What is the evidence that soqqlrbt6 v5 / ,ywuz2.lund travels as a wave?

What is the evidence that soueb3(+pe mzha; nd is a form of energy?

Children sometimes px( e/ gady)28tso8oqe lay 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 can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the ots2eatoy xqd)e8(g8o /her.

When a sound wave passes from air into water, do you expect the frequemd3c:2auy2x 9caztn5ncy or wavelengtcc29mat n2d auyz:53xh to change?

What evidence can you give that the speed of sov(y:sa 0drhbn u.0r/jund in air does not depend significantly o n vrs.( djr0:ab/0uhyn frequency?

The voice of a person who has inhaled helium 8nx+3godtm6 wts qo9;3yji/ esounds very high-pitched. Why?

How will the air temperature i 18)ar5e(+kzjmlv ap ln a room affect the pitch of organ pipes?

Explain how a tube mig4/w* 9rdvfygfnw0 e9nnod1 6bht be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example isw n *bdw946oed1nv f09 yg/rnf a car muffler.)

Why are the frets on a guitar (Fig. 12–30)tu(kw:tg/xxha63.f y spaced closer together as you move up the fingerboard toward th t 6 /3fgutk(hw:yaxx.e bridge?

A noisy truck approaches you from behind a building. Initially you hear it but4uqy w l6(-gez cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explquylgzw(64 e-ain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sa/+; fmomzc5f eid to be due to “interference in space,” whereas beats can be said to be due to “interfez +ffe5mmc/o;rence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsnlq(q hf:(1jx16s0:xir + lmdubd mb6 D and C (where destructive and constructive interference occu1 q1 (iljnbmh+rsd06q :md x :l(6bxfur) move farther apart or closer together?

Traditional methods of protectyk )fhg.3zr+tg jv76 /d6 rdvking 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 levels 6ydr thf.+7grk/ gvkz )6j vd3reaching the ears?

Consider the two waves shown in Fig. 12–31. Ecr-mtu r5slz5(vqi3 w8str4 7 ach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 1vc-5r4qr itw(m s3l8st5uz7 r2–18. 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 if the source and oek* (vx : 9vc/dqkm3wobserver move in the same direction, with the same velocity? Explai(3/wck 9qkv:mevox d* n.

If a wind is blowing, will this alter the fr pl3h476y:9vwiaf lln equency of the sound heard by a person at re yhfi vwl7nl :apl3649st with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various pp9gu1ln02-8 cq0/clwxc k bt :xf oeq-ositions of a child in motion on a swing. A monitor isb q8luxgxfpoc-cen0 t9q120k-:l /c w 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 of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lisej2ewa 3 s9szm6m9 av+tening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengt+ sae9a39 m6wmevz2 jsh of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the en1zrxz f*) h;vpjix . mrb zav4*1;ut9cho of the sound reflectrhz1. vuz*xi abm r)4x1 tfp*z9;j ;nved 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 6zzt7emm*6 tyin 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 u )i r6r(o9irodrifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heardir6o uoir9)r ( (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. 77v1 fkjxck:eThe splash it makes when striking the water below fv j:kc1 7kx7eis heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grouc5it/5e +epfv wy gq.rcb/j. 9nd, 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+ fc.tei95v./5yrwq jcp g/be 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-second rulkg-7s yj-gy :ae” for estimating the distance from a lightning strike if the temperature iskgy: g-ysja -7 (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of hb*9dlj q (cj.120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound le*xqsrn a/fj+pl:2e v(vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneous va4hqi1sn +*mly at a certain place, what will be the sound level if+hnivm41s aq* only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a /r ir;vx ;jcr:b;nqdrc/m.j2be)*zi s5t 5pbcertain distance from an airplane with four equally noisy jet engines 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 intensitir/sri. bn;)b t5;; c*ic 2mp/qjrb: vdej5zr xes, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fcf0sq )+crud* d)vlqk:0fi i 7frw0n zz4,)qjor a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac4unwi dfq+r,q r 7)cl )0zv0f:0)sqjkcif* d zh device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a per fz17yr(exfi wnt wxi:9*5,do son speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere 1tnz7 x ie y*,fx:o9i5dwfrw(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 strikesdxtrkmi e7hp8 fn:puj*; 5n wp5 6o8n: an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at t zx ia*(l4cb7jf+bs;buk2 /p vnt -r(250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound leve(7au*/l-4pbktv2nbjsx irztc b+ (f; l in decibels 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 13e yo/xw50cot) 0 dB when placed 2.8 m in front of a loudspeaker on the stagey0o) 5/coxwte.
(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 ah-oh:61bblkv )h ezwl 2y w3+n difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this am- 2w )b lwhlvon6h:3yb+hke z1ount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)e+ 5.) eti 4mlbljdj,k by what factor will the intensity increase? Incre.,dljiem b k+tl4)e5 jase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but *p.x rb a2vbm+n3x8ay one has twice the frequency of the other. What is the ratio of thevpx xb2 + arab8y3mn.*ir intensities?   

