What is the evidence that srynt,zhm2pyga om x:,h 6.50round travels as a wave?

What is the evidence that soue ;ai,vruc d8/nd is a form of energy?

Children sometimes play with a homemade “telephone” by attaching s o2 nh* 1 f*xmyorxb/h3k4:-km5nawc 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 t s-2cbahyn5*xnx owmkh3: / kfo14*rmhe other.

When a sound wave passes ff 4 md9w bm+r7*;*jjef4m ysuprom air into water, do you expect the frequency or wavb pdrffe m; 4jm9jms+* uwy4*7elength to change?

What evidence can you give that the 1 dmzy 1gvhs. :p2es6rspeed of sound in air does not depend significantly on 6mp1e1:gyzv.d2shr s frequency?

The voice of a person who has inhaled helium sounds verbmcuc h5opxcttr)64ulae1,g5r2l*8y high-pitched. Why?

How will the air temperature in a;0h jswjb9yl y*o3/im8)y lny room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to re c kjl9io543xeduce the amplitude of sounds in v53i9 jcoe4kl xarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) s484*okrna6 l zo 1slsxpaced closer together as you move up the fingerboaxr4alzsko468 lsno *1 rd toward the bridge?

A noisy truck approaches you from behind a building. Inbinr -dgu0e6 4itially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighte bn 0dgiur64-er” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be duef x1acs1pp083xm0w lo to “interference in space,” whereas beats can bxswlfx mc8 0110aopp3e said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowet 96kkcy*;rb3 8r8ek*nkwmy 5e qh:pmred, would the points D and C (where destructive and constructive interference occur) move f;*ye r9cq 5r:k tkpb nhykm*6ew38km8arther apart or closer together?

Traditional methods of protecting the hearin, q0 5/g2pbl s*ivjhzlxw5 0pcg 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 headis0*plpj2zc bqlw,g 5 /x0hv5 phones 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. Each wave can be takk6. *lp3xte ,dc s5phought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compd3* cx,l6.5speak pkt onent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samwu:w8f lxoqqp.f/x3 h *fn:,ie direction, with the same velf of.p* ::8xqxfq,w hinw/u3l ocity? Explain.

If a wind is blowing, will this ahwn-,f:vj wy 88je;w nlter the frequency of the sound heard by a person at rest with,ye nj8-f wwv;:nwhj 8 respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in9py g6+uz,bjyci vp, * motion on a swing. A monitor is bloyzpbug yj6,,pi v+*9cwing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of a(jnd5m/ms + j)tac:qher shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estmt j(as+5j a/nmd:c)q imate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just beog. doi38n)w) -wxwtylow 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) a xd)n8t3woyo ww.i -)gnd does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aih0jhswd1y7fog4 l1i-r at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day.q-sr2 ;ueqil8kji y3t 2bx. q9m/h7gu Without warning, an 2qj2hbsq 8el 9;3tx u.qr-yui g/kim 7engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it mgfp77vx z5gi-c9gaz5nii c,6q6a .kh akes when striking the water below is heard 3.5 s later. g6vczzc96gf n qgx5i,iih-.aap 5 77kHow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone striksb k4 p,u,kx1je the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the conkxuj p,kb, s41crete, 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 eri yrq i0lan ci-e-g6g*u;-s 2eror made over one mile of distance by the “5-second rule” for estimating the distance from a lightnin c-6 naeq-;i-eriy ul0ggi2* sg strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the painzg(9g pw.xpwt. *5*s4cl vppn 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 intens1 cw.dtsb,cp8qf pv*il 8v5*t -vly.qity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leveq6ua yg1pwp 9(l of 95 dB when fired simultaneously at a certain place, wy(a1upq6 9 gwphat will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fou+v 38 6lr*wltncwjpl(r equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound levwt6p rj l(lw*n8+cl3vel 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 nu kqrr za/))le95dm7 of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise fo)dlanmq9 7 err)5uz/kr each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normzv:mftd ebg 0*q8;n0 92sigiral conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered er0:8 q0i9gbz m *isgnd2;vtfon 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 dsc ). ml4kk8u8 3hvkmr/q-eieardrum 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, krq;v; sqng x1*l)vj, 8; zzmjwhile the more modest amplifier B is rated *jz;;xk lzrnvq, m8j qg; s1)vat 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 placeq5ldr:jq:h7 2)t(f23ax0qfcn e fsnkd 2.8 m in front of a loudspeaker(27 qnlhs2a0t3r5 fkdj::) qxneq cff 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 typically detect a difference in sound level of 2.0 dB. Whk9bhaxq 0rt 6*at is the ratio of the amak0x hq9*tb6rplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whax46gy cn9* y2ress vq7t factor will the intensity increase? Increasersy ge4 vq9n2s 6*c7xy by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitude49bcsh8bt.k4 a. ml*jmrhny0 s, but one has twice the frequency of the other. What is thnr9* jk84yb.b mc.0ahm l st4he ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspondy01ds lcl:( oldge2:gs to a displacement amplitude of vibrating air molecules of 0.13 : cs g01dl o2ydlel(g:mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level bme /fml *c* k)xw- a/6y1xclbto seem as loud as a 100-Hz tone that has a 50-dB sound levmw kb y*xc- c l/x*1)maebf/6lel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the va87 el;g7. pxmk o3dusound level is 30u.vaoe8md kl37x pg 7; dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What isma v.:4 i-pbtw the ratio .m:vw4a- ibptof highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a funda8+ 64 bkgwss.xf wd;8/ad mtlqmental frequency of 440 Hz. The length of the vibrating portion6txs8ag/ .k+dw8w lb4qs ;fm d 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 funda zctwtf- bl2v)7+au q)mental and first three audible overtones t)+ 7wq ut-l)2zbfcva 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 fromrm e -s -gub16ctu6ex9 blowing across the top of an empty soda bottle that mc1 eus96b6rxetu--g 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 with open-tube pipes jjll 9xe)7grs+xj- l 2spanning the range of humanlse9x2j+ r l)xg-7l jj hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic.( edmdqdzo, q4r:z05r What will be its fundamental frequency if ,er05dmqdzz:o d4 r(qit is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is ;z tft2 ezi17z0.73 m long and is tuned to play E above middle C (330 Hz)zizt;2 t7fe1 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 uct)uz nr* eq,55ir,*a3gd t ipipe that emits middle C (262 Hz) when the te r*z*iqig5nut,crd5)3u a,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 rblb.0t(e5in 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofn5a,u* zr t vwt ,+dazk/)yvtn/ zhe7. the flute in Example 12–10 should the hole be that must zwdn ,vvu/y/tnhaa ,.r)k5 tte+ zz7 *be uncovered 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 reso2kpj -85nd rdui;n 0ys*uzuwale. psb ax.7(/ nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closepk *udsw 08und .i;-n5lr au7/yb(ex2saj.z pd pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.8 r,pf:x4 +mkowlz 7u2n0 m long is open at both ends. It resonates at two successik znl 2upmo ,w4:f7xr+ve harmonics 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 ;kga hp+6 -w bam +f0he6r8inj mj2cp*t5kz4 c$^{\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-longvli+meeia ynh(8ui) tz 7:n 74 organ pim7hta7(48inn:e i)vi +el uzype 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 outside an0 k7jg)0l-s ma 1,0qduiq kzjad is closed at the other end jj ,0k1d-qm0 u0 zalg 7ks)iaqby the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2e4 gr(dq5vf w4.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other str(4q 4wrvdgf5 eing? ±    Hz

