What is the evidence that sound travmwx 7-v ih9r ,cyzc9;vels as a wave?

What is the evidence3v/4-d , qkmxyfvd -zs that sound is a form of energy?

Children sometimes play with a homemade “telephone” gi1t 5wj,oykujyf7k0 gb ;/e*by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, thj07bog1ykku, tg ye *fiw;/ 5je sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expe;tu hls u95uu x77bz9njzl.i+ ct the frequency or wavelength to changzuzu 5 ist7l 7+jx.unuhbl;99 e?

What evidence can you give t8 jw be8kw*d jdo+/rg.hat the speed of sound in air does not depend significantly on f jbw8ojr*+k/d8gew d.requency?

The voice of a person who has inhaled heli y)lpzx7t9++z ;tfrjbo9eof )um sounds very high-pitched. Why?

How will the air temperatug k3g5 np/pu2darz 4+tre in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the a93i tgk 1fu2bujv;h 1hmplitude of sounds in various frequency ranges. (An examplfkut iuj91bg321v h;he is a car muffler.)

Why are the frets on a guitcwn/jwtg0mmk bbow1g d0)n 6a7- (t;par (Fig. 12–30) spaced closer together as you move up the fingerboard towg p ntbgb/mt)wc60m1wd7 nw 0 -oj(;kaard the bridge?

A noisy truck approaches you from behind a building. Initially you hear+.rkhf 8l )ue74txi zy it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectionfl8ht+z )iu.7 y 4kerx 11–15 on diffraction.]

Standing waves can be said to be due to “interferenceq +*band fz9c0c+apfcp-s9t 3 in space,” whereas beats can be said to be due to “interference in time.” Exp-3d c apf*s0tzc+pfbacn9q+9lain.

In Fig. 12–16, if the frequency of the speakers were lo5p uapd tk xb o3d2e1r8;c,e)hwered, would the points D and x t5k23)r cad ,d ;8pb1oeeuhpC (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with4 fzde3t /dab3 very high noise levels have consisted mainly of efforts to block or reduce noise levels.d zdatbf4e3/3 With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sun4u.i08dum rd perposition of two sound waves with slightly different frequed id08mu4.n runcies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift v33ypwcd pb.ky*v 9-unkye u93o i,o2if the source and observer move in the same direction, with the same velocityn-.c93p 92ovypbk*wvd 3yky, oeu3i u? Explain.

If a wind is blowing cfwtb,4j 61l2xzf6q k84m wtj, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is tmjb 4cx6,qf6 kljtz8f1w24t whe wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito b h47idh ppe3vg4m*+ar is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highesmvhdphiba 4*7e+p4g 3t frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echop4n0sk yjny4 (pyz-r3epyv67; 8r ct e of her shout reflected by a cliff at the far end yjnve r e(4r367zp8ckty; pn -ps40yyof the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He he,73yn-3* c v ,9zhvc6 zfju9fvkc/aj ef8mn qwars 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-fz vc7h3jacq*39/zv,kw j, 9fc nn6efv muy8–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthg+ wqm41 lfi z;may81fs in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a fogg-1k ntf+e b fu+u* fui*wkj7g2y day. Without warning, an engine backfire ukb1tu-efn*wf7k i 2fgj+u+ *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 makes when striking ; ,kwo(on/zwjthe water below i ,kw nj(woo/z;s heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to tfv9gei oi 6lv f cdra2d2c:1*/he ground, sees a huge stone strike the concrete pavement. A moment later two sounds*d1 cif/e d2v9a ilorf2cv6 :g 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 distance by the ha(scu+ ;ne.yx +24mb0rfshw“5-second rule” for estimating the distance from a lightning strike if the (0;ey . smx wnf+rsc24bah+hu temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level op(+x 0s :egfvrf 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 int7fza 1cmz3 7mbensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultani1 (u8n-pwkqmeously at a certain place, what will be the snm1wiq -8(pkuound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanetcd0bu )v 3hi5 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 )hud503vtibc all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereassxu+)k1p l ;pr for a CD player it is 95 dB. What is the ratio of i1k;lxurpsp + )ntensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal cz -off) 02ruy;: on5a4t3kpvzdzq p6conversation. Use Table 12–2. Assume the sound spreads roughly uniformly q4rc o5)ffz z z0py3p2dan;o-k:tv6 u 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 area8n )5tm1ai:ymyavsnwfz i, wr1+/loam6lq13 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 th.9 cy* zbz*ekg0yfzq 2e more modest amplifier B is rated at 40 W. (a) Estimat0y2zzc9eqk*f z . *gbye 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(v e)m 7r6m tyter;, ywuw8k2w 2.8 m in front of a lou; ttmmr r,v w7w2yee6uk8()y wdspeaker 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 ixr vj- b;zwc (hti1*8r o4rtq+-t kw-a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sxhv1*i8kb4 c ;r t- q-wtjwrt+i-(zroection 11–9.]$\approx$   

  If the amplitude of a sound wave i) kjf+xha.z,topl1v9c ci 6y9 s tripled, (a) by what factor will the intensity increase? Increase by a factor o lic h1ap9f v.k 9ycjxz)+ot,6f    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but onecp7 9- 10cllkxvop:vf2nymh3 has twice the frequency of the other. What is the ratio of their ik o pf97nyl pl0c-cmv:3x 21hvntensities?   

