What is the evidence that sound travels as a wave8i 4uidr-fus/ 6.sbjw?

What is the evidence that sound is a form of energz-c0 : ua, pn,2m(ju1so pvlnky?

Children sometimes play with a homemade “telephone” by attaching a st26t a3n2 pcesjring 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 (Fig. 12–29)3np2c2 s6ej at. Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air in0ty;z8:qm :ap uszr/bi: x(bnto water, do you expect the frequency or wavelengmauz0z; ::i sb8(tpxbqnr:y/ th to change?

What evidence can you give that the speed of sound in air does not depenqot: ;(csg: ywd significantlwgty :;scq(: oy on frequency?

The voice of a person who has inhaled heliumr sxib+ px3)m)nce, g/ sounds very high-pitched. Why?

How will the air temperatv6j r(vj(+:hji je* h wi+hc0xure in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude ;cucl*ctf ;bmx6u.1 )xz y 7wbof sounds in various frequency ranges. (An example is a car muffler.16)c u.u c;lmbyw7xzt*xcf;b )

Why are the frets on a guitar (Fig. 12–30) spaced closer together a.ac6sdq4 qfqd6d51l k s you move up the fingerboard toward the bridgl d qdc46a5sqf.61 kqde?

A noisy truck approaches you fro/c5 4+mkq oztl o+-k.,vx xdb/e vuue;m behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brightq,zlbxo -kx k4+u d t;5.+ emv/cvu/eoer” — 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 “interfere5bj 5l:r5q aktl 5fmu,nce in space,” whereas beats can be said to be due t55kmbqjf lt au:5 l5,ro “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were l/n0r nrtmr2/jq se 5*vowered, would the points D and C (where destructive and constructmrrs nr2nqve /5t0/*jive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who ,, j cjtd+f4crwork in areas with verdj,rfc c+,jt 4y 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 noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave p5a0k-t ei j2k*f)ntacan be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In w teak 2 p0jin*taf)-k5hich 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 an(ix*zp b2 c (26ggmcwad observer move in the same direction, g(m*xc62i bga (pzc2w with the same velocity? Explain.

If a wind is blowing, will this alte+ svntutp 4xo2 8w:rk.r the frequency of the sound heard by a person at 2x: ts4n.uk r+o tw8pvrest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child i i) i7/zd8q jnho,.j,zq0 vy5.byay eqn motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which p7hqzd/qqzn j 8. oy.,0i)y5ja ,b ievyosition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echp xd23 rmea-)skh 5ezuh0du4+ o of her shout reflected by a cliff at the far end of the lakxkreh -2d05heuadzup +4m 3)se. 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 just below the waterline. He hears the cmwji9*x/xs 9 ii41;f;iwg toi,m3 olecho 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 significasi4i w/mioo1t;mlwg3ic 9 9if;j*,xx ntly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wael/3i/ :/h;t adho41c (nyrx f(namnyvelengths 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 just above a school of tuna2vk4-y tu tq5f2g2e+t.zx esr on a foggy day. Without war2te4xf 2e 2.k zqurt-yvts +g5ning, 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 tow,lwyh3, ;5ag o2h2j0asmrjmp of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the ,omwrwhj0 2g,5l majsay;32h cliff?    m

  A person, with his ear to the g5)s zt q(8rffvk5tc4qround, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concre5f8 4tq 5)ftv srqz(kcte, 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 distance by the “5-seconcvbsn6v/i h-b39g jb6 d rule” for estimatinb3ijc 9hsg6- vb/bn6v g 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 the pain level of 12)dagu z9aypc*6ts;sr ss97xo )b5:qzt:v wk +0 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levnf0,lw w6auh-el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a ngp;p c2 1vqxwm ,*fq,-rh;htsound level of 95 dB when fired simultaneously at a certain place, what will be thw,-gr qn;f t ;,xh2p*cqm hvp1e sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally n.jfqy.1ddf 9u h pq7g.oisy jet engines is experiencing a sound level bordering on pain, g. hfqy.dfpq7 jd.19 u120 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-noise r(jy,+obtosy d 5bw7k*qa+ 8nn atio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal a+8( ,s7j b*ndoyb+noq5wa kyt nd the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaki:g6qr+j ck+gqer gq 4.ng in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mogqk re+ g.qqcjgr6+: 4uth. $\approx$    $ \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 slfyr,lvq d59 9trikes 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 W, while :yg gus1q/-n r,0nbfpthe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in:uqg0pnfsnyb/1 -, g r 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, a dB meter registered 130 dB when placed 2.8 m in front of a hn n4kc/+ t7toloudspeaker on the stag h7n+n /ottk4ce.
(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 typicallykckh 2 nb0xehx*m20jj7mnkjac.ct 5p19 e*w3 detect a difference in sound level of 2.0 dB. What is the ratio w15a7tj 9bcnpm h*0c mxxkje3 cke.2h*n0 k2jof 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 tp43m7bs3 k9nl5dcwz fripled, (a) by what factor will the intensity increase? I 3pcb9l ndz43fk7s5 wmncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa 8irsi fu.qi1u,/j4ib cement amplitudes, but one has twice the frequency of the other. What is the ratio of tf 8b ,4s/.irji u1iiquheir intensities?   