  What would be the sound level (in dB) om5okwu06mt 1k xl)w6af a sound wave in air that corresponds to a displacement amplitude of vib51lk0)am kutwm w6ox 6rating 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.(+q.+f rme ytu(b2 5zuq wcama ,we+m 100-Hz tone that has a 50-dB sob+m5 ayaeuqf, +2c(re m+wwq.t (z.muund level? (See Fig. 12–6.)    dB

What are the lowest and highest frxl: od:7ril-g equencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)ir:x- lg7:ol d

  Your auditory system can i s,wn-keel72x, 9; wk1kpvke accommodate a huge range of sound levels. What is the ratio of hi lx kk;ki9n2p,ek w-e1,evws7ghest 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 p 55 ck*xycs.afrequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string 5yk.*5caxscp be placed?    N

  An organ pipe is 112 cm lr/(x)t u ztu.dgx s30xong. What are the fundamental and first three audible ove/d.z0 xxxt3 s)g(rutu rtones 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 frequeni;bv5 qafe8i5 89nrmg cy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wv5 rm;gia95ebn i f8q8as a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build ig25,b 4cbazp-iqy 1 na0pd 3na pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would bn3a aqb4 -gpnc,1b5iyz20d ip e 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 apwb :db0v3i;t5-r 4lj i(fr rrs its third harmonic. What will be its fundamental freqb-fwr r0 bld4;v p(rt53:j riiuency 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 tunedr ttxhvb i:jmh3.) ))d to play E above middle C t)3d).mtvb i)j:rx hh(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) s c 98s-3r::qz0sfnq+m4jap/v fqwxqwhen the temperature j:9:ws-4z/qrq s0s 8cvxq nf+a3fmp qis 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 apqm9 z t85;+icqszls ,hddidir0,r 00t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the ha1k2t a4)cj5s ntpwc9ole be that must be uncovered to play D above middle C at 294k 2t j51 c4tascp)wa9n 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 616pxks x61 ,kj7jcph / 9b::dkkl Hz, but not at any other fre kplj kjd 7ps9 :6hkxkbx,c1:/quencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long isav-odu ih2 8n9 open at both ends. It resonates at two successive harmonics of frequencies 275 Hz i -adhv8on9u 2and 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 xfehro 9v(o.;peg;2k6ow0 cm $^{\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 pv,lu37zqs: pthe audible range for a 2.14-m-long organ pipe ausz7vq: p3,lpt 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 to the je06,f) 0oetea7n *qnkyk)swoutside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waveykw ne6jfe0tns*)k0e,)o a7q s 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 o lx4.z x4jg8zune beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in f4ljx 48zuz.gx requency is the other string? ±    Hz

  What is the beat frequency it q/*m b/imk.xf middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.ugr oj.u3qe295 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separau gjou23r9.eqtely, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork:c0pvtuggbv 1d 0e 5zk gm2;u(z8zgg( and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of bvzgu(cz(gzt2;gp 8: 0 5umv0 dgk1gethe string? Explain your reasoning.    Hz

  Two violin strings are tunezozq /6 *pvps53ar6lk0m ,-; gvxyq 89zaa jccd to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two stpa,sqxpay z-r/;j366 o5alvc9kv0q*c mz 8z grings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idewt:e a078p8d kqcv 2oentical flutes each try to play middle C (262 Hz), butdqc280o:kw 7 atv8 pee 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. Fv k 88dxtge9+sork B 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 freet8s9 gd kxv+8quency 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 3skt ngan5x-1x97pg r ;.00 m from one speaker and 3.50 m9-nn7ga51spr;kx x g t from 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 132.eyg2n2 o ezop1 5h1ma Hz, but a piano tuner hears three beats every 2.0 s when they are played together 5yom2zo1ge n.12apeh . (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 many bo ly3 xz .)o srunyq-bf)pn8 a,xi 2f0gn,l*6neats per second will be heaso)p*, l ,8n-rnyfbfiayou n l62.xxq) 30gznrd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain6we,*ek dux-)b; hrkb fire engine’s siren is 1550 Hz when at rest. What frequendxe,6ehk;rbu) -kb *wcy do 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 engxxt9br)zv . b2ine whose siren emits xb9t.)zr2 v xbat 1550 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 aqoaky+2 c)y- d 2000-Hz source is moving toward you at 15 m/s versus you moving towa-qyky2+cd o a)rd it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equo3y3:9 dw5hd j6ebqd dipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequ bdwhq 56ddyjd3o9e: 3ency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonicr024wdivo9 * hj8blpt sound waves at 50.0 kHz and receives them returned from an ov0*92d r po4ibl8t hwjbject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emq dfxx92n4r a 9l:-z3 :wtxftaits an ultrasonic sound wave with frequency 30.0 kHz. What frequency doelat-:xf43:tx 9q2wnz fx dar 9s the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original sa47 wwaok8*tjt-u xol(o3z * Doppler experiments, a tuba was played 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 stati7-os4*lt8oo( zwxa*w jt3 ukaon at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ul0vl*5d o(0i go/ov0ukr fdot 0trasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in huvug(0k oo0ri0d0otflo /v5*d man 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 ultrasovvg vuug; 80+rnic 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 cidt+**gz2 ze the wind velocity is 12 m/s from the north, what frequeng zei2dz+* t*ccy 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 dmxx7c 6a 6c8:trh :l 6kikq4s fay+w0speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What iljx oy)py(rzgs: c; 61s the angle the shock wave makes with the direction of the airplane’s motion? yc j( yr:xl g1;)6zpos   $^{\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 th4 xvid0)y cgl8)s;xxge speed of sound is only) gxvi8 0dcxlgyx4s;) about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 34)hs j bv excty2s5;om/s strikes the ocean. Determine the shock wave angle it produce4c3;y)o xt hevssb2 5js
(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 zx xit 4 /xu-n(*ldj-b$/theta$ 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 above the ground fly gthyp* + ok;gq8,g*wls3(+htp mz1cying g8so ;1h tq(yhgpm3 y*pc*l+w+kgt ,zfaster 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. 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 lj-rm93gqea(xk0d + a8qrz1kthat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in 3 rrzkx8d-1k(g09jam la+eq qfresh water)?    s

