What is the evidence,urti h;3jh .dx ebo(z/;5al k that sound travels as a wave?

What is the evidence that 2:epdoe) vtvb+ui ;x8 sound is a form of energy?

Children sometimes play with a homemade “telephone /yhr6 dtuyt( zsr53kgd ;a:yng*z 15q” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be (d1rzy krdz/hn 5ts;gg*yat: qy6 5 3uheard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into watenjc 6gq m 3viz996 d( i-f98b:qzwbdaer, do you expect the frequency or wavelength to chang69cdmqvb ( :zjb 6ina9e d8qzwf3-9 ige?

What evidence can you give that the speed of sound in air dol/twh1 c +qvi,es not depend significantly on frequency?c,t wv+ 1/liqh

The voice of a person who has inhaled helium sout;qa( 4 .zydd l k.sgft+/h wj+1 o8bosph9tz*nds very high-pitched. Why?

How will the air temperature in a room affect thciy f3ri +:4v :dl34xu 5igkwke pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun fo*6rx8q w.rpc9 4mwods in various frequency ranges. (An example is a car w8fw r4cqr6*9xo.mpo muffler.)

Why are the frets on a guitar n- d+cq ;gq5fn(Fig. 12–30) spaced closer together as you move up +qqn5ngf;d-c the fingerboard toward the bridge?

A noisy truck approaches you from behind a build.wtd) e4s oev :/el+leu:7i,bpjj;bj ing. Initially you hear it but cannot see it. When it emerges and you do see it, its sound ese e le+l4u;,)d t:jbw7ov bi:jp.j/is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be s/ n+nx;.pa cydue to “interference in space,” whereas beats can be said to be due to “interference in time.” Ex sy;xc npn+a./plain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thep:nvl,if k w*( points D and C (where destructive and constructive interference occur) move farther apartpw( , nivf:l*k or closer together?

Traditional methods of protecting the hearcnt + (fajpj+b3, wx6h-oi 5naing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With(3-w++ afn 6aptnxhjb ci, j5o a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shrxnsv640 u q:9l b4balown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of t6lbavuqx4n9b l0 :r4she waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if fca9gz9 t *g-ethe source and observer move in the same direction, with the same velocity? Explgc -9*ga9zfet ain.

If a wind is blowing, will this alter the frequr c)fogp ;5jk1ency of the sound heard by a person at rest with respect r)5k1gop fj;c to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moni +p3du :;i jqlzrj5+xja-36 nbmme7ez tor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoninnl-+a6+qxpjbei3j5;m 7 ud rz 3jz :meg.

  A hiker determines the length of a lake by listening fu9nn/ obed;s0or the echo of her shout reflected by a cliff at the far end of the l du;nn0o 9se/bake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the02tpl d+q/( )jbljnl2:ejp klw ki/;e 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 / )l(2b/2w+ej l;i ppqt dllk:nk 0jejin seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air 7p;e 4s byifg8ld( o1lat 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 sftqfi6yt :/qhbey 4su/g8yi4hu(5 0 day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Ho :yi4/tthbu86sh e u/qiy4(0 q5fyfgsw much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the w9-mqm9 th.tg r 6bez5top of a cliff. The splash it makes when striking the water below is heard 3.5 s laterh6q.9 rwbm tet-9gzm 5. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr 5ln;4.cpc4 dd5viu-r 1qxbmgete pavement. A momenmdu vd5g;1n cq.4pi-xr 4l5bc t 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 Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dng(5hy7 -tc,cdj3k0ron f7sgistance by the “5-second rule” for estimating the distance from a lightning strike f7n7,c-g goj 0nctd53yk s(rhif the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity if/1ijsy;q p5t*;9 ce1qjnom of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity is x: za7qz(6*-gc(cl ydyu- hcx$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslynd )l,zxkr+f42qi z/fafca:1 at a certain place, what will be the sound lx+a)dr4fz,n i:2q1 fkzlf/ca evel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain d*b lcjma tt *.-ux/bj9istance from an airplane with four equally noisy jet engines is experiencing a sound l*j b*ma9.-ux jblct/tevel 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-nom/grx2 pig2-aht j8cm 4.. vbwise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signalx/2r8ich.mv-mjg pt w2b.ag4 and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perh)pb6o2mv twtnwf7,5 son speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly univtbt)f woh m,72pw65n formly 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 whosmbz gjbg ovffx)2 i a g21t29o4s9tc55e area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplif0ra1v i e(cgu:kc ,9mfier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to eac,9ac: i evk(ugc mf0r1h 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 front of a x zak;xiw3h 91t .zkbe0lc /7ploudspeaker on x.;9 k1ez i lk3ph7wz/xtac0 bthe 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. Wha h+ n2pqc4oc1ut is the ratio of the amplitudes of two sounds whose levels differ bypucn 2c1qh4+o this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound w:k98brwezz 56dhxi4 nave is tripled, (a) by what factor will the intensity increa x85kr:ew dz6h4niz9 bse? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement 2f2ct d vrht.2a53y mvjluz77amplitudes, but one has twice the frequency of the other. What is the ratio o73m 7cz.vf 5tvjar2ud2tyh l2f their intensities?   

