What is the evidence that so,6q d.mlno t*kund travels as a wave?

What is the evidence thatvdzaaou gq2* y5ra4fb/p b6. / sound is a form of energy?

Children sometimes play with a homemade “telephone” by aww qb9s,wpolh j93 r( 8n7bnb,vy r2l+ttaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.(bw 3 woyjhlvb 9r, +279wpr8s b,lnqn

When a sound wave passes from air inj*0gj tpcfp p4+vk/ l: plq+k2to water, do you expect the frequency or wavelength tojqkg 02jkt:pp4llc f+p pv*+/ change?

What evidence can you give that a9w:gqk1(8 bhx4ihyba4mg d -the speed of sound in air does not depend significa wg 8:x (aihky1abd4q94- gmhbntly on frequency?

The voice of a person who has inhaled helium sounds very pd*j ms:h0o-6yh8 wp qhigh-pitched. Why?

How will the air temperature in a room affect thelmud e 95w.na-cqhg-c2w9sf6 8(x kga pitch of organ pipes?

Explain how a tube might be used as a filter to reducy1wwug2 cgsrc;uuh )lv3* o)fsd (8g)e the amplitude of sounds in various frequency ranges. (Ano l ug*y)s 2rdf)(v3c8cus wgu ;gw1)h example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clt-/wcd/ye zkj; te8w7;m.sm l oser together as you move up the fingerboard towarkdy.;j/z mm l;et8 - twcws/7ed the bridge?

A noisy truck approaches you from behindn7 ac8kv* 0ra -r*pogs a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear mor-pk*7ar8 c*g ans0vroe of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats ck2nl vea;z c7+hlr .c6an be said to be due to “interference+z;a.ker726 n lc cvlh in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweobe:gqj40r n :red, would the points D and C (where destructive and constructive interference occur) move farther apab0n regj:4oq :rt or closer together?

Traditional methods of protecting the hearing of people who work in areas with ek0en2rqq ;o6l ym4;tvery 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 noisnrk;0m eolt2 q64;eqy e. 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 kiwww*zy 9;30/fglb xFig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly wfiyl; w9zw/b3kx0 g*different frequencies, 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 ss7wsbe+ozw u-hvy/y4u-ft ,6 aa)n9e hift if the source and observer move in the same direction, with the soyf uenvty+u/z9 w6a)w,esb-7 sa-4hame velocity? Explain.

If a wind is blowing, will this alter the frea ikmdm 74n,-irr/0hq7zo o h5quency of the sound heard by a person at rest with respect to toakdi7o0 47/,rhhq-n5z ri mmhe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor 1c pc +ynl)x79 b;8bfmdavtr3is blowing a whistle in front of the child on the ground. At which position, A through E, wil7+pyt9 cl13a vcbdmn;8)b rfx l the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by ej,zwg t.8 ul+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 .ule,8wzjgt +. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below yemmw a ,efr vr3xzn3 vp);,:+z gov54the 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 m35m v;afgewxvrz,p voe)+:,rm ny 34 z/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 209p9tppm( 3x gz $^{\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 qaf uj:gp/708zyl/ fj a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time pa8yq7f/g: u0j l/zj felapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clifcaes, ,kcc)l/ f. The splash it makes when striking the water be)cs/clka ,,ce low is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to thm3pcv(s rz , w ta;w+j7r.mj)le ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Tm;+ 7ltcav( wmrjp 3z)s,r.wjable 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofeo4mf9iyc*j0+5 :ltz/ oy ddj distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30ji:td /ycyo o+d*efm 594 zjl0 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the p z0l z.wp,xe+sjn- 1rrain 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 ou19p)h kp t noh54kr1bf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired weqxyj5y p f7ii8 ka)3or492ksimultaneously at a certain place, what will be the sound level if )wir k3po f9yk 8i254ejxyq7aonly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certad qi2 qcu718vein distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not cq 21dvuq87iedB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for2 q8rie1,kz8cfs bwt) a CD player it sfc, 1wi)b82r8keqztis 95 dB. What is the ratio 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 soundk)( kvo hiym/o qov,;0;-yyrk from a person speaking in normal conversation. Use Table 12–2. Assume the sounqv/k hok y,moi( yo0y-vk r;;)d spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose abugl+qw3m,g 0bk7e nv,ba8) drea 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 tgl,ojlw5 fre7m,q.n9h t 3( tis rated at 250 W, while the more modest amplifier B is ratet5 notle3l , h(gfmw ,7.trqj9d 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 fr )lnl/eawj*oj6(n) vgont of a loudspeaker on the stage./v) annwo(j j6l)l *ge
(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 mo8yy:5pa. yow l,h27vr7takin sound level of 2.0 dB. What is the ratio of the amplitudes of two.vy577a:k ohtar mlp8,o yy2w sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound b8e9qbt z35 a2vpsl5qwave is tripled, (a) by what factor will the intensity increase? Incresq89 b5petlv bq z532aase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal di6 x(liy priy9(splacement amplitudes, but one has twice the frequeniy((ly ipx6 9rcy of the other. What is the ratio of their intensities?   