  What is the beat frequency if middle C (h0/bpq6krvk3qj h*u( 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 laey+du -r /;5)flhi w7a l-grkHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played sepae-w) uh5y dfla7lglri;-a/ r +rately, 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/sty8ie k u -j+e:9j,tur when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What,:ytti 98jjere + uu-k is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings ay ) z7exx*0ys0,zw:ypdepl7 lre tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%.s7*zy 0yeldp:yx ep7w0xlz ,) What will be the beat 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 n9pk c.yaah 3-snjwfq* 6:l,s try to play middle C (262 Hz), but one is at 5.0°C and thf3 6yan,sa:9l-nc .qw pjkhs* e other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 (p0oy )4yc gr7s k5crbHz; when A acg0 )4ky 5s7ryco rp(bnd 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 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 spemoz,xqv p 1ks:i6y0obp :6 wsg0*q,/rlbu -hr aker and 3.50 m from the othssi,g0p w6v0 bxlk6:q:,zuombhp r1 y /* -oqrer.
(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 suppose ., bljnrb91upd to be vibrating at 132 Hz, but a piano tuner hears three beats b9un.lr b j,1pevery 2.0 s when they are played 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 many beacqe/sb*q-t l3ox d v56ts per second will be heard? (Assume T obv qls 65t *qe/3xcd-= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire en.w *(uimln nyfewje -;r9h 0 m+v)bt4ugine’s siren is 1550 Hz when at rest. What frequency do you detect if you move withu)l; rw e+ht9*y-w4 vjeinm0(mn f bu. a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What 0netl3 4rw zle+x6pyep9c-(a frequency do you detect if a fire engine whose siren emits at 1550 H6p43e - ynl0w9 e+crx(azleptz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourciq/fo d+p)owzd ,.m- iepj p3,e is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cld ewj/pfpmp.qi3ioz- ), d,o+ose? $f'_{source\,movine}$    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 one duwolx 02/p/ns 2k0sp is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. Whatpwp 20dxl/ns/o0k2 su is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sou82kd3/tugqozhw0hb 5 nd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Whatzo d52/buh k3 gqh0w8t is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5k0q(7k0zx w6mgls4ai m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequ xgmiq47 kk0a6l(sz 0wency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experi z9xj60dg8 /x,,su wmz+ htbo6j+rmcmments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the rai0d,, huts9jc /j6xb mr6xmw+m og z8+zlway 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 cp dob gy7prh/du:e b+3-8m, buses ultrasound waves to measure blood-flow 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 73bugrcm+ebh,d:-y / bdop8p is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic /f(flb n 5 yw,-phqu*bwaves 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 g4 5.qjt*s rmtthe wind velocity is 12 m/s from the north, what frequency will observers hear who as j4 .*tgtqrm5re 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 20q(t3 2jh8luewqi 2 rlcph(,*b $^{\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 mj9xmvgp 96h5p 1scjg( /s (a) What is the angle the shock wave makes with9( x pgc6mgj vs1jp5h9 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 th+rysn rngy5zky ., 1uzktf .):e thin atmosphere of a planet where the speed of sound is,kyu5):gr f z1nns.z tkr.yy+ only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wwui3r8 g,p 3 yo2o/zu.o) znivave angle ryozionu)2g3/iz, p8u.3 owv it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle / xmbcu91tsrbn4 wyc/u7t 56z $/theta$ 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 g dtuso r /26,rkdlu 9fz2o(4cvround flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horiz9z l /fdsd,vc2u kot(ur62o 4rontal 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 20,000-Hz sound rce 6 74)l7i 3r:9iuejwbiv3foncb-jpulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is d77i)fic :3e6j9-bw ncr rj oi3l vbu4eesigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in tg gcv k+w6,5sdhe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonym4 m 6(kq:maaj. It consists of many plastic pikjam:a (mq4 m6pes 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 thresho.kg a/ d*qrag1ld of human hearing (0 dB). What will be the sound level qgad*/ a1g.krof 1000 such mosquitoes?    dB

