What is the evidence that sound travels as aqfxz ra u *-3b*o:, -xf68xnup pdooa0 wave?

What is the evidence that v;,q55v 8,o:n-cd dtrczmhk j sound is a form of energy?

Children sometimes play with a homemade “;hcs2ahyc i:m(iqo) 7telephone” by attaching a string to the:; y2iac7hhso i( cqm) 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 other.

When a sound wave passes from air into water, do you expect 7ev ix0l vqu3)oed 91uthe frequency or wavel1li 03ee9dvu xq o7vu)ength to change?

What evidence can you give that the speed of sound37bmue +vd8q 3gy)igm in air does not depend significanmg b yuv+3 igd3)mq78etly on frequency?

The voice of a person who has inhalew:dsgu :*n ,j87s kudgd helium sounds very high-pitched. Why?

How will the air temperature in a room affecq;k 1s6t9ftykt the pitch of organ pipes?

Explain how a tube might be used as a qskc.ey 3i8 2pv 8zjj:filter to reduce the amplitude of sounds in various frequenjjpcie8.3:2skq y v z8cy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spmjlg-td d o1 r0rq9zy8+wx z+(aced closer together as you move up the fingedo+-g9rl(myr+xd01 ztzj wq 8rboard toward the bridge?

A noisy truck approaceds2* wk s(9oohes 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 “brighte(o 29o dkse*swr” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference imn e.bw x 7:*jwvgyycp3xh. bns)2ietr4-3 9 nn space,” whereas beats can be said to be due to “interference n nxym*xbwp j we:t9h.r b)y ic23 gsnv-37e4.in time.” Explain.

In Fig. 12–16, if the frequency of the speaky07ne * 1ugxozers were lowered, would the points D and C (where destructive and constructive interference occur) moveoy1 n *7zgxu0e farther apart or closer together?

Traditional methods of protecting fq8 zv+i+8kgh t6-a7 ;dba/xff;mdiathe 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 ambi 8ti+ ag d;6faf-amqi/fzv7 ;dk8b+h xent noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–315y(nmo5 akr3 ew); jfj. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two componekr3) m wj5o5y aef(j;nnt frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direlple+xrai7 pq 1pujr 526:*oiction, with the same veloci o6pxraji+ile7u: lp qr 1p*25ty? Explain.

If a wind is blowing, will this alter the frequency of t (rb;ht rjmd(6he sound heard by a person at rest with respect to th jh(r;br6td (me source? Is the wavelength or velocity changed?

Figure 12–32 shows va kjgra*y.k(x 5e -vs qf.o o*dhd3+s)grious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground.gxoa h +** (vg.3s) fjk5de-kyrqdos . 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 le*- 2mk,q.u 7ncxp/os ip0ltia ngth of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. p/xls.ckqiua2o t -*m,07 ipn $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wat9 rpthl lu6vpn +q43b)c+mpz, erline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s la4qp rhmb)l +6c +9putpl3z ,nvter. 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 w; z;,q1x bs6sbs;,q5nyp1 y(rocb uhin 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 day. -x33 gwzvnrr 2pxhmx+qm ,a.6Wi hx 2+q,vrrpg3 .nxm-3w6xzmathout 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 fish,    s (b) by the fishermen?    s

  A stone is dropped from the top ofoq*e v**2n lo)y m .1mqkm4up8vk9dbo a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hiobvq. nk1u )*me 89dqy 4vomp*km*2o lgh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone 2 tfms.ewmg(/ 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. H t/w .s2(fmmgeow 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 th ly+d:;u8sj:fpv(rfb ahu5:t e “5-second rule” for estimating the distance from j;srbp lfd8:u5ft a:v( y+u: ha 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 l tc p;x-/na(o786yijk 0orqtrevel 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 levetr . h-5m:np3si,g0**uuhownz)u jval of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound le yoiq(d19tc i.vel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s( 9.i1tyq dico.]    dB

  A person standing a certain distance from an airpg bra vyvbq-f0 c5(,m.lane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if cb.a vq0y,g-fv5mbr(the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas (x3n) etam ljenzi; 19for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background nj;3n1 mt (axnie)elz9oise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe 4yz ):ta+qptyr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the so :y tt+zy)q4apund 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 eary rd1z:l/v9sqh;+8zathos : 3.cv e bcdrum 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 ra:mw712dy ev d mayaveg5ekm3* 2y7v4 vted at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn twmm y*vev2dd2eyv:v3a77km 45ye1g a o 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 placed 2./ws;:b9ln-irb i dz0h 8tmyk28 m in front of a loudspeaker on the wk82zsy/id0rmtb in9h;:- bl stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level ow bpu0c0+ n3eqf 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [H 0qw3cp ebn+u0int: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilkw vmha8zl5v;o, /;uol the intensity increase? Increase by a faz koauw m,5vo8;lv/h;ctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice j 790y lmiu(*aksldxx6z l (r7e bp+*dthe frequen7mdeu6+xd *i(jp lb lly (rs0 9x7az*kcy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a s6)wwo b,wtu 3tqq c/b.ound wave in air that corresponds to a displacement amplitude of vibrating air molecules),t otbww.3 uc6qwb q/ of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sr9uz u eg)2n7teem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–t )e2uunzg7r 96.)    dB

What are the lowest and highest frequencies that an ear s; kn);bw/x8)nr pqafcan detect when the sound level pn8 r wbn)sk/);a fx;qis 30 dB? (See Fig. 12–6.)