  What would be the sound level (*eqy ahrj6u- j d5*)lsin dB) of a sound wave in air that corresponds to a displacement amplitude ofds-5 )6je r*yl*h ajuq vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz w.r. 7)ij8(7k/ ec thh*etx)kkvcib utone that has a 50-dB sound level? (See Fr/) k wi)7 k bx(8tj *.iuehec.c7hktvig. 12–6.)    dB

What are the lowest and highest frequencied 1d;hq88rrd g-fbgi/xy 9gg/s that an ear can detect when the sound level-8gg q/br fhd;9gdi gryd1x/ 8 is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wha-gta2, 9q jnnw lby1w8t is the ratio of highest t1 gw9n,qya8wj tbln-2 o 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 fundamentk*d1w/;zmt2f* z n bajal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the s*dmwj1 z *azkbnf2/t ;tring be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first t wwzq x; 4n9c8,hrz qvm:44onphree audible overtmnx9h:w;wzvc o q, r44 p84nzqones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowingi4c0 js bx+2xm across the top of an empty soda bottle that is 18 cm deep, if you assumexc b+2ji40mxsd 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 r-lbpn *, uznd(k+pwwpp;e2*kange of human hearing (20 Hz to 20 kHz), what would be the range ok- bepwp+lp*k(z2,n*pdu; wnf the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 54aue2ag7zc a(t-ovk4cdx . g+ /0 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at o egac a2d/utx7a4+ -.v(zcg ka length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ataj f7if0g ta;k,y,4mbove middle C ; ttyj0mfgaa 4i, ,7fk(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe ubq4 -yf(lke/that emits middle C (262 Hz) when tk/u e-y4l(qf bhe 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 at 20 x;sl;*st1 d8zdla0dj8w1f-y e ciqc)$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of theby;mg v v9ua72 flute in Example 12–10 should the hole be that must be uncovered to play D abm7a vvu2y b9;gove 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 at 264 Hz, 440 Hz, and 616 Hz, b.l3m;k .q8kw 5ii xlekut not at any other frkx e8il.35wl mi. kqk;equencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates a23mhc*)*rslg lob z4fx jut6 +t two successive harmonics of frequencies 27g 4o tl h2+*ur6zb)mls xc*3fj5 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 4qz o4p2l w4of$^{\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 thunm wroq;e9agpb3) 28ym yq (4stp+k 2e audible range for a 2.14-m-long organ ps )923r+2; kqut8m opymapnebgy4wq (ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the:w:g :parijl+ 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:alwj:r :i+p g 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 ad q:jbkw::pk4ttpxwz1jx /8/ qkt-.h wjust two strings, one of which is soundh: 8z-bqj t1ktxk: t /.4:qwpw p/kwxjing 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mr y .9r9221rom0jb jhwxt7fehiddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while a/ dqnyhi8q+oa3 hy ofy2r; 9ojj52xv 1lu87b enother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played se37 2hy abrnyxoe qo1+8v2dfoh5u;q/ j8lijy9parately, 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 b,rs4m+qwjm z /eats/s when sounded with 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?+w/ ,sm4 rzmjq Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension u nz 9bc9ihb)hb .0i4adym)k+in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? )h9ahym9bbi kind0b4 u+c).z [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tr f1 m23o rjed8u(tqdt056oskey to play middle C (262 Hz), but one is at 5.0°C and the other at 2501do d2e5(sq tmo6eut j8 3krf.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. 0nr3o, vd5rnrpf 3ya:Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 0,5radpnrnyov :f r33 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. sao/; vco3x9i A person stands 3.00 m from one speaker and 3.50 m from the o/c ;oxosiva 39ther.
(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 tuner go/;7u oz(mca hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the otheruzagc/o 7m o;( ?   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 wafnbb. 8tg(k7a6ciwkq, e:au 7velengths 2.64 m and 2.76 m in air. How many beats per second will.:w k6atibc(f bg,n7a8 e7 kuq be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whi25jrm2gjhj-;jyg w m d.c.f8 en at rest.2.ridw j8 .m5-;c f2jggjmjhy What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stilke ath 6emyjg.)121 tll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed1ea.gmy jl)6 h2tk t1e of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moviba/;.ln igr .v)puu) lvn 0fj8ng toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactllaif.; n v8).vn uj0lp)/urbg y 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 fna bye: d7l+qxa,e,4nrequency horn. When one is at rest and the other is movingeal7aen,d+qb ,xn:y 4 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 ultrasonic sound waves at 50.0 kHz and recg r:3eowtc24z eives them returned from an object moving directly away from it rt: e423c wgzoat 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 em y 0pe-l8igwz v0 jzwik,;rf-ih*4,giits an ultrasonic sound wave kwgi,ih*zz--4;fi,gyrjp0i80 l evw with frequency 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 played on a*1(7 x yxj0f dc,uspcg moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while atpufx *xcsg( ,0j7ydc1 rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-ffmsj,r i*1u) y;v4xc)c sefs(low 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 flowing in large leg arteries at 2 cm/s directly awayf1rs(y)s4, mi v*)jsfx cu;ce from the sound source?   Hz

