What is the evidence that sound travels m kjq hlcjf;-7l 4.-w(0c)qb 1zeeyilas a wave?

What is the evidence that sound is a aivmv+lb3c6px 4 aw8p 39wb)oform of energy?

Children sometimes play with a homxn(z+- lo0 0ubaxyth6gm s;r1 emade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other camyr+ o 0b-xu0glx;t n6(sz1hup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you exzry. oo4,)oi-p m,bcppect the frequency or wavelength to c).zro,p- i, oy4 pbmochange?

What evidence can you give that the speed of sound in air does not depend shj/o x9ciuyl o0chtp1p/: l-n ro4,tm)9t. csignificantltpcpo n,j- 9y/hrc c: mu ool1l)ts0t4x.ih/9y on frequency?

The voice of a person who has inhaled helium s f;qd.j rv-f 72df;es9sk -kwkounds very high-pitched. Why?

How will the air temperature in a room affect thezc/a va*:(nqwub.nrlk -yj*vfb j 5)3 pitch of organ pipes?

Explain how a tube might be used as a fil oz.v7 n8ywd;g*uhou5ter to reduce the amplitude of sounds in various frequency rang.u owozy;*7dvu 5n 8hges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo*r gdub2r1d7 vser together as you move up the fingerboard toward thed7 v1rr bgu*d2 bridge?

A noisy truck approaches you1z h8ia8lim .j from behind 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 mor.j z1iihal m88e of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inti fo t;hf rt 0w y28x-c-yu9;gu8ahut+erference in space,” whereas beats can be said to be due to “interference inuh0 ;t twyu9ffh;-g utx28 i+8ro-acy time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woxekgi- k20j8xd cs2 w57vmkl)uld the points D and C (where destructive and constructive interference occur) move farther apalm ij dv-kk 8wxc502 7s2ex)kgrt or closer together?

Traditional methods of protecting the hearing of people who work in art/le9pfrw t4 +eas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relativew9 /e+ttlfrp 4ly 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 can be thought of as a supfa4 b,h9k p-fderposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencie49b,-f dfkh pas farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obse 1vs: 6vsw49lm2 .ywvn gikn/frver move in the same direction, with the sli. 1g6wm: f n2v9n /4ykssvwvame velocity? Explain.

If a wind is blowing, will this alter the frequency of8l8q dveika2 5s4bj5d the sound heard by a person at reb8852vadije 4qs5d lkst with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various po /gn.;t)9ink-hiurx jsitions of a child in motion on a swing. A monitor is blowing a w ;x thg/u)ik.rjnin-9histle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake ymee(4gvyi2 m; h-el7by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of ley(;y7em -g4eim2hv the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship svk3yb x j8/a 5hu1lc,4 +askujust below the waterline. He hears the echo of the sound refle hsl1 ,j84vxyuk3/ac us+5abkcted 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wav*6w((r 9zpxt gpzz*joelengths 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 pauvom.3 c2 )cjust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km c2vum)o3 p.ca away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striki0uqevt-m;mh, 2vx .o cdix;:nng the water below is heard 3.5 s later. How high is tom.i0v ;d: mext,h2xn;cv-u q he cliff?    m

  A person, with his ear to the ground, sees a huge sto 7o,uo *ji9ip9wv7dpene strike the concrete pavement. A momenjou79i *pw9d7vpoi e,t 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 )w;eu lyjev,, zedwq3od+0 y3of distance by the “5-second rule” for estimating t3,ewy yzjo,0 ;ulde+qw3) vedhe 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+9u je/63u fw lswt pe:*b6)m1sqrkl z level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whoczofu.3u7imxu. xh +5se intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prqw(m1 cjhbx2w7 y0 wx4oduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? 1qhxwb7 ymcww0j 24x ([Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fromwf/) : izy*mqg2(3esb- imav q an airplane with four equally noisy jet engines is experiencing a somga fqy3sb e*i 2-:(zm) wivq/und 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 dB, where9(dzf:v tv0wvas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devivfv 0zt(wd9 :vce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normamg,tv. q w2cw7l conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ovwvg7w2 ,cmt .qer a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose arefb*/nwi ,3eema 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 25dav)vq,t7 p:z 0 W, while the more modest amplifier 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 connected inq a:vv)tdz 7p, 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 azq:v wwg x ,,,wrr(l7/6laxtdB when placed 2.8 m in front of a lo laqx ,: w(wa67rgt,zrv l/x,wudspeaker 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 typical(4 c2o-c4 0 d-n;e nzbaqjsdyzly detect a difference in sound level of 2.0 dB. What is the ratdc jzz2bq- aen4on- d0cy (4s;io of 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 tripled, xw ss53 n9w 8kegxv9j3(a) by what factor will the intensity increase9xsgnwk3wv 8ej5 93sx? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement afizxv.ol)ta :4( hf ifeiy +t(-*.rk xmplitudes, but one has twice the freque (ei.v* :kri.fxt ayofz-+(h4lt i) xfncy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave ):k h6n:ugeit8 k g7j gxo1rh4in air that corresponds to a displacement amplitude of vibrating air moleculesogh41gk68 e)u n7 kij:t:xrhg of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level t6d e9 igor(d )dox zwo1s/.q7wo seem as loud as a 100-Hz tone that has a 50-dB sound level? (See F1oqd.odzi )o g(xd wwre97/s6ig. 12–6.)    dB

