What is the evidence that sound trave.3b;fjpou q6(dpph a -ls as a wave?

What is the evidence that s,* x*o7 pty :gum dlm08-ghzfyound is a form of energy?

Children sometimes play withaprr 2uq; b4b ql2a 0k5:vu(;fs/egvw g*1jsv a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the sr5/kbal pg2jqe:s; *u4wfru vqb0v; 2(as g1vtring is stretched and a child 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 from air in2 b2/ bjdfwp6n +4zbr 7u4oerr .blv6nto water, do you expect the frequency or wavelengthnbeu.2w2rj 64r d7/lp b+nbr bfz4 v6o to change?

What evidence can you give that the speed of sound in air dofj +hsntyt :(/es not depend signift :n jfsh/ty+(icantly on frequency?

The voice of a person who has inhaled hel-o8zamv*r1h(y u kx.pik8 zw (ium sounds very high-pitched. Why?

How will the air temperature in a room affect thzi,i m;i;ec ,le pitch of organ pipes?

Explain how a tube might be used ash/3m(ogum :g l a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a cagmmgol3h:/ u (r muffler.)

Why are the frets on a guitarcd;l4*h d-6wfaddoib9i + mp+ (Fig. 12–30) spaced closer together as you move up th id964h+wm i;c dd+lpdoba*f-e fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hfh gjev,4 g/b:92pr:zr yatb4ear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear morebpjvbfyarg24 g4:,e/t9rh: z 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,” wh s:0w4g0igpfi-oa-nb3 ngj e038csn g ereas beats can be said to be due to “interference a0 3 ip c:gj 0sn4gg3gn-oie08nfwb s-in time.” Explain.

In Fig. 12–16, if the frims aw **707d7d euutq*afs/fcn+s,a equency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fartewna as7u+0cm* s/* s*,f7a u 7idfdqther apart or closer together?

Traditional methods of protecting the hearing of people who p2 s, +jvsfm2gwork 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 feeds it to the headphones in addition to the ambient noise. How could adding mors2,psfvj g+m 2e noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave c 0r1x9nann0,m(he ad kan 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 the two component frequea1nexdmk(h r 090,annncies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source an+ ayl48uu oci09q8ty vd observer move in the same direction, with the same velocity? Explailyiuy+o ct084va q u89n.

If a wind is blowing, will this alter the frequency oft/*v43 ekcyq c* qo-ly the sound heard by a person at rest with respect to the soucc k lq3*tvoy-*q/4eyrce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child i:vn5e +(9ze(l pfgq ttn motion on a swing. A monitor is blowing a whistle in front of the child onvzen((l:e5 q gt+tfp9 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 by listening for the echo of her shoiy9ey8hrnswb kb*4a x .+z 1t2ut reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting.w+s zteibyxr81yka*. 42 n hb9 Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship justnr7lot+l .2qa below the waterline. He hears the echo of the sound reflectedr.7 2 a+olqtnl 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 wavelengths in air at 20 ar:.kxlwc9jz, wqzarxc*+)8o0k 8 gg $^{\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 b,yci6 7q)rmgsmh y 9.is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs)6ry yb c7migmh 9s.q, on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clere5j kp (r(w12itd*l98t vzfiff. The splash it makes when striking the water below is heard 3.5 s later. How high is the c( r2jzwtevi epf(18r5k9lt*d liff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrnue t+q u8f x86mtwa8a9i3uvoe0: f 8hete pavement. A moment 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 3fx9m+f ua68 et8hv0ao :eq8inuwut8far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent errou.hc e5dlhb0xc j;50 or made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the hjc u55exhb.0lcd;o0temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity4p m6go re/w9a of a sound at 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 a sound whose intensity i in;-w6vwz6k+ qxd zr;s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fun4tjr m9h 4,.)1 sag)byokulired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: g 1k,tumlj)4 u.ay)br nso9h4Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eq+w l. (rdx2jw(3bgl xxually noisy jet engines is experiencing a +dr2(g bxl.jl( wwx3xsound 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 toynf7v q7; a)o.go 5xlgpwnf35x3 vgd/ have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of f yno.)vfdg7 /qwlgvo 5na 73g3 xp;x5intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outp4i.od2 6gk 0vqnj)f obut of sound from a person speaking in normal conversation. Use Table 12–2. Assume the soundig6 qobo4d nk vf20j). spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wjdov; *c+ t-bd md78cfhose 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 t 4))u6r7bonpcgk q ,njhe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wouqro4u , npjcn b)g76)kld expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placezeao ; .,e3wakd 2.8 m in front of a loua3aekw;o., ezdspeaker 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 z2l ly:0f r6dtdetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [H:yd0rt z6l2lfint: See Section 11–9.]$\approx$   

  If the amplitude of a souip(n lix m ) ui8+5a(k4y+cpufnd wave is tripled, (a) by what factor will the intensity inccx 8 pu(iyplun imk )i+4(f+5arease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fv 8. u7dhrl1vlrequency of the other. What is the ratio of their intensitied1 l vvrlu.78hs?   