  What would be the sound level (in dB9b6j br ybth 7y y3qkzc(m8wtnyg9:59) of a sound wave in air that corresponds to a displacement amplitude of vibrating ah6 bjy8ckb y:gwqt9 3by 9t(y9nr7m z5ir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100- kc6*ul vwt1 lf4nc-92uzb8lc Hz tone that has a 50-dB sound level? (See *l-nz vkc2 buul8fcw6 t91cl4Fig. 12–6.)    dB

What are the lowest and highest freil-ai,6o .yms quencies that an ear can detect when the sound level is 30 i-6,ysmoa.il dB? (See Fig. 12–6.)

  Your auditory system can accommodahjgyx 9xrx kn5dj8yk0 /mx *87te a huge range of sound levels. What is the ratio of highes789x* nxmyxj8yxkk h/ g5drj0t 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 violiv1py+d vef 848vk jb0ziep e:1n has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension musivee0vjv8p kz:ped18 1b4f + yt the string be placed?    N

  An organ pipe is 112 cm long. What are the fun4v,xnuypgs 40:khl/ t damental and first three audible overg,x k:4n/uhl0 vsy4p ttones 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 thelwk * 96,rvzk5ai. b:bssd;t w top of an empty soda bottle thatb9 z; l.krwtaws,ki* dvb6 s:5 is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spax qj 3k ,0r2xj7fdwv2pnning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengt0 x7 2v rjfpqxw2,j3dkhs of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency ofwrjci7 g+z1 r1 t)ja5b 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its og1b)zrj+ iw1r7a5j tcriginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle 1*avz2 cuca2r C (330 2vcuaa c2* rz1Hz).
(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 emits mr)dsp:y1b8 fgvu 4/w -r giq2tiddle C (262 Hz) when the temperature iiq dbp-8g t vr2r1gu/)f:4wyss 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at gc*+qo:,yi,rw qx if /20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutebxb+ 1c0qpj(zqfr1 o : in Example 12–10 should the hole be that must be uncovered to play D above mif 1 (ocj:xrp10bq+qb zddle 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 ca +ar bynmkgb*r3d252sn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies ingb3a k rmrdn5s+22y*b between. (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 reso mr*bk z:*k;mhnates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whr:k; bhz*m k*mat 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 27;ol tf:,tdnxs 5lwm$^{\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 2.1rpn09a e* zea:4-m-long organ pn9p0e r*aea:z ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appro ln1kmp8:my4w pi svzk3urm*x1 k,s/;ximately 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 stay13x1luvnpk; sr/* smp8mk4m:,kiwz nding 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 trwfc+ 0t *1adg ico:jm)ying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other str: 0fi tm+*1joc) wdcaging? ±    Hz

  What is the beat frequency if middle C (262 Hz) f k ud8ocig6 a0k kptyqyy+7+24:ke8wand $C^＃$ (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 *78;kog bz+j*jdj te2x ,nvxx23.5 kHz, while another (brand X) operates at an unko8*,gxdzvxjj 7xbejn2 *+ t;known 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 brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunin-fs tjg4)tzq q8 ez)dt.1 wf9avsk(k. g fork and 9 beats/s when sounded 9t d vfq)(fst)z.azw .1jks g8-qt4kewith 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 tension56 9b:d jfy0-bvq.pvo,lsz oc in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings.v5- boj:pbo0d6y 9vsqzfl,c are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes ii 8eg0rd/)5koz9u rw9tn-o4v) h ahbeach try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 vrt4o5wgnh) z i9iod8/h 9erb-ua)k 0 $^{\circ} $ C?    beats/sec

  You have three tuning fork 1 fdizej 2-r4pqgc3o7s, 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 arjiefpd4c 3 72go-z1qre 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 speake;9 l3 .eyoqb(odocwn/r and 3.50 m f 9; .n3dl ob(c/woeyqorom 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 Hz, but a piano tuner hbt kkecf3te s(bk+: ,t,ks: 6years three beats every 2.0 s when they are played together. (a) If one is vibratingsbkt,tbk,:c3e+ ft :(6ekk ys 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 ax3fatq9z e ,1wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heardatexqa 31fz9, ? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirozmr8gayv121*wi f/r+j*x aken is 1550 Hz when at rest. What frequency do you detect ifg*vw/1ra1 f ixa j8*2k+o zrym 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 xiam(oi emk0c0w,/t; frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed m(k 0/xc0eamw i;t,ioof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift inyofl:ccc+f 1v b :u)hwu yya/h0)w l.ba;.jy5 frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freque: cu.)o1ab;ly0/wj: yuyvfa cyc5h+fw.h )blncies 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 zjehmqg:80i 8l,vdj427y z bg is 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 hol4h0 z28y,b q7igvjmdzegj:8 rns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 k denq2v :xkg9lr96u7o Hz and receives them returnedlr729q v9 nux deko:g6 from an object 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 As it flies, the bat emitstg oga9 2 yzty9b3h1x7b6at, m an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hg7 az2 h6yxgt9tt 9o,bym1b3aear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat t6roh fdeb ;ec(amw*)hv,ks ;/rain car at a frequen ce6d,hsm;rv/wk(h f) ;eao*bcy 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 at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ul.z i: z(ufz guj;34xbrtrasound 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 zzgui b(.zur3 x: f4;jthe expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequenu1/m 9mr ;)aryfkkj5 kzwh2j5cy $2.25 \times10^{ 6}$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 win *rwtz +1iky u95mmq8rd velocity is 12 m/s from the norr 15m9m *tkuz+8y wiqrth, what 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*2y q8k,m wcvf moving 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)fo 0 c-u18hduz What is the angle the shock wave makes with the directiou1 cfuz -8dho0n 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 atmosphe:kt/mf 0jzz b6re of a planet where the speed of sound is only about 35 m/k /m0f:z6tjbz s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes d-+-f(h torfm the ocean. Determine the shock wave anglefdtmf (- -or+h it 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 t 9,dch*r .o;)kt9p- ;qq 6jhznull df$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead 4p o+b.x am+u.1qzcz mand see a plane exactly 1.5 km above the ground flying faster than the 1.o+b.q 4+ xzpzmmaucspeed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that 11g)w kj tbbltpa *8g7sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (iwgkbtlt17 *p)jb1ag8 n fresh water)?    s

