What is the evidence that sound travels as a wav( f,jd) a/wsdtd8od)m e?

What is the evidence that sound is a form of energyg 7 zc,qa tox4.s)nio)?

Children sometimes play with a homemade “telephone” byw tf3 go juvhq7tf+/1: attaching a string to the bottoms of two paper cff utj+ owv 3:t/gh7q1ups. 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 i+9 mbyf+1lmkdvy.beo4 v7k ebk((ji- nto water, do you expect the frequency or wavelenm4 j((1 o+bekkl+y mye vbdv.fb7ik9-gth to change?

What evidence can you give that the speed of sound in air does not depend2siqjh7+ 5hr*-gd 8 om/ usdsd signific8-su7sh d+/r dj omqh* 2sdgi5antly on frequency?

The voice of a person who has inhq8d3(hwg z)acug6+f ialed helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes?da -6xu+abs 8j

Explain how a tube might be used as asxn8n09h0rpxd wk :;z filter to reduce the amplitude of sounds in various frequency ranges. (An exz8;0d0xs n r9hw: nxpkample is a car muffler.)

Why are the frets on a guitar (Fig. 121 adwk/o mt55u–30) spaced closer together as you move up the fingerboard toward taumd55o/wk1 the bridge?

A noisy truck approaches you from behind a building. Init z2imtrx. a dy2iv875cially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffractid.iimyc25z2v x ar8 7ton.]

Standing waves can be said to be due to “interference in space,” whereas beyj48bs)82r i+ jzmctqats can be said to be due to “interference in timejbztm y ij2r8)+q 8sc4.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would(nok*kc.vtgy e +e-- a the points D and C (where destructive and constructive interference o--g+(teo.cvy n *aek kccur) move farther apart or closer together?

Traditional methods os 7o/exi(9f+7tory ;c bz7x wdf protecting 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 /f7yb z7r(xsco d xe7+9ti;wofeeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. 1/hmv jrw6 gf/Each wave can be thought of as a superposition of two sound waves with slightly different frhf/jgrw1 / v6mequencies, as in Fig. 12–18. 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 obse8h7g(2i r gqsqrver move in the same direction, wghirq7q s(8g2 ith the same velocity? Explain.

If a wind is blowing, will this alter the fre,5 9voiemtse*y.ba/ iquency of the sound heard by a person at rest with respect to the source? Is tho *ys,9ai/v eti.5e bme wavelength or velocity changed?

Figure 12–32 shows various posit(- lwmly imvi3*xd6d7 ions of a child 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 tdwmm7yiv(*- lil d3x6he child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her swxma6*dn;i7 4r0v /su sn9 pbc 38xgaghout reflected by a cliff at the far end of 3s naibvdn sg69 *xcxprugmw07a 48;/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 hisaa e 3(t-nbd7c ship just below the waterline. He hears the echo of the sound reflected from the oca37n- bt( cadeean 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 in air at 20 7*tpzc* qjky*c 3:fursnp: n4$^{\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 o:-x:6vxi; v hdiph b(of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How b6i:i( o:vhxvpd h;x- 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 of a cliff. The splash it makes wheupx3car5 b24 gg8jia(n striking the water below is heard 3.5 s later. How high is the cliffaj( x28 3pgc45aruigb?    m

