What is the evidence that sound travels(7fek t)rs(y6dk kcd7 as a wave?

What is the evidence that sound is a form 1s,utfta -)zt of energy?

Children sometimes play lwy;b/kla4e rr)ydemj cb2qe).17/w with a homemade “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 cabre)j/d ;cbew w42yl1 )ykre7 / .lamqn 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 into water, do you expect + k b;xpnuz:/gthe frequency or wavelength to channukp;+xgbz: / ge?

What evidence can you give th,mhbkbhd x1:g0 qxo84at the speed of sound in air does not depend significanqkh4xg0m8:b o1xb ,hd tly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Wpnb broj3uy h+f+p* 5)hy?

How will the air temperature in a room affect the pitch5zn - o2vns9ox of organ pipes?

Explain how a tube might be used as a filter l/czeags(vgk k ,7n-5 msy-n :to reduce the amplitude of sounds in various frequency ranges. (An evz(l-/ - e:7ys5nmk ngk scag,xample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30w3j+meg / i h7gh8ufyh;b2se*) spaced closer together as you move up the fingerboard toward the bridhuggisj fh /w83ey7h *2b e;m+ge?

A noisy truck approayxtjv (xpg(pfv)y(-8t.- fm nr1*j vyches you 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 more of the high-frequency noise. Explain. [Hint: See Section 11–15 j8(f ny-pr ymxyj-v(1vvpt g*t) fx.(on diffraction.]

Standing waves can be sj)p yrqbz:* )bxsw z40aid to be due to “interference in space,” whereas beats can be sa)*jpbrz z)wx yqb0:4 sid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the sr s.gdr. h5qpb(1g/ kgpeakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther ap(gb h5qp/rdsk1 r..gg art or closer together?

Traditional methods of protecting the hearing of.17 tpreq ;/sph;hxlm 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 electronical ;.h ;p7qrps1hx tme/lly, 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 ,,vvdxe n 79nlof 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 frequencies farther apartl,vndnv7x 9e, ? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samel vxy *+ tu9e7r:z1mxk direction, with the same velocity?rmt7u:ek+lx* 9 v yxz1 Explain.

If a wind is blowing, will this alter the frequency of the soed8 l,c:zxm o7und heard by a person at rest with respect to the source? Is the wavelength or velocity,doxze7 m c8:l changed?

Figure 12–32 shows various positions of t0pnhdah r;;,i (enb f8)r)xn ton- ;sa child in motion on a swing. A monitor is blowing a whistle in front of the child on the )n;xrtpohrnf n b0;ainh ( -se)dt8;,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 lyg*xy j m),*rub 2)mszistening for the echo of her shout reflected by a cliff at the far end of the lake. She hea)ugmy* smrx*2), yzjbrs the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jp xg 3sb3y; 0gz:flnfd+cqj6e27 e:ajust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawj0g: + pee723yq: anc6x; 3jfzlgfdbs ater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a9x vh+n7c nn-ui9d 2vmt 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. W-dp si22vtmqnv9t+;g2k ym8d ithout 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) by the fisdim 2nq89dtvmstk2 y ;pg +v2-h,    s (b) by the fishermen?    s

  A stone is dropped from the top of avxf-ge0*r ,k+j(tkmy cliff. The splash it makes when striking the water below is heard 3.5 s l*,f yjrxe(+v -gk0 tmkater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrets: d tgnw:7 jgec5/yftq;1rg 3e pavement. A momee5:1cwfq: s7gtd 3 g/n;rgtyj nt 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 by the “5-second4sb .dz 7b chgd+jz8)n rule” for esbc48z.)s ddz+h njb 7gtimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le 0p 58axd6a3-khgo/onz8 rdkfg.xbd,vel 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 ofn 5f 13gv.pk63fdxund a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired c+; fnulfquf500 s5xr 0r 0p08porikasimultaneously at a certain place, what will be the sound level if only one is exploded? [Hfsr;0 5crpauq08 rlu 00f5x0ni p+okfint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fofegtykshzr/0n; hod- v+v,)6ur equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person expk/ d0e+y-hg ftvh6,rn);o vz serience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have *+gn )ginai 3wa signal-to-noise ratio of 58 dB, whereas for a CD playe 3n )n*iiga+wgr it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output ofqdh.t un0 y 3tl7.( i8mf)oshq sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rough3mfst8l .qh.uy q)don 0 h7ti(ly 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 whose 5q2pln:3yl gp 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, whiniz a3x)t ai+zo5:oh8 le 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 az8 :on5ot +h3 iix)azin 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 placctanb0+rv6 (3v.bvwz ed 2.8 m in front of a loudspeaker on the stage. r6azwv3.0t(vc+v nbb
(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 d4a5fabp ta: f;ifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secta5a af; p4f:tbion 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will th5.m8rqd aaq6 se intensity increase? Increase byqqa s8.mad5r6 a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twnbz l kr.d6 lty,3.+ldice the frequency of the other. What is.yzd l.n3t ,+l6brlkd the ratio of their intensities?   

