What is the evidence that sound travels as a waxho35w rrwg*-ovpw ik;c:5 3k6eki1lve?

What is the evidence that souc1m qa ,ry7+nund is a form of energy?

Children sometimes p: jzf-jo4 nd1r::cuxvv;ve h1lay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched v1n v:xj1f cehdv:o4 uj-:rz;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 il3o h(15ht1jm4g0b aksz3o jdnto water, do you expect the frequency or wavelenkoamgbtld(j 335hoh10s z 41jgth to change?

What evidence can you give thaty w0if 9hpg-s ;a-d,)vxyge(k the speed of sound in air does not depend significantly on fr-g gp yfh vsyekawx(;90d,i- )equency?

The voice of a person who has inhaled helium sounds very high-pitl.mlq 32i9z omjm3 zbn*db hh)ibr69;ched. Why?

How will the air temperature in a room affbnnw 7pa5f.99zkv03 is jgj- cect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of,54u rlmh ik3l sounds in various frequency ranges. (An example i4klurhlim5 3,s a car muffler.)

Why are the frets on a guitar vt efp0.;8 f3 fo sjur5z xbmq8eng75 ,pg5ed:(Fig. 12–30) spaced closer together as you move up the finger5j rez 3g nepe7 5f,x db;f.p5v80 gmus8fqto:board toward the bridge?

A noisy truck approaches you from behind a building. Initially g/s16 ioq 6ebaemqcc1i2f6 j.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-frequens6c2febqei1o.gc/m q 6i6j a1 cy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “int.1+k rweur lk3ego f7 8;-ozqderference in space,” whereas beats can be said to be due to “ik7; w ogodq ek1+f.8urlzre3-nterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowere(3ueo bkx 0)fl cic3-ed, would the points D and C (where destructive and constructive interference occur) move farther apart or closer)bi(0 euo3-k 3xfeccl together?

Traditional methods of hnl+ i.6 nj-fxprotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound fi+ln-x.n h j6levels reaching the ears?

Consider the two waves shown7z)9cdvc .6d u l.tp1id-oixj)bec lu y*pg+- in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18.cdz dcg* j1tv +.b7)6-.yx9l-p ol u) diuiepc In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift ;8xmqnih k.6z2tf( tuif the source and observer move in the same direction, with the same velocity? Explz x2fi6qtn.( umh;8 tkain.

If a wind is blowing, will this alter the frequek+v2/v (x+fa q 6;puqlu)b iplncy of the sound heard by a person at rest with respect to the source? Is the w+qpa2il ub ()/x6vkquv +plf; avelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing, drhhkdyu* -4. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound ofd4h *uyr-k,hd the whistle? Explain your reasoning.

  A hiker determines the length of a lake 487v1y l w qksoyo07iyby 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.8yoyo70lqkv4s i1 wy7 Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of z4.z3 ghgv syw*:-aahhis ship just 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 svza h:hgws zagy-34*.ound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthsjh5 3spp- d gp28u6dxq in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy ,4aozr9j(ng cczd 1s2day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much tjr4do 1n29(,c a sgzzcime 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. t(e6mdu zhu0 7The splash it makes when striking the w6tmdz 7(he 0uuater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the gbhzjt is+3(+t round, sees a huge stone strike the concrete 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 far +ih + tj3sbz(taway did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ove9fyvw)mcp s6qdb9 7 d7r one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if t)c96p7sy wb9vqd m7d fhe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 -m0xxjo6 d4,wsjaoub , rn mk( lo)/+gdB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound len z(io:+x3 m wl.zha7xvel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when 8 a1wep yrtm2xj5: 6dvfired simultaneously at a certain place, what will bev1md8a2pt yx:er wj5 6 the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance 7fypg6+itq*4 2w bvm7i)u r jbfrom an airplane with four equally noisy jet enq gw+ 7*yi )vpjfi47rt2bub6mgines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signalz gl)yrt,47a+ce n5 erofyr;(*tj y9v-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for 7),* eergayyor4r;c tny5 +t9zf v(jl each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversan 27tmlvp2m6b tion. Use Table 12–2. As2vp tnb m67lm2sume the sound 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 whose area iu vcexdhq-4shh4 c2 ).s $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier,xwq(q hwd:d1h ev fk2f1t.c) B is rated at 40 W. (a) Estimate the sound level in decibelsh fk)cdevd. f 1htq1xw,(2q :w you would 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 d)a em fa0qzin5d59hey) h)t,t B when placed 2.8 m in front of a loudspeaker on the stagm qthyz,atf) 0d5a9e) i5)nehe.
(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 difference inat8+6x ipcc bm/n5m m90z5z pe sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by thim5i 0ta5cbp86c9mxepz n m+z/s amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wigr0zj;5 x,za dll the intensity increase? Increase by a 50,za; dr zgjxfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freqntt(/t,m6s 0 )4 6qbxvq ygvwwej bn2n++c2xfuency of the other. What is the ratio of their intensit 2n(gxqtvtw/b xn +bvy+, j6)qfen2t swm0c64ies?   