  A person, with his ear to the ground, sees a huge stone strike t9qa2 efsp3y q-c- tw2she concrete pavement. A moment later two sounds are heard from the impact: one travels2cf9w -ept 2y3ass-qq 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 zxb(uy (m)kxst+:1izz 5 5avterror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temper uz5)a 5 s( (k:xb1ytxizv+zmtature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the :n5yys,j wshv 7wvdm 53g*uz (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:ru;zbxdd7u + intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lb5gvcvtt+gd, cq +::a evel of 95 dB when fired simultaneously at a certain place, what will be the soun,c t+d:vbggq:t+a vc 5d level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with foza i1, q66bxgz3k5rd our equally noisy jet enging zr ,od zqx5k6bai631es is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for 5 -5qnecudlm)a CD player it is 95 dB. What is the q l cm)e5u-nd5ratio of intensities of the signal 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 normujjv/ hv29t1e al conversation. Use Table 12–2. Assume the soundhj19tj vv2/ue 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 strd.8,23nyu(xgyzj bm xic mm*:ikes 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 250 W, while the46ug(b .sbk 3pec*3 r yktgot9 more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect yk6 g c3(tptb k3u*br.s9geo4at 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 kc9nvy5 i,0hxw3sl0)fntz.u m in front of a loudspeaker on thhc3x nywf9 ivut .0s,nzlk5 0)e 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 of 2.4 gi h1qoqf,k*s;y2 nf0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–92h fq41osnf;g*kqyi ,.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensp65eqd4t5 o ke fw00oh5-pdxh ity ino5px00ee6pq wodf5kh-td 5 4hcrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but6z5gn let5qjr/j2j19kober7 one has twice the frequency of the other. What is the ratio of their intensitiesq rr5/nj6zbt7ejk 1 jl9eg25o?   

  What would be the sound level (in dB) of a sound wave in air tvac/tni( myoha+ +2qm6 w0s s6hat corresponds to a displacement amplitude of vibrating air mo +s maow6y+av hsc6(m2q0i/tnlecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as ay yp0j ,r0jg9w 100-Hz tone that has a 50-dB sound level? (See Fig. 12–60gyw 9jpjr0,y.)    dB

What are the lowest and highest frequencies that an ear can detect whenmpttj1s n4cvm0e s+, 6z2n5,jrpvh: d the sound level 41t5jp,0zmj s+dcv: eph6nt2r, ns vm is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodata48spz1cnj : c)wbn;m e a huge range of sound levels. What is the ratio of highest to lowest intensity at c8swmn; ):4abcnz1 jp
(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 frys,hl*j.vhy8 equency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensiovj8yh h.y* l,sn must the string be placed?    N

  An organ pipe is 112 c57 u8qafc8*nb9e m n;p 1ayiyxm long. What are the fundamental and first three audible overtones if the8x1 uin8cab ya 9yq7ef;pm* 5n 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 ex2 (b1bq cvqm:8k3aetkpect from blowing across the top of an empty soda bottle that is 18 cm d2cb8:ket v3(qm1bqakeep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with ope* 1axzv bd 28xv/novi +s*ygf+n-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of*fn/ *vsyo 8bax dzvx+vi+g 12 the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thirdtn7 x,;sloohve d9q2z;.3zp mpb6d9 a harmonic. What will be its funbts lozm hxpadzn679 .;dp;9qv2o, 3e damental frequency 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 t*yktq ri 01ehq .sx5;3sh( ufbuned to play E above middle C (330 Hirkuesy0 x;qb13h. * t(s5hf qz).
(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) whe q:gndi 8l/ou/c;inc -n the temperat qlc-n /g:in o/dc8u;iure 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 e.kv2 s :hl9cz kjfq1(at 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 hole n: ual(-mc ;g;tjrk.b9 zn2jqbe that must be uncovez92 kurjajn;b g(:c- .m;nqtlred to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate dc c5/o803nr azmrabslo;1g e6;kem,at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open e/r0lc5 ; nk6az;,sdbecrmo g3o18amor 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,t*d*32 ynw3fgml ees is open at both ends. It resonates at two successive harmon3tn w,ey3*edfg 2*m slics 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 qefa1nebp:a i2ul 51ib 2 3+ah$^{\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 .gfp; ivifk*hr68fgt um)2*wfor a 2.14-m-long organ pipe arh piuf)*gvmw 6*g .8it2k;fft 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximen cfvv7 y4 c.;)fh(jhately 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 in the ear canal. What is the relationship of your ;eh.f njcv(chy4 fv7)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 w o,vxa2 c;;q(zfxpp l5vp( v7adjust two strings, one of which is sounding 440l2(w;qppvav5xz( v7c;fopx , Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and :svj5rr +1xrs2ilu (v$C^＃$ (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 he*q k;ii*zk x 1pqlhd62a0*h operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by0kh hip a*q6xk1zi;lh*q2d *e humans when 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 sounded with a 350 h la(vy4/2 qs4(rsiev-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Expa4 ( 4 lh/(veqr2iyssvlain your reasoning.    Hz

