What is the evidence that sound travels as a wave nw18vz* dz ttkl5 xs/)0h+ich?

What is the evidence that sound veli6l vcl70 :is a form of energy?

Children sometimes play with a homemade “telephufsf:5 ab4zrn2, txr2xg4/s k one” 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) ask xrbff5 g2 /xnr,:z4st4u2. Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes fromi6b,k cfpne/c8:+b;5wuh f lbl1; o f;p;akhi air into water, do you expect the frequency or wavelength to chafhbw;ep :ffb c kc;/ 6l k1;ii5;oa8ln+hb ,punge?

What evidence can you give that the speed of sound in air does not depend signif:hqv)f+ et wh.icantly on fh :vw)qhe.+tfrequency?

The voice of a person who has inhaled j3/ k07jcun:ye(kq hc helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch;st+j.a1s:3 hlsrab t of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundsef*t km(6mdpd s d1;i( in various frequency ranges. (An ;d6(tm *i1pme ddsf(k example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) sq:u yatqj)ik3p:; s+wpaced closer together as you move up the t+q j :)w3ip;sak :qyufingerboard toward the bridge?

A noisy truck approaches you from bj,n;:x)rncpv+h g6yw ehind a building. Initially you hear it but cannot see it. When it emerghp:r6nvjy n g )w,+;cxes and you do see it, its sound is suddenly “brighter” — 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;b:zx ,udy 9ksk 7n6m wypo0a0 in space,” whereas beats can be said to be due to “interference in time.” bndpkk 9y7: smxw,6uya0oz0;Explain.

In Fig. 12–16, if the frequency of the speak -zqk(k,rh)hv ers were lowered, would the points D and C (where destructive and co zv)k(,r-khh qnstructive interference occur) move farther apart or closer together?

Traditional methods of protecting v iws;5ghv11n 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 cou 5;n1wvvs1hg ild adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. 3gn1m prs9 ff hjbm)kvl+) 8c)zikb1-Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In wf+1g81bk nc9h)) s zlm)jr3pvfbk i-mhich 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 soumuz+ )gkmm 7s -azil1-rce and observer move in the same direction, with thea)7l umz+siz m -mgk1- same velocity? Explain.

If a wind is blowing, will thisz*t+ve le( lka v+x(3o alter the frequency of the sound heard by a person at rest with ret +vl*vk( al3eo +zxe(spect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chuj ,vk. ir7bp+t, hb y,ohf-s*ild in motion on a swing. 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 of the whistle? Explj,-r., p ui v7t bfyk*bh,hos+ain your reasoning.

  A hiker determines tr12/+sxu t xawhe length of a lake by listening for the echo of her shout reflecte ta2u/xs1+wx rd 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. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shif 5:pn: gmuyxw9(wtg s/j ;xql ;dzn9;p 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 sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with n;d:g9:q x wx9ts lngj ;p;/uw(5y mzfdepth.    $ \times10^{ 3}$m

  (a) Calculate the wa+bu4aduvf5 w ;kzg6y7velengths 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)phr g4 viai-4 vshj67 tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time 4hgrhaiv)j7s 6 4v-pielapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cl. yyfnkp7+l57u ol n)sr 2of8biff. The splash it makes when striking the water below is heard 3.5 s later. How hik )un2sf8rl7. 7pbn o+yyfl5ogh is the cliff?    m

  A person, with his ear to the ground, sees qlqd (q,rr2v, vdqv 1sn/g*8 wa huge stone strike the concrete pavement. A moment later two sounds are heard fsqv , g*rq 2d8/rl(,1wqqnvvdrom the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mil i(8 v/wffa/omh+g c,me of distance by the “5-second rule” for estimating the distance from a lightning wg8o fm/fiv/ (c a+m,hstrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atl(9lvq.ou/ jx the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose ngg+ejfb at;/k ..( p+u6zlsr intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound c68 )hyc tx3selevel 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.t63 ycs e)h8cx]    dB

  A person standing a certain distance from an airplane with four equally noi+pr-l+9u.f ; a3*nbv roeawn o :kuzk3sy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain r 3:wbave;or+z.pufl+nuk-ok 9 a *3nshut 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, whe i;c,nksgml /5reas for a CD player it is 95 dB. What is the ratio of intensities of the signans5;g/cl,k mi l and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal ceuawzq+ 1z,k tmhhme59 p7z+ 5onversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphuz1m ++9th eae,mz5k wq7 hp5zere 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 eardrumh,li9a0 b:7ureeq1kuv/e d2w 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 250 W, while the ; kyj9+ wi0zlydy1o+i more modest amplifier B is rated 9 ykw 10yjiyzl+d+oi;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 to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in fronf u9pdrzw a6n 07;7febt of a loudspea6wf7n b0d efr97a z;puker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typicallyw9rlk;wdg bf0 w7:k 8wa9bat4 detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.7a 0ww ragkw :lb99dbft4kw ;8]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whtkh) 6uxt -) 1fzu+kosmfq5z8 at factor will the intensity increase? Inu+ )m-f z5t 1k8soqtu)kf6hzxcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but ot2r gz/ a0a5onne has twice the frequency of tho0/r25 g atazne other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air t wytzo/5(ear7m ld4k7hat corresponds to a displacement amplitud4( /km7z5ty eo ardw7le of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see 6 b.io s+nz /vhyj/io,m3hg)g:ju2lxm as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig.jhzih.gyj v3il +g)uo6,m// sn xbo:2 12–6.)    dB

What are the lowest and highest frequencietbiy (p.ezt92 c 8l yu(j8u3hgs that an ear can detect when the sound levezp(3bc88uy tgjt.lu9eiy2(h l is 30 dB? (See Fig. 12–6.)

