What is the evidence that sound trave99msz7z(ae ig 06-uhnfl*sesls as a wave?

What is the evidence that sound is a for.*d(,c cug jhbm of energy?

Children sometimes play witjsz0431d-8p sx fuqend g7zp0h a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a chi1f-d pegszjx 8d 7upn4sz30q0 ld speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from0 -e fjtpzap0/ air into water, do you expect the frequency or wavelength to f-0 /p0pz jtaechange?

What evidence can you give that the speed of sound in air does +k0lmqs6jq3f not depend significantly on f m qfq6kj0l3s+requency?

The voice of a person who has d,t2iyt uvm 25inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect n1us+bbljtn/ (p6rufx p :0c5 the pitch of organ pipes?

Explain how a tube might be u0cfp 65 r7n/ypc m.njzsed as a filter to reduce the amplitude of sounds in various fr 7nc5mrz6nj f p/.yc0pequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as ytko 7mis :4z/6x y-qf-ucnkr8 ou move up the fingerboactqs :konzr-4ixm -u8 6/ fyk7rd toward the bridge?

A noisy truck approaches you from behiopj68s-uf el3 nn 5;yayr.4djnd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-fp.aly nfn d86j43e5 uo rjs-y;requency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferencm,atb;sa pklx 8j .,gj/nwhl3r 2-yi9e in space,” whereas beats can be said to be due to,8 am3kbjp/nwt.-hx l yi2l,s;r gja9 “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poine8-.:kft +pgl pb9qpjts D and C (where destruc l bq8.pf -e:pkg+9jpttive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in arn3 6g17ruvph oeas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce thpnu 1 or7g63vhe sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of asi(cj0;2c:-r natxklf a superposition of two sound waves with slightly different frr;:ajctfik0(n- x lc2equencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move /t : i9kxlvsdfxn4y37in the same direction, with the same velocity? Explain.ylsfnx /9xvid3: 7 kt4

If a wind is blowing, will this alter the frequency of the sound heard by a //uio n7e vg.p/i,5w sqpu wh*person at rest with respect to the source? 7oh/ve/s5,i g*w/uq pwpui n .Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on ebz2:q q15i ;d0 g( 6hem.t,xcyuaqmga swing. A monitor is blowing a whistle in front of eq x(b: me20gq5qcz.; ihudamy,6gt 1the 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.

  A hiker determines the length of a lake byq/,1 uj:eairt-k j5ji listening for the echo of her shout reflected by a cliff at the far end k,qj1i-j eu:5 ajrt/i of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the si z2opz,9i ic3t9w,v pfde of his ship just below the waterline. He hears the echo of the sound reflected from the oceanvi3,c9pwzz fo ,i9t2p 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a 1mds ytd2j p9ofs ((jf5yc08jsix /-ft 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 ;lz 6gfq;rr4 3pgvqp d3fr m5,just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awarf3zgl 4fmr;pdrvq 3 5p6;q,gy (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*c*gues5vu,k i++0 bitx 8bbd of a cliff. The splash it makes when striking the water belo *gt, s+e85k biuvidbc+x0 bu*w is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huj6x76miy srfo - +lz.kge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels if6 ro-67im+z.sy lkxjn 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 urt muba8g:m24+qs6w*-oep kmile of distance by the “5-second rule” for estimating the distance from a ligho*q k-2 r+emp atmu6s:u8bg4w tning 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 120 du -5v( ds2k ueamnx0 /4xtx+wlB?    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 /vcdyenha5 6es t)iz41ws i1 .whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firedia*nszt-8 .p j ,vnh 6p0ul wxt2r34sw simultaneously at a certain place, what will be the sound level if only one is exploded?,nt*6xtsra 2nzjl0iwph psw4 u.-v8 3 [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallyc44akaam rrk a x5gx eb:9(+:k noisy jet engines is experiencing a sound level bordering k:4km aaexkg b9x( 45rcar+a: 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 a4/ycusl h9e sd,ly6 (l signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of 6 lec(lusd9s y/hy,l4intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power o jo( l,xkzu5t6utput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere celxu5tk6 o j(,zntered 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 striker .awp a )8xbaouo72;gs 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 ap7.v bc7 u-yhl)tb qx:t 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poin)77:ulqcv hb-pt yx b.t 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 whenfh6:pt)/izx7 rf/ij g placed 2.8 m in front of a loudspea 7xzp6//jrit gf)fhi:ker on 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 dp3 lkl*y s4q)oz 8g,bpifference in sound level of 2.0 dB. What is the ratio of the amplitudes gq4kp*yos)83p l,b lz 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 ipib2rct0c2: antensity increase? Increai:2p c0ctbr 2ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenuyg:jl3to6f:fc l f1(t amplitudes, but one has twice the frequency of the other. What is the j6 fouc:1 (lgf3tyfl: ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that c7h,ydp 4i- hj41nypyfu2 f go(orresponds to a displacement amplitude of vibrating air-4yf 2 j(h 1fn g7,dy4hppiuyo molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud a) whuo(h)rt22rt q et)s a 100-Hz tone that has a 50-dB sound level? ( w)teuothr)t2 )r q(2hSee Fig. 12–6.)    dB