  What would be the sound leveb2;(lnphxg :; 5mwafvl (in dB) of a sound wave in air that corresponds to a displacement amplitudg(2v5l ;xwpn ;h a:bfme of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100f1tvob )-:5s e ngq-ij-Hz tone that has a 50-dB sound level? (See Fig. ij -s)vtoe5-qbf n: 1g12–6.)    dB

What are the lowest and , 6s9ehrlab +pnuh+3y highest frequencies that an ear can detect when the sound lev6p 3hb+u selryn+a9h,el is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodcf) r3i+k m;-lz5elojate a huge range of sound levels. What is the rj-c;5orfi3lz ke+ l )matio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequencp(7q5 ,hfhmne z:joa )y of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tens he,f q7m( h)zp5n:oajion must the string be placed?    N

  An organ pipe is 112 cm long. What are the fund)r7 p119+ 5x8 /wi zn;zylnsjb j,abzwm3f vqdamental and first three audible overtones i9;s na vp, xqizz 1mw1wbj7jb f)r83/+d5zl nyf the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blo)7os(r)fk4 t o:ic tsin ru/3gwing across the top of an empty soda bottle that is 18 cm deep, if yo t i)c4/rsi gro)(stnk7:ouf3u assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipedua oj48qgmqs.-7m. fwyd74lu(o5j ks spanning the range of human hearing (20 H7du8su4q.jm.j-la(dokmgfq 7 5y 4 w oz 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 ha8(j kod 6qu y g3 k9pzjqt5l.1hh21dtas a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if itl1j1d8dka putjq.(o 62ktz q9gyhh35 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 plakho .sj,or-we/ / fh/my E above middle C (330 Hz)o-/rwfom /j shh,. /ek.
(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 tvp9i a8a6/ ey)ek5n lmhat emits middle C (262 Hz) when the temperatur5ainpy9k8/)elav6 e m 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 at 2o +hhcmb rf*l,2y,x9 eh++c.+ ta:cs9kgw wyl0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the ho v. a4 gqb0jtr+nj;e6qle be that must be uncovj b0erq+ jna.vgq;6t4ered 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 2g i c;hmqtb.c5kg 2 ,-.dbl)xn64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is h)-bbq cn,mx.dig c2kg5t.l;an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It reso bf26*xp0nz e4zy i2wgnates at two successive harmonics of frequencies 275 Hz gfni 2y*e60x pzb4zw2 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 y+wr0i/ ep7 p-: rrbmtm:9ifp $^{\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 fo,j,f ukzo3z+ik x 6;*ftplr .qr a 2.14-m-long organ pipe at oi 6 u*3;+f,kqlztxr p,kf.zj20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ,lr/s 92lksl his approximately 2.5 cm long. It is open to the outside and is closed at the o2h s k9r,/lllsther 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 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 ag9+:8pj hlf2 r4el-hxihut3 when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stt93 euh+24 pxh-f igjahl:l8 rring? ±    Hz

  What is the beat frequency if middle f8wu p;- vm8nwC (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, whiia(.pvtnc-3r 8 5s(s y.f fro;,y8c mh0vchpble 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 simultaneously, estimate the operating h cis , sv-8(r0c5.r(3m8 bhnc;y.aoyftppv ffrequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz dwy b1ch/h8qd goy ,sol: 7jp.v*-w2o tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is s o1 q/h:,odv-h2c8ygbl pw*. ydjow7the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The t)rmh s *xbz3 luwq, ob8u31vb0ension in one string is then decreased by 2.0%. What will be the beat frequency h bxvwo 03)buuzh r ,83sqb*l1meard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle7zmovi-mhuq3bwm0zqom .d:m7k 7 07i C (262 Hz), but one is at 50hi: mi7.z 7bovmo quk 7mw0m qmz-d37.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hasah2kfstq7 *bgnvg : wc04 o-1b a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What s:fgc gkt2 nh7qo*-vb4 a1b0w 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 so )ug 6wfb1h;opeaker and 3.50 m from the other. h wougb)6;of1
(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 to2 da5d/ ox-id1d edx;e be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one i dxie ox/d2dd 1;-a5eds vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengthsy3c6h ssie+ dzn5l6/ b 2.64 m and 2.76 m in air. How many beats pere lihc3sn6sbd+ z y6/5 second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cexex)j4j + .xgartain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move xx)+g. ej 4axjwith 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-9ak j d)11ng njxfakr9 y+.rf if a fire engine whose siren emits at 1550 Hz9af. n1j)rd1k9k-y rna jg+fx 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 youqos pq5r5lf8 jkexy 1*no1z1+ at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? ef*1+spr 5yo1n5oqkqxl1zj8 $f'_{source\,movine}$    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 os1 g9 7nso0.rh6y9 hy)lvvo3 zrlmpw1w1q)s 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 avohlwzo6y0vosys) r 1 nhp1wgr)7 9lq.3 1m9s 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 sound waves at 50.0 kHz and receives them resz gc3u 79go:gturned from :cgz9os g7ug3 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 wa:4j4d(fn7c ji jdu2p ell at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 2nij:fj7upd44cje d(30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playedr vdaj1dop* 94 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 frequency was heard if the train car approached the station at1ja9 4or dpvd* a speed of 10 m/s ?   Hz