  What would be the sound level (in dB) of a sound wave 0 i5 gyfkrwvouhr0ywnymw(-su+6/1 / in air that corresponds to a displacement amplitude of vibrating airr m(6w/1sy5-i vow0+yw u/h0gn rku yf molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudg:3a 1s-;y- culgwcqr y0dri+ as a 100-Hz tone that has a yclgs i ; 3d-gc1w-+q rr0ayu:50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an b1p zx) p0k5 brxskt- 9z/9olfxb5 p*dear can detect when the sound level is 30 kx5xxkt z *s 5/1b0pzfpr99dpb)b lo -dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whatz- b 9bsj0ya;z is the ratio of highest9az- 0s b;jbyz 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 hal xhzh l.-m*v4s a fundamental frequency of 440 Hz. The length of the vibrating ml.vl -h4zxh*portion is 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 th x *8wkh0/gobazd l. n:1qvxf)ree audible ovokn b gzwa xx)vhd.*1qfl0 8:/ertones 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 from5ot1zipn p6:vrtvy ipi4 6i)0 blowing across the top of an empty soda bottle that is 18 c0yrip5: t )ov6 6i14zpipvt nim deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with wpn9wp.m,08rl :dz zsopen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of s zn90m,. pld8wzrp w: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 harmonic ef8 s9amcr.-i. What will 9a8c-r smfei. be its 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 long and is tuned to play E above mid8v o 4h1wls7osdle C (330ls1h o vs47wo8 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 (262 Hzm:6vfhh y k*n thg/8q:) whentm/k6 *:hhh:n yv8fgq the temperature 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 20 7m 9*+v.i*i6fxzzq enhhzhx.$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flu)l.t klipm 5 z--2qrvzte in Example 12–10 should the hole be that must be uncoveredrp. z-m-)itlkq 25lvz to play D above 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 616 Hz,jb7 tma8t3 homf8 l,+s but not at any other frequencies in between. (8t8o7f3 mlb at+mjsh,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 a4k q0wy5t/lmh t both ends. It resonates at two successive harmonics of frequencies 275 Hz and lmhwtky0q54/ 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 q;0op ;/c r0s0giwaasu5ijg )$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 7cb cxcxb/yg2(i(;n k 2.14-m-long organ pipe atccx (bcg/yx2(b7ki ;n 20 $^{\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 *x-1uabhu,tk+r 0f ju;h .s ctto the outside and is closed at the other end by the eardrum. Estimate tu,u0jt-1sa;k* uch hr t+.xfb he 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 when688f va1ty-uzgsmpje/ 3 swl)vz-vq ; trying to adjust two strings, one of which is sounding 440 Hz. How far off in freqvs;yzm q f/j g1vv8w ze)p-at-3u6s8luency is the other string? ±    Hz

  What is the beat frequency if middlqh..cw,mw0 hje 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 an:yw ,jii8lvh* (aq7pwother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill walp,jv7(i8*w ywqh : ihine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 be6iogp(8;hf c a r -equc:xo,4kats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency ogcuf,h ke ao:cxro- p(; i86q4f the string? Explain your reasoning.    Hz

  Two violin strings are tuned6z) /;9 d x f,plwzyrs. n 2c3e7ub9hqgxt8fhm to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be fgqny 7sbzm 89t;6, 3 lu/drfx.xpc2weh 9hz)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 fyqfwgfk l x w+3q6pf3:+b -*aqlutes each try to play middle C (262 Hz), but one is at 5.0°C and the othe aklq qf6f:w+-g3q b *wpx+3yfr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 H(3zyeq5jyc *t j5frvz+od6 r +7bccx2 z; when A and B are sounded together, a beat freqdc z56 v3eq +* (ycxftc+y rjbz5o27rjuency of 3 Hz is heard. When 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 speaker n6vg-p6h.cn- goy8w 4 paq7coand 3.50 m from then c-6aghpny46 o.gqpw-vco87 other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be 7qe),g 8vt kyq2z:f *d8/katljx3yna vibrating 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 must2gttly3:j e kqz/vn, 87aax)8fkqy *d 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 2d)n12woe -i- l;bb idw.64 m and 2.76 m in air. How many beats per second wi1ei2ln ob)wd-i d;w- bll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enj65 m u4uupjj,gine’s siren is 1550 Hz when at rest. What frequency do you 6u ujjjm4 pu,5detect 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 frequent ;z pfri)e*8-eqh),kifkl1d,mz x *g cy do you detect if a fire engine whose siren emits at 1550*q glek*p h-dirzim;8f x)etz,kf1 ), Hz 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 source is moving toward you o l wm5n c *:8pf: w6naeo5-amgwh.n/vat 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Arn mcwwo:5f -* .aw5hvnp/8 langoe6:me 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 o1k3b; * qgdbmzne is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a bea1k3bqdb ;m*gzt 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 sound waves at 50.0 kHz and receives them ret9co9e;n 0,: jjlv )m d9stwmveurned foevns jecm,0v9dj9w;mlt): 9rom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall atnqm * (x et1*y2ilcc.q z-pt.m a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does t t1p-* c.emmxiqzn 2yc*tl(q. he bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playw6x 3b+d) znmled on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequex)mwdz3+ nb6l ncy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultra o 0md2zjvn0g7ts/l4xsound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the ex4l oz 20/7gdxtsnjv0m pected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect uw-2pqa( +;dsjzxyizyzua )/;oxj /( n sing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind x af0 2*37qnzs .mku ypy3lvs)velocity is 12 m/s from the north, what fk. *nzxpf 0 )u73mqav3ys l2syrequency 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 if its (3 3d, ol1s -k:bb/zrhh9b-yd;2opbd go clgjspeed 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 2.7r4w56g r bydg3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mot6r4g7rwg5y b dion?    $^{\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 atmos pgb4cktk 35doiz3mv 34t/63gqsv1wf ,qv gv0phere of a planet where the speed of sound is only about 35 m/s g4d3gpv q f1gb3t034vcq/,kvz5 3votwm ks 6i
(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. Determin0 y6+za+s;ntoq hpglj xn0k+iwr ,(f2+ m;sbte the shock wave angle it produces kmxs,pl ao+;(6 q ifshwjyn tnr+2+bz00t;+g
(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 o 37 jnyszto8v *1l4ci$/theta$ 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 ag4 lyby( f3w:hbove the ground flying faster than the speed 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. Debyg3( wlf:4yh termine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulduk n7bux8;m+z wan4:ses 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 pul:;w 4bda +7xnzknm uu8ses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range 7nookv8z p*l8 czw/s,? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists o rv8p75i. w;j5c:pk zyuka9sof many plastic pipes of various lengthpuky:rp o8.ciazk 59 jwsv ;75s, 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 fwih 7zp0c+f2n5h (y mm from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sounhfyc5 nimw2 +h(0pzf 7d level of 1000 such mosquitoes?    dB