  Two violin strings are tuned to the same frequengv- ;f pvs9x,)hhgji*cy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beatg;- xv9*fis, gphj )hv frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try ta-zuxdrj +c1h0kf z 20o play middle C (262 Hz), but one is at 5.0°C and the othkz1f0 u xzdrh +0j2-acer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44up9-3 drlv e ww,jj7pt*n8vut ah9/b*jrq 2s91 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 frequencies are possible when A and C are sounded tnt a 2 rvshbw83799eu* j9d*lj/pt,-upjq wrv ogether?$f_A$ =    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 speaker 8qfbo/ phlx lvwh-0ntlz0pu 1 9b7.q2and 3.50 m from the other. 9ohnhl2 pv7x81llqt fb/pzb0-0w u.q
(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 (wb,jgmi +mb5wzr ntp; 8 5:xnat 132 Hz, but a piano tuner hears three beats every 2.0 s when they are playbw +xm:gib5m wr,;n5t8( pj zned 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 wk4hly4 f8j4sm6 : bpo3bo ro2of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be hlj6:bw4 hbop 8mr 42soyo4f3k eard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sip6(y7evj9ho/-)u o yz-olfcfnu +mk3 ren is 1550 Hz when at rest. What frequency do you detect if you 7 (fvjeoycnz-9) hu/ofym3ulpo-k 6+ move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freque3aiq:f ksd4m2/wom9nkb)cx) ncy do you detect if a fire engine whose siren emits at 1550 Hz moves atw mkd /4f: )ian)3bo9kqmcs2x a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20 uy5((as o,, agc(q skkzn8(tp00-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sam,t ao znp c(sy((qk,u 5(8askge? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When onem72u tzrm7v4e is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fr 4 mmetz2vu77requency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason/: oi dlku7tvq wo3qgz7p ./q6ic sound waves at 50.0 kHz and receives them returned f 6 o /q7vg.po/t:3u qzwidl7qkrom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat eiw0u-9h2jd -clf/yd rxube -/mits an ultrasonic sound wave with frequenc e2dw-h cfu-jdyu09-lrxi // by 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was j.)qaur mtm09 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 ther u.j)9atm 0qm train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flo;h 8cx,r,y3ob x 1yff6w7dar(f fj9pfw speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flbh pfr 9;fjf7 a6cr3xwfx doyy1 8(,,fowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavevzb 3 86x(gk ou0nhe,bs 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 sfm6 - lhsj.q(-u,qicyound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are qh-mc- ly sj6qi,u(f. 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 xg-5/ys;urp4e : o pfuits 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 :0w6 (sa/h jod ma+g9g jzteg2speed of sound is 310 m/s (a) What is the angle the shock wave makes0mgjz hgo/ds a(e: +j w2ga69t 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 atq0 id rw4pe rs ,-((ytejpjw;4mosphere of a planet where the speed of sound is onlyj r(de jt0wqirwp 4-p(4yes,; 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 m/s strikes the ocec- lkr/w wp+,d2,mvdzan. Determine the shock wave angle it produck2dpmv ,z+ -rwdw,cl/es
(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 nvz a9;+bysu84 4qhe w9 4mmdw$/theta$ 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 gro x4kz*:h uq8x cpf:.jdund flying fzu84x hd* xkp::.cfqjaster 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 sends o (z eiqe,-o7d20,000-Hz sound pulses downward from the bottom of the boat, and then detectzo-ieo 7 de,q(s 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 human0dt lery9i4 qqsy;min8 f0ok-;x(.o 8z0 mjk i audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Itwbt )02 o app.zw)g.qf consists of many plastic pipes of various lengths, t0)f..a owpbw qgpz)2which 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 threshiki iow05s0tco*a ylfo( +5 q0old of human hearing (0 dB). What will beq5(afl0 5oso+iw*yoik 00ict the sound level of 1000 such mosquitoes?    dB