  What is the resultant sound ler3m-xs/ul/ xsc3aja . vel when an 82-dB sound and an 87-dB sound are heard simul3ux jacsa //3 xm.slr-taneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What n. zh2ge;gv m4 -jyag/is the acous - e/yahmng2v4zj.;ggtic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpju2;wu;e-hi; b ,hentut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is it,b we ;eu-n;;2uhjhthe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivl ,gl9,styx(be devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power inte glbtyl( x,,9srcepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the ga.h1ba4sm9) cga3.o t*yk9hzof* g putin, $\beta$ 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 frv6ducqd bh 0-+equency 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 ohoo5* *vr f cr)y2ch,cm long between fixed points with a fundamental frequency of 440 Hz and a cfc)hv,o5*2r*ryho omass 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 8 yzsa x,5tiwfqd271f vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when ts 1xf,i87z 2wt5q dayfhe 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 2d 7,dh.pos)u0xf*/t rv ut 9jn.10 g is near a tube that is 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) withr0s dxd vtu/9fp)t*.7n, oju h the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fuh bkw9c qm2*(zll 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 in1*gcr.n cst l, the 500–1000-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 mig srl,cn c1*.tnimal 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 isr, 4 uuk2hkkggx51j7f stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train1hukrj 4 ukxg7gf,k 25 approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train wh ptil2kq42f+r9i-+a m /ppmrhistle as it approaches you is 538 Hz. After it passes/ mf4thairm2+ ppqp r+2k-9 li you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed oflgv; :odc k ;w+q)6luo cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose thcw:ku;ov6qld gl ) +;oe 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 frequency oal ./*1tmooo; gzcf )tf 11 Hz. The solcgfz)1 amo o/t t;*.horter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statr .gzpp v68)9k8hmaghionary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beath 9zmk)vp8h pg8agr6. 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 ccyiwc4 z33gz:fdqvxl ;45cexj-w4 -in the aorta is normally about 0.32 m/s what beat frequency would you expe -qvg:c; jc f4dxxy5c44l- cziez w33wct if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth 40dngz :qfysc 5o(dz io u*:k(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 freqn ygi(o4*d0:sz: q5ozk(f duc uency 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 moth. hv v3wgnhwx:mh nj )g+p- ,pss6tz:) 16t1vvkThe 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 ech6zh6kxs13+,)pn p tv gnmw:vsgt-)vvh jhw1 :o from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sig djne 4 +/wuf7gfga5w1nals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequenc/ewa1n fug4j57wd gf+y 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 compromisedokq3eyk*ma;3p 3. fc 6sy rpq/ by the presence of standing waves, which can cause acoustic “dead spots” at 3y /3fp k;e.s*aqyqko36rm pcthe 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 “sinqll ea8 z9*e1xloq 19gging rods,” involves a long, slender aluminum rod held 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,” ool9qx91 zlelea*1q8 gr 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 inp/oq (*gvg.+weq2tat a frequency of about 1000 Hz*/ne2 (gvqip.qtgo +w 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 atv4kt:rt.3bt *ww; qjanj 8 pr, Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly :.wb tjra,tnk3wjv; 4*qrpt8 overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat h4 v 7ic0x0e(f lc;fvais 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