  What would be the sound level (in dB) o4)y;m sbe59hc n 95vcwv4r;u /dbnps gf a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 m9n)nv;bmd ebs 4sg ;c/hpw5cu4yv5r9 m at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve o )x9lrun5;qrl to seem as loud as a 100-Hz tone that has a 50-dB sounnr)u9qxr;ol 5 d level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear caalq blq31m6qaixilln o(73:-n detect when the sound level is 30 (l31oml -lqliax 6bn:3qaq7i dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soundblorr 7l *;gg. 3 4cmv+zh7ohq levels. What is the ratio bh+37hg7*4.mo cgoq z lrlr v;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 frequency of 440 Hz. The lequ 7t5+ya k0noq.7lyfngth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strinu7t y f+qlq57y0ko.na g be placed?    N

  An organ pipe is 112 cm long. What are the fundamental antoz /wj(sh27g d first three audible ovz(o wsh2/7 gjtertones 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 from blowing acr+nw2by 0z:xj ioss the top of an empty soda bottle that nxwi02: +yzjb is 18 cm 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 open-tube pipes spanning *ugir;l7jo4p a r 2fo1the range of human hearing (20 Hz to 20 kHz), what 7ra4lgup ;rj 21ofio* 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 harmonift, o t9,cbj:qw0/zskc. What will be its fundamental frequency if it is fingered a,b,ct0s zkt/wj:9qfot a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lo r 4fohbf4prip4(imy) j:47a vng and is tuned to play E above middle C (33)pb4pyro4hff7i 44(iaj mv r:0 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 Hz) ws2 kh4j.8 npji668tz tsm: knthen the tempesk.26jn jmt t4n:ths8ikp8 6zrature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2.kzdl/hmaenuym37 8 rgiw;**0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the h8 e5dt+riqo4ibn9l/flute in Example 12–10 should the hole be that must be uncovered to play D abo hi98i/4+nboqer5lt d ve 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 rlk-1+z ,poham esonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or oh, +p-kzma1la 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 resonatesb8p+3i9 y xypvu (arb1 at two successive harmonics of frequencyiv 1r(bupaypx39+b 8ies 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 ruwsr 7gs9sstqi/0f+x2 z6 9 z$^{\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 frup( s06dj.i for a 2.14-m-long organ pi6djp(usi0fr . pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is opef b5ilnqx o./uhil7m**c: u9vn to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audu /9*iil q:n cxb v.muoh5l7f*ible 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 x,8ad.e x-xfz0s g,3+pzs8u fr+lke0biwoy 4every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strif ryag8s okbpx,0xz4.i,f+-e3sde l u+ 8w0xzng? ±    Hz

  What is the beat frequency if middle Cicgnp 7 r;g*u8w+. kfe (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 i43o)4j jdxfs kHz, while 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 ti4jx )s do4f3jhey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with 6fv4u z er46r.lg1okz zls: )ya 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of th4kgu)ylf z6lzrr: z6o.1s4eve string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fr8wn vlc.8c.p wu/t5za equency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency . zw8.cau t/lp8wn5cvheard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fezhuo) j) 7i4wlutes each try to play middle C (262 Hz), bei)7 w4h)zjuo ut 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 c5;g;ds* 8jzqgnd2mt4,ptb;x m q3 tgB has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frdm bdqtq;5gtj83g m pct ;,sn;z42gx*equencies 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 ,ipcz pvo cpjtc::yc **wg (c:t(um*1m apart. A person stands 3.00 m from one speaker and 3.50 m froo,z* pc(1tpcw :m:tuvcpjy(** cic g:m the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 13fzw-q)a ))hg7h2z r tt:u8nr (s2xtgu 2 Hz, but a piano tuner hears three beats every 2.0 s when they are played togeth2tw) a qth7 grn 8u-xzsug tf:z)h2(r)er. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How mlo qu6;);sjlz+mzc 1w any beats per second will be heard? (Assume T = 2wlzl; s) q+m61 zuoc;j0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s szjcso9s/ic u 1df7w7,iren is 1550 Hz when at rest. What frequency do7,fj wc/ diouscs91 7z you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire e2+ r l 2hauwedoj7n.o+mmj83ungine whose siren emits at 1550 Hz moves at a speed of 32 mdja+lnh 22wou873+r omje um./s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift i2szyw1uujcrl r g6h6a1r4mv-3o v(f 6n frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exm z1vrc(u6-orsljf y4u32vh6ar 6w1gactly 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. Wheckt0u en 9 :m*wmn;,win one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.w: u 9ntmn0iew*c km;,5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic so 6j hz5i -bxs3:iiht1ound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the re6h1-zs h:xjtbi3 o5ii ceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, q-z b0wrk2v6 ythe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fyvk6w r 0-2qbzrequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a yv m,s7;y g zr/:hovj0tuba was played on a moving flat train car at a frequency of 75 Hz0rh7vjys,g ; om/y:vz, 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 at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supposqrhf-9 0)+n77oncm)j(mkk z4a r mpgje the device emits sound at 3.5 MHz, and the sf0mpn) 4()k7 9a g7rhm-zc +jk nomrqjpeed 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 using ultrasonic mq 0q,qxq 3.qj r 6by(v,bv2ybwaves 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. Whgw)zu;( gnir38t7 *c vpu:mnhen the wind velocity is 12 m hm8p g vwuu;7t( n*nz)gi:c3r/s from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object mov vqz oxd;0k /nuga91m/ing 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 where the speed of : hn,e h.ebe/om+; 9/amfvv-/gskzr fsound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mo. n:mf ve/z/ khog+-;bre,fse9 a m/hvtion?    $^{\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 the2s*g*7 vfx zm9oz 5dqk thin atmosphere of a planet where the speed of sound is only ab *od92qgv s*5xkfz z7mout 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.h881,zj58nwnomk s . c7,albm g+alut Determine the shock wave angle it prn,l18z ,un bl m5s8 +7cha. ajwo8tkmgoduces
(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 3ai4/(z vodcn $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheayle8yyl-)e.p d and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time yp 8l.eley-y)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 s mz/, g*dkr-vqonar device that sends 20,000-Hz sound pulses downward from the bok *, r-/zmvqdgttom 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 pulses (in fresh water)?    s