  What is the resultant f rmo :ru*tf3xg(v39/z(k yre sound level when an 82-dB sound and an 87-dB sound are heard sim ru:/o kfv9f meg3z(3tr*(xyrultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed i1zdld ( 2wnl0sn the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equall(l2slwdzd0n 1 y in all directions?    W

  A stereo amplifier is rated60; i nipsovd/ at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is di; 6/pnv0iosthe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsbndf1nhu:jrr(. l (j lc 62wg 7s,b1as. 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 effebg.dscu,fr: h1( nnj 67( ba l21rslwjctive 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 systemsb*fgrez8n,bf+pg; u *, 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 i2h:(v4bdwmp nr*x, ituned 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 mye5 l,sd;:z,vbdwxk6zdw t. m 6pycm+u.5:qlong between fixed points with a fundamental frequency of 440 Hz and a mass per unit length yukws tz5wmqv;6l, bxp ey :mdd,.+.65dzc: m 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 vkuph9q*9 9q;sh+m ifehbb 8k2ibration 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 wmbhq9ph2h *k sekif q 998bu+;ater 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is :g g/vn 7qrrd44 6tbwtopen at one end and also 75 cm long. How much tension should be in thdg n4 7r4g:bt v/tqr6we 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 7dxl7 kz906,3 u m h1rfbvfx ;zk,fyaxobserved 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 3vu,tkzz9 2et range coming from two sources. The sound is loudest at potv z9z3u,etk2ints equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cd)qq i(xfn 64conductor on the stationary train hears a 3.0-Hz bni q cd)qf46(xeat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as iugp)9huh b -(,gwv c7dcb*q n-t approaches you is 538 Hz. After it passes you, its frequency is mec(hhu u *)-79wbvg-cbqdn pg,asured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spqs 6d3bxis; 6peed of cars just by listening to the difference in pitch of the enginbis3 d 6qpsx6;e noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. mr4j szwqkz( -3l/cb +8xicb/The shorter one is bc kx/4(j br is3w 8/zqz-+cml2.40 m long. How long is the other?    m

Two loudspeakers are at og6y)w) j mjxy8 gsno1*pposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shoswnjg1go j)m8)6 y *yxwn in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 nia) /p0c8gm dm/s what beat frequency would yopdim)c/80n a gu 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 of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while t ;)keo6dhc 0eche moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wavo ;0h ck)ec6ede detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moc h44q2 gdxt/mth. 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 one chirp retuc4/2d 4hm gtqxrns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was onc7a0s*jqlnf 9mk7k b i9e 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 shakq9n l7*0 fi7 sjbk9marp (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 comprokn png.j /9zq68or lm( 1g)whzmised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider l p n(m9kz ngqw6zr18ghj/).oa 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 oono .1ryat**“singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint.1*ooy ro*a nt. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humkzwoc 071s ga* mmzw22an ear at a frequency of about 10as mow kc zzg722w1*m000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boomxfh *a x 4h0k3)plifu0sw wu1ga*ed2 w:-5pu k 1.5 min afte u3u2-f01phdlw :*u*xg5h 4)ak0kwp x wafei sr the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is o,y7q.- uby1 u 3zrwlyny+ov 315 $^{\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