What is the evidence that sound tra 8xvu36c8rqkuvels as a wave?

What is the evidence tzz-i :m.m*xm ts6 wqn8hat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string tex 5wx*ct0f6; hqph6uo 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 (Figp*cew0hth6 fqx u6x;5. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes 5c5hilr j5bkfpynr*t dgk j9sc2hz0 ) 7t,s 8/from air into water, do you expect the frequency or wavelength to changr*cbh/kty5tk7c0 snd2sf5 8pji hz9,ljg r5)e?

What evidence can you give that the speed of sound in air does not depek3t .sx(tmcs2 nd significantly 3( mk.xc ts2ston frequency?

The voice of a person who has inhaled helium sounds very high-pitc je/ s/o2gi0h yne1.cthed. Why?

How will the air temperature in a room affect the pitch of organ3.;6:dqn myyls t f/ 98rpxprn pipes?

Explain how a tube might be u+ 2j eges92bgjsed as a filter to reduce the amplitude of sounds in various frequency ranges. (An examplebe29 gg j2s+ej is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c0(dzq,g5t *5qo emlz9 bip)rmloser together as you move up the fingerboard toward thqze p0 ,(md ogl 5qiztr*)5mb9e bridge?

A noisy truck approactp, n3t4cz*a6 hc,yelhes you from behind a building. Initially you hear it but cannot see it. When it emerges an6h ptzy,c,n t*ca3l 4ed you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatst 6,ovvv eo ,n0u;+flc can be said to be due to “interfere,60c,+oenul;fv tovv nce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the point v4k8qfdpcd.x .g +3vns D and C (where destructive and constructive interference occur) move farther apart or closer togethe.cpk+n48vddvfgx 3 . qr?

Traditional methods of protecting the hearinqu6dvlom: 7ld +y:-imp-o1ki g of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then fed+yqp1iil- o-uv6 m::l dmko7eds 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 sunut/v, m c:ut fe59o5hown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are theu ov:t,95ufmc5 /nt ue two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and ypfjh2/+h ; -ku1/ s zl np(i8ivkk4nfobserver move in the same direction, with the same velk ni-uv f2(hhys1fn/8p li 4;+k zj/kpocity? Explain.

If a wind is blowing, will this alter the frequenw/mtd 17d10:ki ob yeccy of the sound heard by a person at rest with respect to the sourwet:01kcd ym/7b1d i oce? Is the wavelength or velocity changed?

Figure 12–32 shows varim9dq- xqy1v9 aous positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound y mdxv19 q9aq-of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the u5;oo jjdj ets e8ys4q-f/w63echo 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 l-4wfdjqsy 8/;t6sjej e 5uoo3 ake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just ho8 5luqn)1bj8)km ovbelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2b1ju8l5 mvno8hq ko) ).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 wavelengths3 x.pkyr6r -kn 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;/ hnix02 eeyr school of tuna on a foggy day. 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)x ier;2y 0ehn/ by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. T uf::rl4poj k1.rhn6a he splash it makes when striking the water below is heard 3.5 uo: ajk6 .:1nrhlfp4r s later. How high is the cliff?    m

  A person, with his ear to the ground, sszh jo8v(rwf .oj frw2)kl vh:;3nk;3ees a huge stone strike the concrete pavement. A momhkz).jl;wokr2 j nsf r (o3w8v:f 3v;hent later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance b)k4weh3bvfpv;tx6z : y the “5-second rule” for estimating the wtz)fb 3vh :6pv;k 4xedistance 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 vl j tr*y0gs-lp72w9 wj;ytqk-d:u;pat the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of ag*u(ukc*8ag8 +wklk,;pk gst sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sopx4gr:w6+ngwoh7; g9qzh n5q und level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, nozpq4 967o:hhqwgg5n ; +g xnrwt dB’s.]    dB