What are the lowest and highest frequenc/bxec/; t 2nkw1n/kzjv 1c /hbies that an ear can detect when the sound level is 30cwcjk x1n// 2/1nkb;zv eth/b dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rang5x c.mau- mt,re of sound levels. What is the ratio ,um5xcma.r-t of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has akyc.ah* jj +avi.,boc- 2*dvi fundamental frequency of 440 Hz. The length of the vibrating portion i.d.2 y*jj- oiv,*vcb+ac iakhs 32 cm, 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 first three audible oy5ngup x5al; zo)81 jhvertones if the pipe is jgax)l phoyu8z;15 5n
(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 th 2luhi9n)cz5 fe top of an empty soda bottle that is 18 cm deep, if you assumed l 92nzch5 i)ufit 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 pibkjln274l1 (gd)v kt mpes spanning the range of human hearing (20 Hz to 20 kHz), what would be the kj2d nb(47mvgl) t1lkrange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third ha+9ht(:zp3exsvhci t * rmonic. What will be its fundamental frequency if it is fingered at a lee tz+xh(c3*p 9h:sti vngth of only 60% of its original length?   Hz

  An unfingered guitar string is 0./sy ups+4xg lx hr++r9jbt:.bk.+zfp73 m long and is tuned to play E above middle C (prh pkj4+sts.9l+ubzx/:r +yb+x g. f330 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 pipe that emits middle C (26f1s;-n+-2jsw ju z fni2 Hz) when the temperatu+ isfun sw--12j fjz;nre 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 at 2 f5vwtzoo-6fnjl 9 75c0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o 2rwkqaiisxa6m::/4mm d/v x0f the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at xii6 m qa/kwr20sva4mx: :/md 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 pih)b: oy d w(b(pqt6qz.pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (dq t hz wb:.obpy(q)(6a) 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 -u/mqk gay6,1egyv:p two successive harmonics of frequencies 275 Hz and 330 Hz. What ia/:- gu kepv gq6my,y1s
(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 hyi*x84t9 nc 5,libhf$^{\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 jx1b3 dofz sgtgu,22(g +ad s0a 2.14-m-long organ pi2gj2 g3a zusgs +tfx1d0(o db,pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long..nh:j71xuha 1 ymiat+k(j t6l 6mjcu; 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 u;(cj6mha ta711 nkihmu 6xy jt+:j.l 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 clwiac16dq552 ;z w-owzko 3gs when trying to adjust two strings, one of which is sounding 4- d62 5q1o wiwgo3;w cazl5kzc40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequj+liq5x6er1 znif/ j: ency 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) operateqh2h;uz 3-k9r e vdflwss8,u8s 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 pl9, rhq- l8uskw8se2;vu 3fzdh ayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded withx95i49 xdvp e )2wm*rmls dbd9 (x+eim a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is th ri+ x9 v5dm2d9wimelpeb(m*xds)94 xe vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensid;:26 ozj tv/p5jp p 5tmd*jidon in one string is then decreased by 2.0%. Wh5izmd vj j o5dp d/t62;pjp:t*at 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 try t8*p q4a; salf:)yjpi.h 8dp ,lghfn(u o play middle C (262 Hz), but one is at 5.0*fp(ag, yud.njh8ih pq 4pa:fs;8l)l°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuninghd 05xlu*vbm / f b/q1v-1x2tqrzf6en 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 are sounded together x t/rqn5fvdx h1m-q 2ubfelv60/b z*1, 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 speaker and3nws, u )8ysh2+ aozbb 3.50 m fr+ 8, h)2oysabu3zwnb som 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 supjo(,+ah/* kkq ie-sgq2j7 8 3 owamvypposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played toget,kmw( pgo*vaj/i+8sa-y qh 2ejq7o3 k her. (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 2.6vz0 0tai pl b:n*ll-s76 m in air. How many beats per second wi:z6*i -al n l00vslbtpll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain pk0.1tl uuxt69c9mwj- e2vvxxpyh s051q) ta fire engine’s siren is 1550 Hz when at rest. What frequency5y)lx6.mthe xutwutk -pj 99vcp0s0 21xa vq1 do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you rg;66yaal xtg kx2i 8.detect if a fire engine whose siren emits at 1550x;a2x r8t .y ig6ka6lg Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifww.b43a w3rjaw nhvq.4 m)fi;t in frequency if a 2000-Hz source is moving toward you at 15 m/s br33.4).4aiq; wawjw wfm vnh versus you moving 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 si2.2+x j oggalbj 4j+vyngle frequency horn. When one 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 horns emit?g v+jga +lyob 22x4.jj Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason j rhd1keoywy2v,x 5*8ic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound w2 rh*y e8x5jyv k,1odfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s Aoa 6zoxz6a m 7z1m/.cvs it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freqz./ m1mvxooz z 7ac66auency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originasum f ;()zoy3d(kgzbjb*qy5 3ybn (5 ml Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identicn)*q(ybyg zjbm5bzoyd 53((fs ;m3ukal 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 ultrasound waves to measure bloo s* fz6li7xp-dd-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 freq xpi *f6dslz-7uency 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 jjz a8/h)zu/j 9)r3(i )u;e mwt:zuocvryp 9 uof 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 is 12j7 k:-g8:sm, kp( envqpsgr.h m/s from the north, what frequency will observers hear who are loc mvpeg(:ssq.pnj:grk8h ,k -7ated, 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 landashmby :j: +kbp;nj2 c9j 6aj7 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 yq(cn1r o ,s)wzz 8nn/310 m/s (a) What is the angle the shock wave makes with the direction of1wy/,rn(czn zn) 8sqo 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 atmospherehwcd3pc /5(k4k 1b9 wh2oiakk of a planet where the speed of sound is only abo3cd h9wp5/kwoa41hk2bci(k kut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave:abr:kj 3ler - *s8o:ihuj9t g angle it p3a gij: rt *sh8: jl9-:beurkoroduces
(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 ox( uw)o :cu/w$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 ix jaywy.j-51l6 0leghs8 wq)km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has trav0 )i xw-lyhjs.w a5j6e18g qlyeled 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 dve ,l7rlcdlt*3r 7dz :evice that sends 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 th 7,dvr drectllzl :37*e minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human au 9kg4 zo9eynf sak p3q :xsu2ags5oi0yq0-7)sdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. I3/emdp n3d yn9 ykwx36t consists of many plastic pipes of various lengths, which are open on bot/yd y 9d33em3xnwpk n6h 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 ) v b4me-slolah 01q9ti1o5d vperson makes a sound close to the threshold of human hearing (0 dB). What wibv )o1 0e4svitdmoq5-la9 1lhll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and lj qg;)2hxm n,an 87-dB sound are heard qxnl ;jm2g)h,simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in dtt 03do,:m( gt umh,fgqrq6)the open, is 105 dB. What is the acoustic power output (W) of the speaker, as6gd3f,udq qot)t,(: g trhmm0 suming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at0 mi+l0 jakq-x 1000 Hz. The power output drops by 1qik0jam -lx0+ 0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectieazw-1 : - rq5tgc+nlqiw:fox)o tf- 8ve devices over their ears. Assume that the sound level of a jet airplane engine, at a di-5woz) wfq- x+1l g:cteao n:r8t-qfistance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems*e*o e.1nwzwwmjyp(,, 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 tu o07xg+/pe7o eld(d vgned 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 point6f64n a jmjh-kev 3o(xt+lab.s with a fundamental frequency of 440 Hz and a mass per unit length o k4mo .3vel6nh 6+(xb-jtjfaa f $6.1 \times10^{-4 }$ 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 vibratione)gtbak 3ag76 h tj/r*axh.f0 -fv7ya above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening 7aj3b67a/hy 0.* h )vttraggxk- ef afto 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 s) x+)m,han2v2 rupq trtring of mass 2.10 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 )nptrv,+2x umhq a) 2ris to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was ei cvhehn66ce+ 5.9nbobserved 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 500–1xl ubz4/ k0sykc-cs12+/qs en000-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 level is minimal at a poincnzsx-1/ lyb 04s k+ck/ s2quet 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 stationa m32x-fqbf4;zl-wl m ery. The conductor on the stationary train hears a 3.0-Hz beat frequenx3w z4m--l m2bqffel ;cy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle a82mfv 4qluk:sm. s :9mb.zp1zl7fh l es it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume hl z kv2q.9e48mbsfusm7lz.f: pl :m1 constant velocity)?    m/s

