjgm p7:k4cv h0:j8ytond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain x 9p90wimfz zd18 3v;uk(ofqxfire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with 91( 0 pu ixmozv9qd; kfzw8x3fa speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What q -+ktf65bwtulk (p 3xfrequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s tqpxlfk +53u(b tk-w6
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you ykz-:3dn x+fccq.f*q 4p3c mcat 15 m/s versus you moving qdkn + c3c4 mzxpq. f3c*-fcy:toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one isfn ,76lg/ce xf at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the hlnf 6/e g,x7cforns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wavestab pz.cw d2xwz-vb(-q rb:i 2r4x 96n at 50.0 kHz and receives them returned from an objbtwb2zir2bp64zan: q wdcx v(r-x9.-ect moving directly away 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 Adbxrbs8ens( dg7(9 4q9i6- i 6pqww jns it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What nq8b e-s9grj6s w pi7bi n9d(wq6( 4dxfrequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was 84 maj(,h zbn(vcndt6played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station a, cm( tznj46(h8 nbdvat a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speej8 b+cvfe4fzf r* jw*)ds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is tak+wev f4j*fj)z*cf r 8ben 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 usinqafv yiu)j;e,x q0)x0g 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 velocity i .f2ega o.c)sp1 yopnf.vkv*2s 12 m/s from the north, what frequency will observers hear whofseyon.)p2.vg2vo*p1f .k c a 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 it a5ju db,. :2j/ctfhlvli*-bws 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 sow+mj fh c5fn8h t8n;yw9b94tv und is 310 m/s (a) What is the angle the shock wave makes with the diy94+vjc9 ;f ntfbnw tw5 h88mhrection of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speeqb(6lc*iic n6nduh5e4i) n y+ d of sound is only about 35 m/hn6q*nc d+iy(u c) ei5lb 4i6ns
(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 /f(/ :0m,v ytzojhxpdthe ocean. Determine the shock wave angle it produces zyh,m: tv(fx0dj /p o/
(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 7arsve6wk3nmbq sr1gi71 an6 c4d4 /n$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane2d5w 9k5cbnx; ;pfrjx 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 distan9 nw;bj2k5x; fr5cpdxce 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 2bfo7c4 z ku2x-0,000-Hz sound pulses downward from the bottom of the boaxk -zc2bu o47ft, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibl8 idr:bh4l.r re range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called yb0f9 cgat kdx um u75*j3l:.b +;ed4wlfja0ha sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bot4btjl g50d; a awje0 y9f.uchd*u3lf7 mk +bx:h 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 persou 5h m(3bfwczt:g/a6 yn makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 sucucb(z5ga/ : yw m6t3fhh mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and k:m:qkd:e db j(ud)3 ysp.:qs an 87-dB sound are heard simu:syq )3m( eb::kuk.djpddqs: ltaneously?    dB

  The sound level 12.0 m from a loudspeagbfwi m*ry)cl4/ )cm6aq 0l6aker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radia *)6mmay /ig )cbrwlf0 q4al6ctes equally in all directions?    W

  A stereo amplifier is rated at 150 W output at uk5a8c vlz -ddysb))hfkn/s .l)3i*g1000 Hz. The power output drops by 10 dB at 15 kHz.c8)kk hs)*za b5v i/dyu3d.snl g-)l f What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their c5.sf yt/*vu: w4 va:lh7hfa dears. 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 fvw5a:cf7luva./ 4*: y shdt hat a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gzn 35s*tw3ishfh,u x 9ain, $\beta$ 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 tun oce+9n ywix51nr84lned 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 wit0 573z yngm7*dxsq gtuq1;s uih a fundamental frequency of 4d70i*g ngqzx37;sq us5 t1uym40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fill :(c x(voa6sgbed with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at:((vcb gsa 6xo 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mebcek0, yyt c60fe5bwx +d:55 uigig:ass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should y,ki ewif60yg: 5ud05e5+ctb:gx ecbbe 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 resonate as xx, shggk); rik+l3j)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 rangz-)w(8ribj cbiu /t,ne 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 level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the soundw8b,-cz/ji)ru(n bit ?   Hz

  Two trains emit 424-Hz w0y/ umvkowox pdt97 2k7d- vi0histles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other tryom70o0 -ud7td xkkp9v v /2wiain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appaa ,vcf (3:1wplfqq+xput70yroaches you is 538 Hz. After it y,lfx vup1 0qtwfp3: 7+acqa(passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thephp1x2 :chzwzx/m- 8 k 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 halved) as it goes by on the straightaway.p hz/pxk8x1:cm zhw 2- How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a b5iebyp 4q)i7 gr c9t-jeat frequency of 11 Hz. The shorter one is 2.40 m long. How lon 4bp5r-g9jqc7y tiei)g is the other?    m

Two loudspeakers are at oppositeku,,gae+5z wsqn:h j5eyly6, ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig.s,e la+ :6jqz,nyuwhgky5e5, 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 have passed him, at C?

  If the velocity of blood flow infvcn+qq/ 7entbs2 ;o 2 /) 1u0 iutymctd0hc7a the aorta is normally 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 cells? Asn) qut/o0i+fya7cnmsq17 ;v2t t0h b2/ce dcusume 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 w8l;k;e w 5sfq mplex/.hile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflectm 8x;swe;eq k5l /fpl.s off the moth?    kHz

  A bat emits a series of h2-/sc52d ,mmqquclmz quz:ir) 7mm g7igh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms zzcml7dq: mum m5 c2,s7mug/)qir-q2apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1w 2dnc mm/:0 3;mf4bviciz4dh2–38) was once 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 crea2i ncb44dcdfihmv3m/:;zm w 0te deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can bh9w4 b-wmaje/ ) (thrp ibhe3-p; hsd6e compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing bm3h;sb e49/-r-)whjhew( tahi6dp p waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves awv m )hnd+:0: as7n9jxhb uc4m long, slender aluminujb7saw :4m +c0nnuxvh m hd9:)m 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, 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 human ear at a 4hf( ,t+ qyx-2gnzzk01qlrk 0+ d zryafrequency of about 1000 Hz ,qz+x a r(fy4yr1kn0t+ zh0-2gz lkdqis $I_0$ = $1 \times10^{12 } W / m^2$ 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 atg tm o(1titp05 Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is5o1tpgm 0 tit( the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15i(d.zl/m3 zb zxe,xl+ $^{\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