What are the lowest and highest +2z+aueqik sl y /(gqxj2(z6wfrequencies that an ear can detect when the sound level is 30 dz(yl22wze6x ku+aqjq s+g /(iB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound+ -gja;+h nkka levels. What is the ratio of highest to lowest intensity at ++;k njaa hkg-
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundar1kv f+, .t cimgjo,rvfv3t7 i2;zec 2mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a ma, ccv +o gi f,2;3vt1re.kmtifzj2vr7ss 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 audiek( p8 79vlzlsa/1bqxble overtonee 7pz/k(qva89 xslbl1 s 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 fr5. db:e7zkhlo ws+:0fg* zgtz 7edsnm gv:88hequency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubeg: gkzzth5* 8 s7 dsbenl8 z:dh+:fo wv7eg0m.?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build 9k u 8xd2qnl.6xyagl,zo1 jt6a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), whaxyzxk 6luo1jq.86a gldtn,29 t 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 harmoha e0/ ld2 t-8wlrkbz0nic. What will be it/a blk8ld - etzw0h0r2s fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m l0,-lqq + iumk fn*xt9nong and is tuned to play E above middle C (330 -0q lnu ,f qm+tnx*ki9Hz).
(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 (262 Hv+4dw j:2- pqsoguz: tz) when the tempev+ wduojtgs: - qzp42:rature 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 atq 4w8p8vz;tea 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 Exa ;vd; gbxgva19mple 12–10 should the hole be that must be uncovered to play D above mvb xg;v9 1dag;iddle 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 p3dx; yudw7f.616 Hz, but not at any othe.y;wfpx 37d dur frequencies in 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 resonates at two suit ) d ip (cn;bftle/256k.-rh sa/dcjccessive harmonics c 6d;dn ct2f.i(ips 5h)lrk teb/aj/-of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 -ac.m:l b:bf k$^{\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 ygt5lnaf9l vln 76zt twzk .o;58+kb.audible range for a 2.14-m-long organ pipe at 20 z yn8glzk fwkt9v; 55tt labl .no7.+6$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thd mg8xaf2(sz 3kt06+(a tqb une outside and is closed at the other end by th nt6mt0b3daqg za8 +2uxsf k((e eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s whev4i8 id+3ylna n trying to adjust two strings, one of which is sounding 440 Hz. How far off id +38y4ilnavin frequency is the other string? ±    Hz

  What is the beat freque6tz /nvquvozh1y-20kncy 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, whinc7+bnjd-j 9 dn3p) 5yczd5elle another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneous p3jyz n9dc7 5n5ec)-ldb+jn dly, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9vceq60 i 4 t;i.ld,wj)lrb mf/ beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explaijcrvfwdtilm . 0;q l)b,4 /6ien your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in 4t7n) s ;essa(uwkar(one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint:sk;st s((7 ru4)neawa Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutjjzp u5cf)2r4es each try to play middle C (262 Hj)frz uj4p 52cz), 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 B has a fr,qu,n*rwy ar 0equency 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, the beat frequency is 4 Hz. What are the possible frequencqun *wy0 ,ar,ries 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:h y 8xkv+mcykb1v-7c one speaker and 3.50 m from the oth8vyk1 b c-c: 7vmyxhk+er.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating fr96j+5 vdsttir0u b.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 m5v0sdtiujf b r9.6+ rtust be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in aaco ;f,67 hgev imk.0oir. How many beats per second will be heard? 6macv g7foi0;kh ,oe.(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirenca(7fuw ga *9u/6ymyx9y)r6ug 5d tjy is 1550 Hz when at rest. What frequency do you detect if you g*wm)/ycuud fyr5x7 aytu6g(6j ya9 9 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 detect if a fire en+bfc4ir 8r. ujgine whose siren emits at 1550 Hz moves at a speed of 32 m/s ubc4.f8 rjir+
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift tjh 99(exn vk7sm(wm- d x 6glp-nhy-0in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m70(pxdlm 6n9t-h kh(sv 9x-- nwjgemy /s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When rvy7) t4g.qh2a3 ghg+ b0j 4xd- lww7b 1wxnkqone is at rest and the other is moving toward the first at 15 m/s the driver at rest hearahxwjr4g-bw d177h.g4 vql x3ywg2 nb)0t+ qks a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic s /.etq m;ni,nqtr2l: .8 sa q6tbs rf8wrt1ic8ound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s W21b8qies/qfn 8lttc:6mri.,rwas tt8q ;r .nhat 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 emitsz7fqfa9s.nd z h 9qaad(k.c07 an ultrasonic sound wave with fres9 azqqdhf7.d fk7a a c90.nz(quency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expel e ppbyh.o;u 6-rj(n-riments, a tuba was played on a moving flat train car at a frequency of 75 Hz, p uye.p-l(no6r h-b;jand 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 ultrasound waves to measure blood-flow speeds. .3v :wbg gef5oSuppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is ebgf5 .g3wo:v taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonir /,pc h-jee.:eh; ofdc waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits s;p4kq. 3owlqsound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what f;os k4lqp.qw 3requency 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 movingo zm5f76p0j,l4 rnmi h lhx5.t 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 zw2q01xqu l l3where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motqx3u12zw0ql lion?    $^{\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)om. iq) :al2-zzb gdo thin atmosphere of a planet where the speed of sound is2lmaz.iz):o ) bd-gqo only 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 traveling 8500 m/s strikes the ocean. Determine the shock wave annd pzuq4n3d9frgr 32*gle itg*9z34fddqn rr nu32 p 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 /mj63)o6 )zwxufsmkpoe .z8 atob ; y3$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove ;l e 6j h9(keo:vpn8bn6*ntborhead and see a plane exactly 1.5 km above the ground flying faster than the speedk:oven8(hj*96n eol b;ptb 6n 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 that4cc5.50 sox uxguj*k r 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 the minimum time between pukxj0gu4* r os xc5c.u5lses (in fresh water)?    s