  A person standing a certain distance frjvgy6 g, w*t)eom an airplane with four equally noisy jet engines is expe)e6w*,ggt vyj riencing 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: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBdrd7na w73t*embw0 d 6, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noisebwdddw37me*6rn07 ta for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ou:cm mx6wfnn q d2;gl h(zeo.((tput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouthewcz lxm6.fmd2nhgqn (o (; :(. $\approx$    $ \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 eard9jv1ge0 xmgw,/,h dp,docw0brum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amply/st x,qbxy/d0 g.1uw ifier 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 cond suyqx gb/0y.w,/1tx nected 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 o vux1sxm 8hf2;)rxv9af a loudspeaker on the s2m)a;h vr8f1 xu9vsxxtage.
(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(l+w-a35+p oisbnl -q: dyzui difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amoun-z3l +ub-+pn qosii 5:ya(d lwt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is b88hte/ r6lqz5sl2f2emj)sl tripled, (a) by what factor will the intensity i l/fzl2b m 2)elq68seth 8jsr5ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal disrycg5jd sq +40placement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities? cdj4+yg0q5sr   

  What would be the sound level (in dB) of a sound wavuk4dbk l2 s.r/n ec/.ie in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300cen sil./. budk/k2r4 Hz?    dB

  A 6000-Hz tone must have what i-pcjdw4+v r5 7h)mbg sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12bhc -dj4r +5mp )gv7wi–6.)    dB

What are the lowest and highest frequencies that4(1i wmq3ask 7h 3mpli an ear can detect when the sound level i h4q3( mlwp1sk7i3mai s 30 dB? (See Fig. 12–6.)

  Your auditory system can ac6hj14 obm c2xds7 4ji cb-e6cvcommodate a huge range of sound levels. What is the ratio of highest to lowest inb7mj12ixdc4o eb6 h 4svjc6-ctensity 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 fun6n 4l: g 8h ec snkcgta)-.cgdpap(,r7damental frequency of 440 Hz. The length of the vibrating portion sdlghr 6-t4ca7ppeagcc n . :g)k(n,8is 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 fun id)b;5t w3cw7pgv yr q*s0-dxdamental and first three audible ov 5tdcip3g0v* x7wr dq-b;)sywertones 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 )2+ fc/2r blcptq vrpjp(d9(vfrom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tub(rtlcb pr) pv+ q 92(/jcdfpv2e?    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 s(q:a. +i2i d :wt5pfrb fj,ggdpanning the range of human hearin(d + qggjtr,5iwf2dp:i :fb.ag (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonicdt1i*canh ia,;i29 xz . What will be its fundamental frequency if it is fingered at a length of only 60% of its origi ai d9 *t;,haxcii1nz2nal length?   Hz

  An unfingered guitar string is 0.73 m lon(md0zsr+yqpm;, , ffcg and is tuned to play E above middle Cy;m ,pfc(m0 +rfzs, dq (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits m8wmta :2 0s yr,xaalrb1zh 47biddle C (262 Hz) when the temperatura48a:ramrs,b2hwx07 l ytz b1 e is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune ragm ,e0qz:z *at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examp-c 28: mxaoxx a vx-uz4t6x(hyle 12–10 should the hole be that must be uncovered to play D above: x24xvaco x6u8(htz-xyx -am middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 615d:iqcm8ye m,cot he.e5 5zw(6 Hz, but not at any other frequencies in between. (a) Show why this is an op8 ct, im:emy cd55oe5h w(zeq.en 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 et6 ow6mj 0e-uxtz9 ,mi5 krd-nnds. It resonates at two successive harmonics of frequenciesm,5eiwn td t- jk69-0u6zmor x 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 aefqh b0g)u u19xa6 d2$^{\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 range9 u:yexh5t yf) ikhh,obhr.2, for a 2.14-m-long organ pipe kh fy:bh2)t ,h.rhuy e,9x5oiat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximate;9g s qoh1hcd-ly 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your a- odshq;9 h1cgnswer 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 tryi/x8w+jl,wuv7lw00 w ald ogw;/f; wrfng to adjust two strings, one of which is sounding 440 Hz. How fl,ww wwjw v0dof;87/r 0wu;/l glxa+far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Cnz0l (1u-foo2j hg)-aj0d2 fwbc (aff8b+dvi (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 opety kg g,hz5cb 3+dlwoi3u95r0rates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be hea ob 5u3w i+93drycgthz5g, k0lrd 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 tuning fork p5d(c ..xe*zqm3 kz ; ex+rsr-tec6b yand 9 beats/s when sounded with a 355-Hz tuning for. r xexzb- t+y6k35(d cseze.pq*c;rmk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned toqz.ucyiap1z ::38h6f5sj 40i lanifq the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.hffji1z ic3y zsq.a 5uia6:nql80 p:4]    Hz