  Your auditory systemoys3vtkk (8up xgx bu96r,.c6 can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at 869.6(k uxp rutbsvoxy ckg3,
(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. Tj7 i +/,a(fkpwudz g-uhe length of the vibrating po+ip,wfa(/ud - j7zgukrtion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first t+wy 89zywu kgtg1f1n*hree audible overtones if the pigywuy1 ft1 n 8z+w*kg9pe 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 exa4(kib7 bq qpo1ne4 e:0w8 )3adnq;sgilowo2pect from blowing across the top of an empty soda bottle)q 7g1bsq n onokpw(w;8i2eed40a i 4baq :ol3 that 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 witdbff/hyj30g pxp71 805wqd au7-p ismh open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be 7/a5pi pj 0-3f1h bg8uyfx0 smd wp7dqthe 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 Hzsjbeb,e , ax,+ as its third harmonic. What will be its fundamental frbeexjb+,as ,,equency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abo6(u(kr ij mqk)ve middle C (330 Hukrim)6j ((kq z).
(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 piplep,z a20tuw7 e that emits middle C (262 Hz) when t2p 0z wat,el7uhe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune axk1s)m 5nmq j*t 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 th/) v+,pvtwwbkkk 0)rle hole be that must be uncovered to play D above middkvv/p0 wr)wktb kl,+) le 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, 440fj 1x; 8-vgwd za/msq: +(qazg Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe q8:mjaqf/v za gd1s(;-+ xgzw. ----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 boq bzde9ezp97c6//pe p eh1-ixh00k rkth ends. It resonates at two successive haz/-0/ch0xke 6ee i7p9 1pzbep r 9hqkdrmonics of frequencies 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 7+4+mg9ih vhjd 5w9 x nfjd7ym$^{\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 2.14-m-long ofbr.rsm. 6jq/x mmp .23fp 6mgrgan pipe atb ms.pjmmxf2qr.6fr / gpm.6 3 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lon +5f-wj )/:butqkc wxzg. 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 in the ear canal. What is the relationship of y -b)cj+u/f:x zw5twqkour 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 /mh.ie9zxyir2 x 7kp8strings, one of which is sounding 440 Hz.7p28kx ie zxyi/m.h r9 How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (26y;io 9 u 8huhsqd;wtc40fsmv7 4z2w) e2 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 kHajg1z st 6nh//z, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when /ats/zj1 6nhg played separately, 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 soundersa ,f4- qgl)ox-+b hud with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of)g,oh+a fuqlsx-4b- r the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequev3qlxcu ;2l3dncy, 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? [Hint: Recall Eq. 11–1 vqcx ll2;d33u3.]    Hz

  How many beats will be heard if two identical flutes each try to play middloz3an s ml j8z4vk4b7,e C (262 mov7s,83 k4nbl4aj zzHz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin8eqd hri )b13cs ,;x+dvzg 3smg forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B ) v+8 bm ,rzdic3g13;xqhssedare 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 frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speayzhc1k um g9z(s (a*0aker and 3.50 m from tma(y(hzu9 *0gk sa z1che 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 supposeotet +sbmbf -rd,. (3jd to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played tjd -obt3+re.bs fm,(together. (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 mkgxul.;2 s fgf 3n5/ 53wf5kplq.kbdpany beats per second will be heard? (Assume Tnqgp5/ x3 ff.55k2u lg3.slfbp;kdw k = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wh ip,2k/ z :ltls5kr1ozen at rest. What frequency do you detect if you mov/zlki ol 5pt:2skzr,1e 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 engmftp sk u)3/yn -4,e1bu9y7yb. lp bjkine whose siren emits at 1550 Hz moves at a speed o) k73n-m9e, b/y b41. splbjyptyufukf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency q02gbsi8 :od.v thy-yj 12xulif a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencisbj- 01h8xov2qg2l dt.y :u yies 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 same single fres l7,mp:h brf4quency horn. When one is at rest and the other il,h7 4spfrmb: s moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ult0(8puz s d,zk+ joyc4qbq 14bvrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly a8 + 4qs4 kzpub,(j1y0o dqzbcvway from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall;v .n .kxb *irxb,*qewupg y7; at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in yx.;b,i v 7; x*bpw .k*negqruthe reflected wave?    $ \times10^{4}$ Hz