  Approximately how manpt*y1 3xj8 ixfy octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display /wz +5 ky7gv lghj v-oovzf.)6called a sewer pipe symphony. It consists of many plastic pipes of various length hz6vlvg -foz7/+g)5wyj.ok vs, 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 makeiv j 0,ml144,ky gbx8pwa m3mgs a sound close to the threshold of human hear1mbm x38w klp,ayg4,4gj 0vim ing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sc;ldcb9ln8u6q iznltth v6 191/d6k z ound and an 87-dB sound are heardnhd9lk 6 niz/c9 c1bl;66qutlv1z t8d simultaneously?    dB

  The sound level 12.0 m from a loudspeak52mg:.iazq c c c 7tb5xy1(mfyer, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it ram ymca2: bx. f7g5qc z5it(cy1diates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pow) 0cqjp*3;pye chy5u wer output drops by 10 dB at 15 kHz. pjp0h)cy* ewy5cq3 u; What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theiru.zom-2iaf) *tf0*apt 5pzfo * p 0khc ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power int*0ih*pm5a*a zt- of0z2uf) pct .kofpercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the g y :2ct.3hcrxgain, $\beta$ 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 tooja3 m6-8lhgl5 6yq)m jtllo0 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 ,iywza is7357,u4 smasid doir/qmc25f+mp) 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of5 s2imas 7ofm / my,+wr7 )scpz34i5u, diqdia $6.1 \times10^{-4 }$ 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 vertiljszf b* 0g+qrt7u;k, og ff26cal 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 wftu2l6+ k0z s;7ro*qgjgbf ,fhen the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube 4 vyx wb9w+ gqjaetz d8g/ty,u3y5)p2that is open at one end and also 75 cm long. How much tensiont vbx/ w8pa4+y9w)2g, yjq5z3dgt y ue should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wah*yu(7u nfnm *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 frqgq ht b;gaxx97o g2ou l*6)pl;s1i:com two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about lsoox2 )u*tixa 6qc9b q glph;g:;g17and 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 whirl f9 5k+v4aagstles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving f 95a4g+lrkvatrain?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftedyj 6:.m pntc0r it passes you, its frequey.:mcn0jp 6t dncy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening tow e2l (/4 m-rtknuz76 xaamas; the difference in pitch of the engine noise between approach4u6 m-rza xea2 ;7m (nl/kastwing 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, soqmrfta*w*v5j wd-,pm 6 2 9zwjunding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How 6pw awmt*vjwzr9,2 mfq-jd* 5long is the other?    m

Two loudspeakers are at opposite ends of a railroad car aszp,vpoc,+ w 9d it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) h vpd,+c,p9owze 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 fl(qi *0g(tqyc6 flhvq 8ow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed l*(iq(fyv6c qgq th80of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth isoc:3 .g0)6kn5 -b7umnsgdy vhb jjr-c flying toward the bat at speed 5 m/s The bat emkd7n o:v3c -6b-jbnjh)yg sg0c5mu.rits 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 frequency sound pulsep)eouy sq. oh r(udyba180g8(s as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long.o(rsy pde gu(ha0b )qu1y8.8 o 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. 12–384btaghs zm7. 8t,7m+brmrc , m) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to 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 fr sa, g78mt4m hcr.rztb+mm ,b7equency 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 c3 v1ywa 4,ofpr 6dac+san be compromised by the presence of standing waves, + yofr1s, ca v6w4ap3dwhich can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a l;u ptbil,qe nsx 2)f(j,l* qj:ong, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Wiqn,xlf *;) tqejl(:,u2jbs pith a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency ofeg ;pf9e,n hvp0wi.a(z 0hn4r txpu d)p2:0so about 1000 Hzphr9s,oz )v0ptd4iwp ue fehp0( gn:a2x; 0n. is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0.ihqxjshtws r-p) ; z5n*:fo7t/ ezs/* An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’*zjh7zrwe)qf/ th/p is*on-s : x;s 5ts altitude?    $ \times10^{4 }$ m

  The wake of a speedbbpx)auk a/:k9 oat is 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