  How many beats will be heard if twqd6zorp5 )1, th8 ugqwo identical flutes each try to play middle C (26ho1)qugp z ,w56td 8qr2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork wsnmv eo//j3q(eiu 96 B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When3 6wqi jueves/ o(/n9m B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C 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 sdl n)av 6ch-)x/fo tr.peaker and 3.50 m from the ott) )nxaflr6 v-hdo /.cher.
(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 vibr )-o4 nkunyny4ating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must bnn4yo4 uy)n- ke 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 wakuu,/kfn8k t9velengths 2.64 m and 2.76 m in air. How many beats per second willukn8f9k,/ utk be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whenj2sjrt5fw (lf1q.of1 pyw4 5 x at rest. What frequency do you detect if you move with a speed of 304 r(t1of5fxyw qlsj5w 2fp 1j. m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fir+-)q(ydv ndkze a4st*e engine whose siren emits at 1550 Hn4 td +d)*-kezq aysv(z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz s,j0r btpl(uq7bti )49q9 qn4zi/ly ,-n fctxqource is moving toward you at 15 m/slt0 7rq 9nxj4l/4q,cu-t9,bbi nqty (z)iqpf 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 equippeycc3zx.-30h05gxpztychq s 7d with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What.c3h-5zyqzxx3 hy 7 csct00p g is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anl;:bfm le78fg s (4pacn0 mr9dd receives them returned from an object moving directly away from it at 25 m/s What is the receivepgn0m;caf (7d 9l:sf mlb48erd sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the ba;7guk;nkt) uygt+5g wt emits an ultrasonic sound wave with frequency 30.0 kHz. kw5)u;t ugynkg7g +;tWhat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppl1/)ikstg9k z6uz z k9ler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a secondkt9 kiu/z sz9lk)z6g1 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 ultrasougi2ge4,2bn-.c m api /4eqbs qnd 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 15mcbe, iqe/ .4- gspbqi2g4n a240 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 using ultrasonic waves/dicl-,uk16( mw ew6ykt:r vp 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 bq plm:/nx38q is 12 m/s from the nortqp3mq bx8l/: nh, 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 moving on land wo7 ab(dmj ) yf5lyfy:x f;.5jif 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 (4 .ct,++eg. supzp+jdnl vew(a) What is the angle the shock wave makes with the direction ,e.pe(.+ ldwv n+ jctpsgz4+uof 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 speekhy+6-k 7q wood of sound is onh o -kq+ykow76ly about 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 travelingxtkxgd9qr 0 *: ;zdbml/c 8f8t 8500 m/s strikes the ocean. Determine the shock wave angle g xft; dxbmz89lq tdr80*:k/cit 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 i *,d2baegtg ia;ir /4$/theta$ 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 km abo.fgh/n01f y r/*d ttr2kueq5e ve the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dfhn5 *re. kg1ytr/et 2/df0 uqistance 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 s*:dy-l8e 5qjosyp 6 ydsyg1k8 onar device 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 yd 8oq:ej6sp81sd* yyk- gyl5is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the3 qh8vt0-,wjtf:-)ffybdn0p8c5vo2 fdfkf t human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists teb4na( gz r;b sj*)hueb0;q w.j /mi,of many plasti.u )qh*b;;jriz, /nsb40t (eejag mbwc pipes of various lengths, 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 da)pxcfsi6 v2508a j9i lwv ,tto the threshold of human hearing (0 dB). What will be wtvacxp9vl i d5ja8s,0)26fi the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an r4d y, dpy yzsqt-108s82-dB sound and an 87-dB sound are heard simulta pst81d0yz4ys, dr-yqneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,1ha myy 1,o)cc is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dico1m, 1 cyyah)rections?    W