  What is the resultant szq)(j:wb ibg-ound level when an 82-dB sound and an 87-dB sound are hear (ibj-q) wbz:gd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placedr ya-euxl5 w/9xv.wogt2r.9p;a 1mr y in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assum- grl5vrw./amytp2 xeyax 9;r9ou1 w.ing it radiates equally in all directions?    W

  A stereo amplifier is ratn +1xz:g px:gugm3 b6aed at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powezgx:p61ag: nxu m +3gbr output in watts at 15 kHz?    dB

  Workers around jet aircraft typically gy4xu0dqls23 zu1g eo 5fx(5cwear 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 averag 0xuo3lxsz4 dugey1qcg 5f5 2(e 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 gaiw.d g u//sse32yd4 p9(t8 wt0ct9gq lbhzd)h in, $\beta$ 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 frequenc8,2/0z dv dhyd d)q,m kk;blisy 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 uko6sc5m ldyugf1.9( with a fundamental frequency of 440 Hz and a mass per u 5m6g1dyfsl( ukuo.9 cnit 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 vibratradk7 5o p8kdhq(h85zion 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 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 frequ8dah ok( 7dhqzp58 5rkency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube ii vr8wyz0io1(t::xw that is open at one end and also 75 cm long. How much tension should be in the string if it is to pr0iyow:wi81rzt x (:i voduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop;2s o-.d. ugn(lb qopp ($\frac{1}{2}\lambda$) 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 500–1,ck * -9j ljfo4vb;cii000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the otherc4*,-o bij; cj fvilk9. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. 9yva7lg67m3 : pctbx pOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whvbplx 7y:6mgpa 97t3cat is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. A20jzioby 0rm(4u ,hx gw o1u4ffter it passes you, its frequency is measured as 486 Hz. How fast was the trugbuf4 mx i0jh012o 4r (zo,wyain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spe(i44b 1.uy.gkwqs fa med 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 af.(m. g4b qwy1 sk4iuthe straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, profac 55w+6z.uyv2pp *ydf3wcwy ;:x eq duce a beat frequency of 11 Hz. The shu;6 wyeqcfxf3wc+ a.5d2pvz w:5ypy* orter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as itds()ntqc0lm9-j0ssk 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 the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have pass sdsstj-q0nk() 9l0cm ed him, at C?

  If the velocity of blood flow ifmif eeq c43(hukz- 7:n the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed oq74fh( zm3 cei uf-ek:f $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mgdh,f1b91jsv oth at speed 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 kHz. What is t gjb1vs 9fh1,dhe frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mot0fc d1;a2dn jth. 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 the echo from one chirp returns df0t ;jnd12ac before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38nts v; hir*pa ..54rnw) 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 music;ns 5rnhiv tw* ra.p4.al 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 prbnk, x(uyx+ 4nesence of standing waves, which u4(yxk,nbn+x 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing )0lzzt; nbwp qyi,s- -rods,” involves a long, slender aluminum rod held in the hand near thenz)-z;pw by qsti, -l0 rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, 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 theh 6bm)d:i6vwzb t o02omc,1fo threshold of hearing for the human ear at a frequency of ab,woci0tb)2hdob v6f1momz6:out 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 .frdj, q;t2bzan0 e;wm8 6ejx Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after tj2q.w me86f; r,tnd0bae j;zxhe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat r0*f5 q jbhr+eis 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h