  Approximately how many octaves are thew5zkb7irb-f8i gow/ 7re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symph2od+efj( w5 a+4ihw edony. It consists of many plastic pihw4+ 5+eadj if2do(ew pes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a)84c9 d xh5srndmz 8kj person makes a sound close to the threshold of human hearing (0 dBchkdx)9 d 85mr4jsn8 z). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultandw//v4(hk rv6 2ruae+*g aib,mtx7 mct sound level when an 82-dB sound and an 87-dB sound are heard simultaneously?xvreudv b(c a6arwm+/m2 th,k4g*i/ 7    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wb410cq9kmr n u ico-e7hat is the acoustic power c9q no7u rck1ib40em- output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W/;s k 1hufj+ry output at 1000 Hz. The power output drops by 10 dB af ;s ryk1hu+/jt 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft tc bsl/l; tiq;v 5/g;luypically 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 has an effective radius of 2.0 cm. What would be the power intercepted byb qlcusv il/g;/l;5 t; an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications syst d dicyr+f0 k6(te:o0rof(t j;ems, 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 freq b/5sc9s lhya;uency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundlz-e7mz7fi(u qt 2yi0amental frequency of 440 Hz and a mass per unitq itf72l i7z-( yuez0m length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube iqyzuz-3 s,98ggwf7e filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What zui7g ,yfq8w-3sg ze9is 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 ,8gsu gl ;4ureat one end and alsue, g8 lgs;4ruo 75 cm long. 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 one full loop x7:yota yp 4g5($\frac{1}{2}\lambda$) 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 rangsk.54c6zkcdj spz/ :x 27fv u6k (ustde coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m s6vxs(k:jz.k/z f4p c2sc6kdu5ut7dfarther 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 conductor ocvudl vd: +8k3n the stationary train hears a 3.0-Hz beat frequency when the other train approachesvclduk8:v +d3 . What is the speed of the moving train?   m/s

  The frequency of a steam train,u( jj6awl ;zz whistle as it approaches you is 538 Hz. After it passes you, its frequency is mea w6zljzju;a, (sured 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 lis/l rd6xam5 /fytening to the difference in pitch of the engine noise between appfad/m6rxl /y5roaching 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 1eg/y7n g8i7y- u7d nwm1 Hz. The shorter one is 2.40 m long. How long is the other?m7g yend-/7 u7wyg 8ni    m

Two loudspeakers are at opposite ends of a railroad car as it yh4 lcq12hnc8 03g zafkk3 t3mmoves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 183kq 0cg3y c nkhlfa4ztm2h3212 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 abouoh9z 2p-d o ;bnc)fs+mt 0.32 m/s what beat frequency would yf;2dh zb p9+osocn -m)ou 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 the mothtlpg8m,0h zcao 91c y8 is flying toward the bat at speed 5 m/s The bat emits a soundc01 hyalp8,9cmgt 8o z 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 pulses as it appro vx2l5)03yx e8ptkct o d(p:8 4bxuzyaaches a moth. The pulses are approximately 70.0 msxp0xvtpye uzo5 y3kl8 b2: 48)dct( xa 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. 12–38) was once used to send signals from onv/2p6fly;4fng2kzyx b ;w 1yve Alpine village to another. Since lower frequency sounds argf vlpx;n kzf;/y6 422vbwyy1e less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listeniib*byw zh4q9 xw1 ,;.nfv)fa eng can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressurb4fz,ef1.hiw9qn) x* v; wyba e 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 demonstrat;9 t3jvf+ja b sng6bev 4/b1f x3rgy)xion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, rin9 fjevg;y4vjn6st 3+ bfar b1/xgb3)xging 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 frequepwfp97lg9 l4 x;ptm)hncy of about 1lf4 xlpph;9w97m t gp)000 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 vas f2+c 5y):gienvg0 ground hears the sonic boom 1.5 min after the plane passes d5ygvs:gc+fiave) n 0 2irectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ;(i cg8rhr;fgis 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