  A stereo amplifier is rated at 150 W output ng * (v pyv2f03eszo-lat 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powerv(p-3e f zylsovg0*n2 output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviceq4 4j0s yajf:+zdog3p4 4 behus over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2+u:q4pja4g yzd 3o4h4j sfe0b .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, the l,, waa(hrmru+q ;xv2gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a dicts smtxq 600/ u9m;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 witiir-76n lf:zdh a fundamental frequency of 44if rl7: -6idnz0 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 fillw 2 ;qy ywarh1xa( d j-j.xsr8s-,kg2ved 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 0.395 m. What is the frequency of the tunings,;wva 8r k-x .y1j 2dyrwsq(2xg a-hj fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is ope*2vb) n)c o*rh+hgznen at one end and also 75 cm long. How much tension should be zhv) o2c) gb+re*hn*nin 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 resonajs. a4ndm2es,ic6 5sgyy7 j6gte 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 s8)ow8h) ojbqz mp 9y.r.4bk otwo sources. The sound is loudest at points equidistant from the two sources. )b8o.oybw8.k4 j)pqos zmh9r 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 sound?   Hz

  Two trains emit 424-Hz whistl g v/l1. o/go.ai7uewtes. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train app1o./ aiglgo w/ue.7vtroaches. What is the speed of the moving train?   m/s

  The frequency of a steam train th+ .u(tzcfq9 whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 4c.+ft(q9ht z u86 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 lis8v dumi -22wtskzis 13tening to the difference in pitch of the engine noise between approaching and receding cars.iv u2d3t-2 1swk8m zis Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat fra,8gif lswwhxtwea8shb )09) r9 x 0k5equency of 11 Hz. The shorter one is 2.40 m long. How long is the oghx9 )8l08xhi5aefb),0sarwswk t 9 wther?    m

Two loudspeakers are at opposite ends xbucm sw)+6xzbs44 6i of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frewsx4x iu)m 4z6csbb+ 6quencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in )j. g(jjl t7lp7a v2nkthe aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50 7.)7jpjtl agv(nk jl2-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 while the moth is flyin9+qb g xyv(gi4g 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 af+v(9g4 bigyqx ter that wave reflects off the moth?    kHz

  A bat emits a series of high f,sco fhuvyya )/:8;b srequency 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 s:;/ ,ac)sbu8fyovhymoth 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 toby2x f8m3 /c, vxbox,i send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenho2c v,oy8b xf/m3bx xi,rn 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 be compromised by the presence of stand8 ,xd5g3c5 n:hv8x 3eglb)hux:tizz ying waves, which can zhy 3vh:bu:5 xe tx38xlig8zgn d5,c) cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invol -kod3fwi dxo*ttb,48ves a long, slender aluminum rod held in the hand near the rod’s midpoint. The k,odx3fb*d8io4-w tt 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 threshogjpk:or s ug7:,b co1fa o*xod,k11k2ld of hearing for the human ear at a frequency of about 1000 Hz i1os1pc akbj,7 :r ook:fxu,dg*1okg 2s $I_0$ = $1 \times10^{12 } W / m^2$ 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 sguqzp e:6;aq-ab:g; g pn*-iuonic boom 1.5 min after the planq;-b ggug6q-anz:;: *aeup pie passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is heu*m1/1 mpz;cjm/8k ayy 1lj 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h