  The Doppler effect usi z8 inqg22-3hixq)0f-vlqiblng ultrasonic 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 v)x 5o gj )tiyh(cf+4 djw/8evsound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers oe5gc t4 /j jvivxhd()wf 8)+yhear 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 p4ch+)y )- t,wvc,)n exo1s/nepnuloon 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) What is hg8-- e kcpgr2)o(, ijtissg;yg6q-athe angle the shock wave makes with the direction of the air o-sg;gygi gkaihj-8(- cetrp6,sq )2 plane’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 of a planet where tm7k-7r+c iqw7g 0dlrs he speed of sound is only about 35 m/s qw+dl-rkcm 7 s0g7ri7
(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 thp/yq ki+g2i86s5vjqy e shock wave angle it pr6g j8k/qv +yqi5ypi 2soduces
(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 v8a jeasoli7u;2qj:n g1/ hp9 $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see ai twr/ll i8u*zuju3h5v(+ail9 (0jbd plane exactly 1.5 km above the ground flying faster than the speed of s9+l/ d j8h(rul0iwu5u*(l i jbv3a ztiound. 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 sonkjd3 8nt0 nc:nar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 d n :n0t3kjn8cm, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are t zej9r8l c* er*fzep,*here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a v.or6mhkb:h u/yw fz5)4cpp4 display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, wov 4/4wuk5z hm fp)hyc6 .r:pbhich 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 xeme rs9k*o;( close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such moe* so rk;9me(xsquitoes?    dB

  What is the resultant sound level when an 82-dB sound and t dnc :pi :ylw*f/t6r(an 87-dB sound are heard 6:t w:tcpld fy* rin(/simultaneously?    dB

  The sound level 12.0 m;wi ;5u;zhp m5l,saqd from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiathml5i zawup;d ;;5sq ,es equally in all directions?    W

  A stereo amplifier is rated atfsfj3b,.dbpu+5xj;mv 5 ln8 o 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output inuob;8sflbm pj3+x5v dn5.,f j watts at 15 kHz?    dB

  Workers around jet aircraft typical2mp xiy ,q 9wiyg0njw ;7q9.kfly wear protective devices over their ears. Assume that theiwy9.kq 7 fmwi;2ny9xg0jpq, sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communib( n(atnj1c3 85*m f zup/gjzncations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequencj 1/c y20:s oqsnmd v( nd7bwwo4e..tfy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental lf aorx2 vc3a/i4d dt 9b:k7r)frequency of 440 Hz and a mass per unit le:/92l74 tic3darb)xdf vr ko angth 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 viw( 1mc+ p voeg0ic+,mertical 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 thec1 e o+,pwmvc+0(mi ig 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 fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open +acg j68**on wu x1*n ggexo9mat one end and also 75 cm long. How much tension should be in the string if iaexun *wocg 6m8o9**j+ng 1x gt is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to rk3su(,(t9 w 64ffyq59okmxepi ak6 dresonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two y: dgb qo+iz0)sources. The sound is loudest at points equidistant from the two sources. To determine exa )zbdqg: +io0yctly 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-Hz whistles. One train is stationary. The conductor e.nf( +barxd6on the stationa. 6 f(dn+baxrery 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 ic:p) 91;ow.qg motd zk;kccl/s 538 Hz. After it passes you, its k9z/mw)ot o ;;cdq1 :lp.cgck frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimat,t1l krf r)kn+e the speed of cars just by listening to the difference +1trn)fr ,klkin pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes du xjsed1eda:8vrkp.n28 e +f4fwz20 , sounding together, produce a beat frequency of 11 Hz. The shorter o0vdkep dd8 4a+.28 2:enf 1ejfw zuxsrne is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppositepp5pdx nzacn 7c7yo4d0*6u;ph;p 2 z g ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical soun 774p2dc;ag5p;z y*0d hn pc6 pozpnxud 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 passed him, at C?

  If the velocity of blood flow in the aorta is*v5z7fosktji 3yq ,bab 9+dn+ normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz u 5ya+d 9qf3obntsj*iv , 7bk+zltrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a kj hg9d(uvl+ 2moth 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 the frequency of the wave detected by the bat after that wave reflects off+9g(vlkdj 2h u the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ap y7aiwoa9f9bl e,71 stproaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. Ho 99f7 tl7s oeya,a1wbiw far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals frowww jtu. i8-+w6orow7m one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table .+wjwwwowu-o i8rt7 6 12–3.) Model as an open tube.

  Room acoustics for stereo listening(l e6 9xevnpbrg,)g9w can be compromised by the presence of standing waves, which can cause acousti gpl we9ern6,(vx) gb9c “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 rods,” involves a long, slender f0n-*8z 2udvc0)l szh govqw: aluminum rod he)0ozz h8cnl0vduqg v -*2w:fsld in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, 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 eouzp u s97(z x 81awi1za9i6zjar at a frequency of about 1000 Hz ispua1awois89z7 uji1z 9x zz(6 $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sone) 2ur3-ll rfmic boom 1.5 min after the planlr-f2)l ur m3ee passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1 dgqjyb9 -u2 e:/1jsrwbm-eg25 $^{\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