  Approximately how many octaves are there in the human audible rm( ,mbsdh4iexl bv643, 00p nryeq l4aange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sycwcz+ h2cyu( cz94 6krmphony. It consists of many plastic pipes of various le(9zk cyrz4h+ cc c62uwngths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threwoh,fo 7l-p tjww0 s d9lhk;)7shold of human hearingdw7k, lhs97l-)w;ow0ftj ohp (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound a9-9:wp5a hxy;wqjr ph re heard simultaneouslhjyw h-a q;99:5wprpxy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the ope(+qi(.ya oqvsn, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates .+iqy so(q( avequally in all directions?    W

  A stereo amplifier is rated at 1-df *5jnsa ,ys8nw s)p50 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in yfp8s) nja sdw n,s*-5watts at 15 kHz?    dB

  Workers around jet aircraft typ+kpe tlplt8k7k+ s 111nx3ez rically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and thatt11k8t7lk1ze ns xpl3+krpe + 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 systeoz :db:n* o.z nyvndm*;a t+d(tc12a rms, 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 eu dq8-y 3t uy1vxjj8v1n2 qf: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 fqhi *c rti01c;ixed points with a fundamental frequency of 440 Hz and a massh1*ccr0qi;it 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 f 2*ra rqhy-xt.s :+nrlilled 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 tola -:+rr xqh.y*tsr2n 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 2pp iykw1pd0uo-*av52.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental moipky 5d1* -oauvpp0 2wde) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wafl mc .99w*rkqhtqiy-* c8,qs s observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from t:) -5dgfi tk:r9x umxkrrd7 t+ mm33mewo sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about adet-t+m)k3kmf d rr9x5gr m3i7x u:m:nd 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 traiv5hby )tofemj0, ,pip nh; nou;;j83un is stationary. The conductor on the stationary train hears a 3.0-Hz beat freqo 0;i;boj,5vthp;jfm3,)pun8hu e ny uency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you ip:09l3hp o wp*( fevhq(res6awyvaigl 7,-3r s 538 Hz. After it passv v 9, 3gshlo(a0aie y q-f6r7wh3(r: eppwl*pes 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 thw00kw zzff71 id:32cy sgdx 2be speed of cars just by listening to the difference in pitch of the engine noise between approaw0xd02bkgy31zs wczf7 :d i2fching 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, soundingnlxj e9mz9,j ohu0naa h--e-1 together, produce a beat frequency of 11 Hz. The shorter one,ux-90j -n9lzhh1oa-n ja m ee is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves i quarm /t;3j9-hp3tbpast 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 have passed him, arbm3uhq tp t;aji-/93 t C?

  If the velocity of blood flow7h5pjmw o-*k d 3;qraw in the aorta is normally about 0.32 m/s what beat frequency would you expect ip*7hwrj-oad w 3 qmk5;f 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s q2ena)*x3z8:n;byivj-i g +fn-pxc vwhile 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 reflects off the mot+c)nzxn-;iv*n2fex y j8 iaqb:v3 p-gh?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a motr5yei9;.ms e kh. The pulses are approximately 70.0 ms my5kir e;. se9apart, 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. 12–38) was once used to send signa, ww /.fn oibw p47hvii8kkv:*y3zl5p; 5v hqals 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 overtonv/ hn*5;p7i vzokkwa i8,wbl:ph 35 4qvyif.wes 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 stnz3 zw5j-mnw t/h75l eereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the5 ww3en -m 7th/jzlzn5 fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” ig 4qz6x,kz/fvl+z* msnvolves 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, ringing so+*,lg/x q4vz6 zmfskzund. 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 heari-e;jlp91 /i kfojb;rl ng for the human ear at a frequency of aboutj p1 l f/jobe-;rkl;i9 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 Macq62m v4pww8ph h 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes dir468 qwphv2mp wectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 drm:99iu3kf p$^{\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