  At a race track, you canp kwyj54o mpg79 ytu s/):vpyfnql0 ); estimate the speed of cars just by listening 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 gyo5pj;t :v) 4pnf/ 0l supky)m7ywq9 (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, s4 jcsu3 gv.vf3ounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How f .gj v4s3cu3vlong is the other?    m

Two loudspeakers are at opposite ends of a railroad car a3q 7,ri+2qg6i kd1xo m cas1eis 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 iq7c+qok1i3 sx,a2 e m1i6gd ris the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally aboauqri +c-a 9n8n jg49out 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 bloodc99-4j8 n u ga+irnaoq 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 the moth is flying toward thehrlb3mpf0ng :d --m3v bat at speed 5 m/s vh0ld3gm3- :-mfb prn 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?    kHz

  A bat emits a series of high 6j w*xojr9:+ +aqu c5p .aocbvfrequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from o *a 5jp: c+69cqa wo.rvobj+xune chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from i/ ,6z+b8tb /xte zi:l c/spugone Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model iclut 8t/, bz/sp6eg bixz/:+ as an open tube.

  Room acoustics for stere. lf+ nn*xy8xr;xi,pge )rd (fo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressf x,*y +nfi8lrpdr);xxe (.ngure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration,-oym h.m i*pn,f o5cx) called “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 c5 m pn)ifx*,oh-coy.man 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 frequency oncpms( 2*r jt t8ymodwg7o: iz-5hp: :f about 1000 Hz is2y:pz 7tjhpg5*r(cn wstomd 8i om -:: $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic b1t*11rbsf tax oom 1.5 min after the plane passes directly overhead. What is thex bstt1f1ra1 * plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1:9ak h;y,gvg d5 $^{\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