  Your auditory system can arr*p.ei..+ 2: 4 gnk ldy*t( ubaunbxxccommodate a huge range of sound levels. What is the ratid2a xuet.b*px4.*.n u lk i rb(y:nr+go 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. y2u 40rcnoo,)ht*dn l The length of the vin)t0d hnyu2,*cr 4olobrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental 9qv x (ec 8rryem*vv+)and first three audible overtones if ter) v*(q+c v9rxy e8vmhe 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 acro,tqa h7/jisbpd4:1vb ss the top of an empty soda bottle that is 18 cm deep, if you assumeddbits:vq,7/jpa 4b1h 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 the range of:rjag;/lk9 pbh vqrb c sl1(+i acu7). human hearing (20 Hz to 20 kHz), what would be the range of the lengths of;gslqp+.(:1 uvc)/abla b hkrr9ci 7j pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5def)u98 tm;15f bpbm e40 Hz as its third harmonic. What will be its fundamental frequencfb91 umf;db 8pem)5t ey if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73764nsa oz 0jcu m long and is tuned to play E above middle C (330z s4 canj70o6u 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.+q/0xyw x05qo ig ipfbo1pq 1 an open organ pipe that emits middle C (262 Hz) when the temperatur 0p0y+/i5qf1xbq.gq1wo xop ie 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 6r5ha.* tx7p a3ibtv81wkuz/w7 d ytmat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpie.8h h,y a)dcstb2yr7mce of the flute in Example 12–10 should the hole be that must be uncovered to play D above mmc. 7sd)b28 ha hyy,triddle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 r6aqiox03d fr7lcc ) : tkwa/-Hz, and 616 Hz, but not at any other frequencies in between. (a) Showc:dka0xo wr 3/a6clf)q-ri7 t why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates a 7/x-mzjyc wtv6x ), khkh byy2)zl23wt two successive harmonics of frequencies 275 Hz and 3kt6kvw)2y zbjz7hx/ ,x lmh)yw-2 y 3c30 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 //z3)u0kvde ta qqi6p$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.148/h eha ap 4u ;,q*vr5ts6uzuv-m-long organ pipe at 20 5t46 q v,; h8u*hsrzuu/pevaa$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is tqfomyz6.c2)1i*lo.hb6 x joapproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves f1h6.oq c 2z*xot lbyo)mi 6j.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 when trying to adjust two n7 /hoi4r0m8k jw b-lustrings, one of which is sounding 440 Hz. How fau0o k8lb j/i-7hmw4rn r off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2kgw- uy6j**hj 62 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another n .jdn4p(q4ohqvnx z6xl2 m)) (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 qlxv)xn dp mzjhn.q426) (n4o operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded witj; 0z 3v e/uvw6tr+o oygch+k9h a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your r;cz ktj6vgeyo+93v/+oru h w 0easoning.    Hz