  In one of the origina)q ves(vla1:s29p+t( v mz juql Doppler experiments, a tuba was played on a moving flat train(vtqz )vu1j92p(el m:ss v qa+ car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mea-fhs fx xqgc r4z56 9-;n iinc/q3jm3psure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is 4z ipjq r;nq-gnh-3 ff3/xx9 6mi5ccstaken 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 ultrasonict g ra)b0rwj0h;7-tinmoj) 39i6 opkc waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity;c( xzgwzr 4v4 is 12 m/s fro ;xvr(4 4zgwczm 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 moving on land if its speed at 20n a02i1c1x mks $^{\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 w9* mv/6ez0e ;zyjx/ js6dmyw lhere the speed of sound is 310 m/s (a) What is the angle the ;69ed/zlwjy6ex /z mjmy 0*vsshock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere o um6jl78uu l*ylc5f7tf a planet where the speed of sound is only abolu7658umy fl t *7clujut 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. Determine the shock wave angx*jdttx7ir .+zz .x8 vkky( -ele it prod -z+8jz .t*yi7xter x(.dvkkxuces
(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 o6f 6+.re8smr +4qvlpvd yb8o$/theta$ 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 g55: ue9aluuhabove the ground flying faste59 guluhaue5:r 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 that sq mjibv00.3u hends 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 time0.mhji b30quv between pulses (in fresh water)?    s

  Approximately how many octavesy0kx ) 6st wh 39a xwu2(;u-6tlpchkkn are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has gciejx 27tv*;ry5m)ra display called a sewer pipe symphony. It consists of many plrv;rg*7iyj2 me5xct )astic pipes 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 person makes a sound close to the threscgd;5ftt8ui 1hold of human hg;it d1ctf u85earing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 84ti 9 7l3wl:cwesexxpeb 9+h82-dB sound and an 87-dB sound are heard simulta3ilhwbte 8 e9x pec79:l+xw4 sneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10maevzi/:7u j 05 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directiej7: zmvu0a/ ions?    W

  A stereo amplifier is rated at 150 W output as a*n*mx8yl( st 1000 Hz. The power output drops by 10 dBls **8a xmnys( at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet airfs gom2yqsf 5a7su5o -a:+ x4vcraft typically wear protective devices over their ears. Assume that the soa:74g5 foo2 msa v+fs-y5qsxuund 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 by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, i, 9(e0ihmyowthe 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 freqm9s bh8wspg .6u0v kwhk*kmn1m2 ;4atnd1mq; 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 cmaq eo ky2f*(;j long between fixed points with a fundamental frequency of 440 Hz aqyo*fje a2k( ;nd 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 vertical omdc4+l3p8k:mia(.aomip 0z xpen 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 water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fo 4:mo0k+px m 8dc3ip (iz.malark?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that i-cq ghe,+r:bcs gr:+:blbk0 m s open 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) ws ge:h+rqcb:r0+m b ,:lgkb-cith the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass waset5i3dv xleb 1pv o9dqj2j+ ), observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hzod3fw2qj0y-v r 7q/f m range coming from two sources. The sound is loudest at points equidistantof3ywf/-q20d q 7mr vj from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hzp38fe+g)oeboj / ,n)dkewqi* skwk:8vz cq93 whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approache)8+egkqs )w38d/ fpoi :vkk ,qwozceej9 3b*n s. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches 9uw: zj*0ktzrhu32 yhyou is 538 Hz. After it passes you, its frequency is measured as 480zy3z:jk 2u*hut9 hrw6 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 zqiyn l0cwu- .l8cy l,-p 3o-hlistening to the difference in pitch of the engine noise betweep nchzy3i0 y-wlcqo.l 8,lu --n approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequ59q (i ss3s-bhqro9y dency of 11 Hz. The shorter one is 2.40 m longdq ss959o3ys(-h bq ir. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a94)5l ,m cze lh(ufisa 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 listenc(mf szlailh4e u,5) 9s 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 ismtw1l x+ 5mpbid k3d ;52rx wz)8wiz)z normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound l8irx5 ;zmw)3 btidwwx m2+5d kzp1)zwaves 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 flying towhb 3bq1h xy(*+:adz8-vsi ykxard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the y*(hxhzb3 +1kayb xs:i8- vd qwave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequen*rd28om*s bejcy sound pulses as it approaches 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 r*dbsomej2 *8the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) p:)qkv8 st* 0yjyxwi.was once used to send signals from one Alpine village to anothery8y. p x:*tv)wqj i0ks. 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 close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listeniw1 mjmk wpd+- jtpk+( (-(ncgdzio7z1ng can be compromised by the presence 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 d1jdzwt((pi7+pc k zon-w-1mgm(kj+ the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a longz9 qjl76g.h)ifc.j gdhjw ..b, slender aluminum rod held in the hand near the rod’s midpgligbj)7jh..wjd hqz.f 6.c9oint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of + d/lydpsu8o/nu 8tbmd+)td :about 10/ dy/:om) nu+8u+t8 btpsd ldd00 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 0u5kmzcoh/oy8 ; 0rg*6 2k7makb;bn uvx n* ch2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s amc8kb0gu ancohyz2u nm5*h */k 07b;rvok;x6 ltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 13k8m 5s cg/8zs e 4kwmvdck;9.pkc, cf5 $^{\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