  What would be the souym p(0*u+b 9otjz9heo nd level (in dB) of a sound wave in air that corresponds to a dib e*+py90o oumtjhz( 9splacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level41qhq fzfd6, v to seem as loud as a 100-Hz tone that has a 50-dB sound 4f,1hqd6fz v qlevel? (See Fig. 12–6.)    dB

What are the lowest andul nct tp 1p;ab74pj/v2 b6ow8 highest frequencies that an ear can detect when the sound lv7;o6p2 48walp ttb1 cpujnb /evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is tubb 9ov0,n+nwwv2 *a rhe ratio of highest to lowest intensityo rn0wb*w+ 29bvvan u, 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 fundp,casp19sm233x t u rtd6tp8lamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what te,t 2dp8 s c1r9m 36l3taxtsppunsion must the string be placed?    N

  An organ pipe is 112 cm lqit ;f0 ;py;kvong. What are the fundamental and first three audible overtones if the pipe isifyt; k0 pv;;q
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top lhh4lvd bi;v2- 7 gh3tof an empty soda bottle that is 18 732hvl;bhv -htg ld4i 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 :b-cd,xhlgb+ :*6 tnhq wuacx4xz10x spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes reb*4 xd,u+-z:hcgxx:1htxnac qb 6w0 l quired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itgggzwx z5m)d) 5:i. mfs third harmonic. What will be its fundamental frequenc d)g x mwgmz)zg5i5.f:y if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to playfk9ao3b/uf xl/+,re d E above middle C (330d9//okf+ab ,frl 3eu x 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 that emits middle C (262 Hz) whenj2c nhfey0d o3j c9/1v the temperature ij91oe 0/y 2jnf3dcvchs 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 /8ewe20oex p i$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moutcp1)4al/e tpra i3hv 4hpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at pe)a i/rp1lv 4atch34 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 rv 0e)lr) so3apesonate at 264 Hz, 440 Hz, and 616 Hz, but not at any oas3e0prl)) v other frequencies 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 isk t7ieldt 9/+a open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What +a/ t9 d7kietlis
(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 atc3,n8gpaq4e)u1u 7wo/ cdp $^{\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 audiblea ;r;or . qdeac 2 9tf-s74k9gggjwxod2dq24p range for a 2.14-m-long organ pipe 2kfds7 qqpj ad r29w;4 x2 o.oacg4t9d r;-eggat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxzloiu,.qi,in uyw68 1imately 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 standingiy1 q8 ,on6iiul,. uzw 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 sdy5:.pxv7 wq 2.0 s when trying to adjust two strings, one of which is sovy 57 .xwq:spdunding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequenzj3;3 ix ug*3/fzj kt3 -rtrnkcy if middle 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 another (brand X) mv) l +0h.to1:)iep u7pjc ;ydmo-kr noperates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the op :.) yi; hknlmpm- rco0vpt71 oed+)ujerating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when ssp7x lq0jv53 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? Exp7slv 0jsx5 3qplain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension: l. 3bwsc*1*1v v.iyhehek cl in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. l*s1h e vwl*c eck3h b:y.1v.i11–13.]    Hz