  Approximately how many octav4fm2w t(zz 6 0 b8yn,7 m/vjctjly;p8xdgxt +ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. a,0vrs n zi-7aIt consists of many plastic pipes of various lengths, which 0,nzs 7rvaa- iare 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 closw6cz1wwog(v29lq vjwc- 4:n 9bl b8p ge to the threshold of human hearing (0 wl4l 6-wbv 2gjqzc91 8vo(c :b wgw9npdB). 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 so ju4)m6sn yxd wuw.0;tund are heard simultan.j6su0;wuynt w 4m)xd eously?    dB

  The sound level 12.0 m from a loudspeaker, placed iod9b 6j9 onm5on the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions? 9 9noodmbj 56o   W

  A stereo amplifier is rat )pb+wmnh-j;jl4,aw ned at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is th jwb+-)j mwhn,l; 4apne power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protect4 x(bp/,idubl a21f qiu.td d-ive devices over their ears. Assume that the sound level of a je lfxbd ,-t/bu(iq1d2i4. uapd t 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 by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gl wn66gri4mq 1gwy ;n) *f;bdbain, $\beta$ 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 evxmpapp n e-f0vi-7:*3l d/bto 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 long between fixed points with a fundamentaizq3; r76shcnl freqsq63i 7n;rz chuency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vjw k13,bvb.rv/ qmm .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 water level is heard to resonate with the tuning fork when the distance from the tube opening to the waterm b,q1kvb/.3. vjwmv r 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 oxd- 1ap)rjmr . pgr+g-pen at one end and also 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? r-).+mppa jrd1gxgr -   $ \times10^{ 2}$ N

A highway overpass was observed to resonate5 w03c:4 ncwfrditni6 as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sou6ak0w8hr9gy,,xtmn n rces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person m0xkwan869 n,ry, gmh toves 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. Onepnh8 ;)mtq*ny train is stationary. The conductor on the stationary trai)qp;y*tnh 8m nn hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trainx3nm nsf./vovy9:o u;w: -utx whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. H xwuvufs9n-v :o.oyn: ;/3 mxtow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estima82l4 ej- pc gog8 av;et5aar2nte the speed of cars just by listening to the difference in pitch of the engine 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 fast8o 5a2l-gg4v2 c;p ja 8eaenrt is it going?    m/s

  Two open organ pipes, sounding together, prolnd b,*g; 8rzx1,evro duce a beat frequency of 11 Hz. The shr8,do*l,e v zxb;g1r norter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at o)sw c2kpr 6pp,:y2wib5od ) ivpposite 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 the observer when (a) he listens from the position A, in front of sw ),62i:op dby52ipk)rcp wvthe 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 lw ohgrc2d)5/0.32 m/s what beat frequency would you exwodr/c 2)g 5lhpect 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 moth is flvatrwwocff i7vx.8p2,s+3t+ ying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by tt3,it aw.o s+p+v7rf8cfwx2 v he bat after that wave reflects off the moth?    kHz

  A bat emits a series of hwmi ;xx 1+a*cuigh frequency sound pulses as it approaches a moth. The pulsesxm ca1+wixu *; 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 returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12– fbnmby(dero5ofv a-5/ -mn .z;ru2 q.38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is closenv-u b ff-doebr n.5zmm/q 5o2y;.( ra to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can becikbi+)e8 mbia7o du 8yuo oq,j *)+x, compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room ),*eo bb +xa)jyco8,8+iq iik 7umd uo5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves 0ed1aujq-kjrr0*c t 4 a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with t qea 1 d0j4kcrujr-0*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 human ear at a freqw6gond,h; jex3:d/ch uency of abo6h xnjh3/,;ewcdg do :ut 1000 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 t5b))/bat dxpshe ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitud)b)bdxt/5s a pe?    $ \times10^{4 }$ m

  The wake of a speedboat is 16 e (vfojr: mp19kjzb 43ulduz7g( r3u5 $^{\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