  Two violin strings are tuned tbiwf1 mr,w;r.o 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 strings are played together? [Hi,wrrb .w;1i fmnt: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flu d 5c/gw,;a1z ommz5ebtes each try to play middle C (262 Hz), but one is at 5.0°Cga 5mwdz ;,zm 1cobe5/ and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hasy4 9h2dc2kbh74+mm :uznp7 su2znbi u 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 beat frequ2uh4dbiubn7p y2mc +zh4 n7km:zs9 2uencies 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 oneosdh ek9ei 5a+46gn vq7*ezf: x(l ,cj speaker and 3.50 m from th ,jz(qx 6l7k deef9+ioehncva 4s5*g:e 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 Hz, but a piano tune+; k(nc.-c ouzn1dhoe r hears three beats every 2.0 s when they are played together. (a) If one is vibrating at hndcn k-o .;(c1uez+o132 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 beats .y)qxz 8a( oi,pxafv ,per second will be he,(vxf8.qaoyz a x i)p,ard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenciz j4)/m (ncrlo 7;lvty of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you mtivro jn4/z ;(l7c)ml ove 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 engine whxhr *s7l35pd wose siren emits at 1550 Hz m7pds3wl5h x r*oves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frg lut0u)d at5p7uz03iv*0 btsequency if a 2000-Hz source is moving toward you at 15 m/s versus you mt ib3u0 t5uv0ps dzla*g)u70toving toward 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 equipped with the sa ,rks6p:9wy i:alc3jaabb e11me 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 frequency of 5.5 Hz. 6bybjrpe1s9k a3c, iw1laa:: What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasyoyk +l41 blwcdz :4vf5ilc2-onic sound waves at 50.0 kHz and receives them returned from an object moving dircyvw2 ly +4k- ofl4dbi:1zl 5cectly 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, tj.km e+ up7vg1*;tisthe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequenp* vm 1j;g +eskti.ut7cy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original-q6djb;s9uy p 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 trasyj-9upqb6 ;d in car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure a wkw ;0yqpxzrxuy 9 g53m9.:dgf:xj*blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sd 3zw:yr.9 x;0f 5ggxq*p9yaj u:xkwmound 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 wa8 n al3kho)yxhrj3l(8ves 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 2)5 rh chq, wb kp:707uzgiwpa570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, c: pgh0z7qwhibr2,w5)7u apk
(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 mo6 )-71n-kwt 7iuc ayvtrlzl r,ving 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 sound is 310 m/s (a) Whau,c -,a;i0(dcq a5 lb yfkfq.ct is the an-ybic.5qaf,k0fqc l da,(c ;u gle the 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 t *zr9mvii b9/qu-u 0zig m8o3hhe thin atmosphere of a planet where the speed of sound isr0 9 izq/ig*bm3ouz-9iuv8 mh only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8m mms6a)d6f 9c500 m/s strikes the ocean. Determine the shock wave angle it admf6s)69cm m 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 k2 zhjc,.gy/csekt56$/theta$ 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 abop2j+ 3 yv+pj we3d9zdsve the ground flying fasp39w+d y spedz v2j+j3ter 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 devcgmg*6ii* .fr ice that sends 20,000-Hz sound pulses downward from the bottom of the *6r.mi gf*gciboat, 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 there in the human 0hun qb3y.ah d;m2rc( audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer++mfo-sz lm)a pipe symphony. It consists of many plastic pls-++) afmz moipes 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 zxc tb,wl -gsl:4s 2*em from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sgx b4, zl2l-s*s: wtceound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dve;iwhv )mhbw).g: ee. f 1n(bB sound are heard simulta e ve bf ;vib1:whe)hm.)(gnw.neously?    dB

  The sound level 12.0 m from a lorvbkznvo( 4(;(ckd6yz07ccvudspeaker, placed in the open, is 105 dB. What is the acoustic power out ov(6vkr07dy( zcncb cv4k;(zput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops 63u9kbaxofc sk,8re38i cq(ob6w. qfby cf ,xqcqri8(f36 okbwe 369o8aubs.k 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet ai7+m,h*lgd *3d d fprnyi72v o+res*ic rcraft 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 e+csg dfro7i2i3n*lydhvd7m pr*+,*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 gain,g l/hhzi77( yn 4c/+,dj(;zgftj wv rz $\beta$ 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 ad. b5w*n c*;lhks gml94 sqo4 z-.thba 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 fixedsyxxdf, *qk*( points with a fundamental frequency of 440 Hz and a ma*yxx(,dfk *qs ss 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 inx 3qvb rp/(qp*gq**a qto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heag*q* 3 xpqqr( vbq*/aprd to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 ntoa *s7 ph,iey;7;kkg is near a tube that is open at one end any,e7* sat kk;; npho7id 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?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full2 ms5gaoyr t), fr(9wq 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.r ; oi82oshgd-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency srg ;oid h.o82is, 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 conductor 6 k:g;h*wsrw lon the stationaryw lgk:sw6;* rh train 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 train whistle as it approaches you is 538 Hz. Afterui6hx*sn4w-qd ;xz( + igwzj f uf)o;3 it passes you, its frequency is measured as 486 Hz. How fast wa(4xw ;u f3z+fq zu6 *w;)gxdjsin-iohs the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeniy6 bn:+bp 2)3ftkq rqing 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 byb iq)3kfyb+ 62n:pqrt on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soun y, 14aw5 ) zm4jzr07hcfgmrp g9vs*pvding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Ho zjrfv5s1,09g7hg*pzy4pv mwam rc4)w long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past o5mcr-e* 1ylua 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 the car, (b)5elryu mco1*- 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(kt u0h o ifzu:y+b mxg54f :aocz9-w6 about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dir u b:4z fi t kgwoy-+ou0ha9fzm(56x:cected 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 sp4: ulgqw,uda d4bf* u7eed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHzbf 4l47:w,guuadq *du. 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 approacsfmm:0anjse,p l eijs-n/ :37hes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that thjie0 :essmnapsf7n- :m3,l /je echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from onrz bqy a2vjy.lr35 ;d6e 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 musicabz35ry 6y ; .rvlaq2djl 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 presenc 2ke dt1 tug iwx-bn*,e.pt.v-e of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roomt-tde2 xn -*t1kpvi g..wbe,u.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender aluminm +o0 9.: ,0 nekiqwxlp)4fhw.xjo kzrum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod canw0l.zxh ki9nkwx0 +fj4:o.e mr) qop, 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 frenxv1;+ufk7/,lrz5 vleb3pv nquency of abo+e/ v5vpk1lxbn7nrzu l3v f;,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 Ma /pez qka5(5gwch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s q5 z5a(/e wpkgaltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15aly79f4l v z buh1/(nj $^{\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