  How many beats will be heard if twt. .d v-9o1yp,g x,2fnam s4 fva4vgyco identical flutes each try to play middle C (262 Hz), but one ,4m v,4vpyoa .g.- 9sfngdct1y2av x fis at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whe. fsfdn, rya s,:p,8min A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together,sf8,:ys ,.padin,fr m 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 standspw3u 3 st.xal5p1.nfj 3.00 m from one speaker and 3.50 m aln3. 5wpfs xp1t3j u.from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are suppos or,rctyt2) o+z6mx w6ed to be vibrating at 132 Hz, but a piano tuner hears rmtyt,)+oc 6z2xw 6ro 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 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 2pdpy 4fe()lp 4.76 m in air. How many beats per second will be heard? (Assume Tepdpl y ()f44p = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certai*o 7wz8o bpkp8n fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 mb88 *po ok7pzw/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you 1 xgjf4ra inqf *df ng67/51fhdetect if a fire engine whose siren 1fg /fqd*fi54nf g1 6 7jrxhanemits at 1550 Hz 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 lz(o l c2xg8k*source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Ar*c8gk(l o2lzx e the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the ib;h 1 sigyu.xa93i7zsame single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver atb xia3z.sh;7i91 uigy 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 ulixe m9 -i*d9pi9 omyj.trasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is theom9yjixpd9 .-m*ie 9i received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall mn4p*( qr*s g24z a6r- zg/xeqrk ,mfiat a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequp,rnqf4gmreazm x g2* ( 6- zqr/si4*kency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving eb+spqnpnba2i ,(utrt o 4s:29hn5i ;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 sias2 ; opentbrtq(n4pbu,i 5h:n 2+ 9frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultraso*khx o5z 33n.sqstpe ef03h( pund 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 blpex3hf o5sq zs*h0.p(n3 3 tekood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wa/11mpu c9mmj xves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the w f-k3b4-l3s els ,dsc)bwdf/ h6k0pdrind velocity is 12 m/s from the north, what frequency will observers hear who are located, 6p4db rdlhk0bwfl d )s33sks/-c-, fe 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 it -z /9i9q /xvi8/jybnpfz 8omls 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 iim 0xrk:;io 1hs 310 m/s (a) What is the angle the shock wave makes with 10:xrk; omh iithe direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet w hsckro ;9-kk4here the speed of sound is only about 35 okk49s ;k crh-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 s(kw s+ju6 jgs+).jhxj hock wave angle it prod+jhxjk 6.js (jsg+uw) uces
(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 wr5v v3szn z)( i4u)jo: zzu3j$/theta$ 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 p(lrtt4vzgk dpq8*1 1above the ground flying faster than the speed of sound. By the time you hear the sonic p1v tp8 4g1*trdlzq( kboom, 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 208 s1m.3klzrko5z pd)w,000-Hz sound pulses downward from the bottom of the boat, and then detects e18lm kd5)ps zo .rwzk3choes. 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 2rdfm+aw wu4)there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal6 eo,njm:tpqrb8) eyf0fz3 :jled a sewer pipe symphony. It consists of many plastic r6:o bf,8z yn e0 qjte:f)jm3ppipes 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 fro.r3y4 q1t5bmn3yd*6cnea gu x m a person makes a sound close to the threshold of human hearing (0mq331xnyu5b.e 6ygcd ar*4t n dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound mz4 e47wb6 cmxare hearm67 czxb 4emw4d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What 9 y:c m09hps yd4a*ok0wocb1j9b ov2ais the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?yvw9ao0 omk2*b9od s4 b1: apchyj 0c9    W

  A stereo amplifier is rated at 150 W output*pt6z-38b+ r- a4gn no 2rxr9di carpu at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? p2ronrruxn8p+ 9*3dg -zi-rbc4taa6   dB

  Workers around jet aircraft typicallye1-ax/9qv.:glg s7 bibar kv, wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be gqbv:vg7-sbxi 1 .k 9a/elra,the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatit9/u6z0c5x (m mjpx 0-xy,rp ojbt9tions 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 tun6rtt c2/ y;x2/yigfzg28th yoed to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fn+8.boinrh b2zps4s) ixed points with a fundamental frequency of 440 H )r .os28phz sbb+4nniz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with j7+iurbx qxt 04eb2u8water (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 furx2+ qe7 xb4t0 j8biurequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open aqv1fb t9*.yjpjs0dl*t one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (i d1lvt0*j*9fbyp sjq .n its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wauon,ubth+ wbc1+7vrl:6ra qfj;8i( n s observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. T1kc0 yo j)u 3c;s( c5npd+xye.lwpn8ghe sound is loudest at points equidistant jnl 3gn (58yp ;sp1eck+ u0oywd .cxc)from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz w)kd( pf3c gr2lhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the gpr3ldfk)2 c( other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appr5l:8, ugajf.l klzn gj( (7setoaches you is 538 Hz. After it passes lufkj7el8j:(s.g 5 aglzt(n, 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 of cars just by lip dt26*81rwu ii albe(stening 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 the straightaway. How fast isai6buirpdte*1 l (82 w it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequernqfb lxf2-gb(l tgz c5cl;8( e7j40 zncy of 11 Hz. The shorter one is 2.40 m long. How leq(cr5fz 2- ; gbf8b lnxlcg(7 ljz04tong is the other?    m

Two loudspeakers are at opposite ends of aewm1es 9l cy0mt/3 m9p railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound fr3cpw09yse9mt m / le1mequencies 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 )ka 20ia,m(j6, g j8vpzgr4yz9tfz psis normally about 0.32 m/s what beat frequencs8p 4(zigf0rjmz9avt6,,)zk y a2 jgpy 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 of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward thegc w:z36wy1d i bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency ofc3dyi1: z6 wgw the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound nn-0 w x+vo:kbuz-l(ipulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far-iz+(lo:0 xwnv ubn-k 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) wawxb 2e,)an;kyiear9 8 s 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 musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) i98 b2k; rxye wne,a)aModel as an open tube.

  Room acoustics for stereo listening can be compromised by the presek4l8adh s62ys/1(*d :d5sxoc k lhd dwnce of standing wavok6ss d(x2 lyhdacw81*lh kdds54/: des, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” gf5fq;y+-ccnyt ( ab +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 cg fb +yqa- n(t;5f+yccan be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of a8yug6um7 iqv2bout 1000 Hz isuqmuvgi786 y2 $I_0$ = $1 \times10^{12 } W / m^2$ 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 s(k.25klbb1msev eyn4bv ag 7. onic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? sn.ay.e (1mgke5 vb k4b7l2vb   $ \times10^{4 }$ m

  The wake of a speedboat is:t5qhzrgtd*+ad84 p l 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