  A Doppler flow meter uskq,jo4frb **v es ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speer4* *, bvkfqjod of sound in human tissue is 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 uspjtu8mf( 6 y7,u el c*w7+ tgtypcbn54ing 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 frecifn 2c0:fqj4 quency 570 Hz. When the wind velocity is 12 m/s from the north, what frequen0n cq f2ji4:fccy 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 la ob7merkapr- o+mu9ml7-6 1nund if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/jbqif994jf(p nl 4o j0s (a) What is the angle the(q 4o pjfnj bif40j99l shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the spe /l g 5rfwrc 8wlmslx)uy5.x3c((2kp3 eii2js ed of sound is only acxg2ix s2wm3jl8 / rw5per( l5uysil3f .k )(cbout 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 850xf hi0 k);19b8s+e3brq h ngsb0 m/s strikes the ocean. Determine the shock wave angle it x1bsfnb;qh)b8i+ 39 0e skhgr 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 4xn9nx 8krbjktb b+.1bkd f3+$/theta$ 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 1.53ws u 1o-suu+t km above 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 2.0u+3s uutw-1s o km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound )mbxek/(qt+ w) z3gk +le xj5fpulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which ie/fk5k3zj)m+ qt lbgx)e xw(+t is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the 5iuia7 e(r;bb0 nrq*j)y p,yuhuman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disp7e 2/ js2fj .rzwau7cflay called a sewer pipe symphony. It consists of many plastic pipes of various lengwjzc77su 2./fj fea2 rths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold o lpsup9q2 ;rkm *yp8du1jm0 5-v9lwz sf human hearing (0 *qu8 s pz0ly;w1dl9-2 j k9mpsum rvp5dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound areb4n0xy 8) tssz(p2gb f heard simultan zpy)fxgt8bbs sn042(eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 d/kzfv;b z1ug4 B. What is the acoustic power output (W) ofk zb/ gv;uz41f the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thel*:m(b5 psy:ufigj 3g02tlu f power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? m 2p5(*fug3b:lyjtl :u 0 fsgi   dB

  Workers around jet aircr8tz f b0(jd3mtaft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear fmt(38djb tz0 has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communiw(541aax dr yct26ms wcations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1d+ yg5 (e:)op y4o8g1)eyudwq cz u9ll$\frac{1}{2}$ 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 with a fundame0cq55k m1sx frntal frequency of 440 Hz and a mass per unit lengthqxfmk5 rc s015 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 fi-fzfcmb ba 7 ,5r.u4i3 afykr)lled 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 thmbka,)i7 . 34bycfu zfr5a-r fe 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 open at onjnb ; /4iw7eys a*rc.dj7wg o0e end and also 75 cm g0ja b ;/.7ynjdc4 or* i7wsewlong. How much tension 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 was observed to resonate as ogvx-xg va9,w0ne 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-H37nyowfgii47hyd*w q9o )ozx9lbfosx ( 2 3/kz range coming from two sources. The sound3gq d7y o ifosh94o)wxb* fyw2nilo 93(k7xz/ is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a 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 cesvn*wio r*:g6ar-) bcmng 5;onductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed owe* 5 vsm:gcg-a);i*nrr6n o bf the moving train?   m/s

  The frequency of a steam train whistle asd.km*)pz(r sp;hft+z it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the traimz).p*pz;s fd r+kt h(n moving (assume constant velocity)?    m/s

  At a race track, you can emk 6vc86q1okqow;sy- u* :jfo stimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the soy fuc 1ow686kqjqom o:k;s*v-und 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 1uknhvn+p8i2zt,g a-9;mx wu together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m-,n2gu 8x a+zn;kimtw9 p1 huv long. How long is the other?    m

Two loudspeakers are aebdp0jnm )2; : rzv4hqt opposite ends 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 frequencies of 212 Hz, what is the beat frequency heard by 4:ebzv2r )dm;q p0nhjthe 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 in0tul9inm9; , hclz3ps the aorta is normally about 0.32 m/s what beat frequency would you expect if u tp9l ml, sc0n;93ihz5.50-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 ( cyf -ki:vw/e*.mbgd while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What img(w:vikyb/ fe .c* d-s 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 pulses as it approaches a moth. pb 2fydw)tn1xybkih 6)j8 *b-The pulses are apf jxi*n1p) k w8bd-bbt6) hy2yproximately 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 returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–3am6vpm )js 0q2b z8/af8) 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. Whe/q pa0)8 vzf6jbmsma2n played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stanwxet upyq)ohtn40vmh: +a; 6*ding waves, which can cause acoustic “dead spots” at the4n :o *quwyxm6h+hp ;tva)0te 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,” okz6y *sh rp 40)la+qtinvolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emo) alk64htr+qzyp* s 0it 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 frequenv*6cybg+p3ps tw *g3v cy of about 1*3by v*gp3 pscgw6+ vt000 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 obseh 4vh**mig: f( zh3albrver on the ground hears the sonic boom 1.5 min after the plane passes direcf:hh(*zihmvg bal*3 4 tly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbi32;bx/t5l ekgas )byoat 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