  What would be the sound level (in dB) of a sound wave in air 3onyauoez; s4k g( ;qd/7u3 ; fvt,a1d(hkcrsthat corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm aov ;31ny s3zr 7/d hae4ku;ks ofgq,uac(t( ;dt 300 Hz?    dB

  A 6000-Hz tone must have what sound level to bi eq n:nh01*- dq s qlbkv,(gyo:b)s1seem as loud as a 100-Hz tone that has a 50-dB sound level *s0bqd) y ,bhkbne1 og(q vl-1q::sni? (See Fig. 12–6.)    dB

What are the lowest a2ei twck/v k:1nd highest frequencies that an ear can detect when the sounckke12 i:tw/v d level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound level(ap149 4o/qikpg zxpmd md. -qs. What is the ratio1dxa(4pm4 / pz- kgpdmqi9.q o of 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 fundamental fre w 8ztvo-ag))oquency of 440 Hz. The length of the vibrating portion is 32 cm )w) ot-8azogv, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental anb t rg tw5g*e207n(;fv6 idjgod first three audible overtones if the pipg6rte ( f ;njtg*0oi7vb2d5wge 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 lvw1)h v:pr g6j4 3shgyou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if yh wgl6:3p1v) vrjhg4 sou 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 *gg vd+mk711eo 0.ofwvlg* gia pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what woulg+w move1og7gig d.lf1v0k* *d be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hadg/r/a ib+ b2bs a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% oa+g/bb 2/bdirf its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunxm3l uxu /yy-0ed to play E above middle C (33lx -3/ yuu0mxy0 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 piktv bwcn:.foas( 5-)ppe that emits middle C (262 Hz) when the temperatupsf.bc:o-tn(awv5k )re 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 ctfc.qc589r 6s-;lnthelm z2at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shou( e9e3nk2ot lcld the hole be that must be uncoetn3c9l k2oe( vered 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 v*olfj: 4be v2nha)i-7;q vn wcan resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frfnliv*e2)vn74ao;-:w vb q jhequencies 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 k mq6a;u8j9 zgopen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is8kqug m;96jaz
(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 8p1n3 :v) pxlks fpz/d$^{\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-,/ i2bgh) a 63zg u+yc,xazjxm;+nscmm-long organ piu3jzmxch azb+/x)gm+yn2 ga ,s;ci 6,pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apw zb(68 ix/q r5a4hgnoproximately 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 in4 65r g8aqbohw (z/xthe 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 2.0 s when /omaj( )rdk6w trying to adjust two strings, one of which is sounding 440 Hz. How fao/)jk ( 6drwmar off in frequency is the other string? ±    Hz

  What is the beat frequency ik1b bxvz6oy: :f 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) operau j9/g5-lnbthtes at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine5gt lbjn/ -9hu of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soun -zxki b)cdttvyl,j xd(3d 114ded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequenclxv t)dz4-x jibky ,3t1( dd1cy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in-lmxe: g h6ro 44y6 ;rpuedj2m one string is then decreased by 2.0%. What will be the beat frequency heardm p;e-42: 6oyx6rg edrumhl j4 when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eac n. +bjb *.m1rof2ebenh try to play middle C (262 Hz), but one is at 5.0°C and the other at 2mbb+.j2n e r f*o.1ben5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz;+9hnf(jhn.pj dj 8o9 n when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible phn+ .hf9djn9j jno(8frequencies 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 7t/ hk *uxt5qe3.00 m from one speaker and 3.5xk ueq5 7h/tt*0 m 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 supposed to be vibrating at 132 Hz, but a piano ts,ndjn,(u; l6m o:wx guner 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 othegj;wln ,:, sou6(dnm xr ?   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 5/ t0 v ),aalqpl9ub8 olwk7ckwr;s0z and 2.76 m in air. How many beats per second will be heard? (A, 5ql9c sb0wk w)r0 alva;8lok7z pt/ussume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a f hvw )gjw*-o+certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you gv f)wwj*-o+hmove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect ife3 nj g8lo:lz5m/he 0q a fire engine whose siren emits at 1550 Heglzq :hm/no0 5l3e8jz 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-boe+e7 zt9:0*5htfp3 tbcj cgHz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same?t:e0*5cghotb +9 c3fz7b jept 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 th9b02o,gtv i u(o btnonglbz )kkr75.8rdu(j1e same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the dru t8 zb(nrdvg0 u)ogrok7ti(b9j1n5b kl o2.,iver 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 receives themgbnjxf2 u bd-++0zq:s returned from an object moving directly away from it at 25 m/s What is the received sound frznbx+ b: dfq j-+gs0u2equency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 tppd.4e+ (osno9zxb; m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in nb94p d(o.s;epxo zt+the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experi, wxzoh3l5a t1ments, 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 railwayh3xo5t l,wa 1z 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-flow speeds. Sa.rwcbme( 8 x0uppose 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 laar xw 0b8mce.(rge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrak2--ht le h,tyre;qqc) mwh)/sonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound (s v r9ep 5(c ctx7nfiks,*u3qof frequency 570 Hz. When the wind velocity is 12 m/s from the norskpue39(57(vf s ncxi* r tcq,th, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object mm,nx swf8*.ab h ik9j9oving on 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 mt r7d 6zsux5-nzpecr. k0-:yjo.pt 9f/s (a) What is thxz 5fysr tz70opn.u 69p-jkc:r. t-dee angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a pl e.0*kb2-o jjefrub(g anet where the speed of sound is only 2jbebfj-* eu(ko 0.r gabout 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 85w inx*w1yz;u9 h:f3v b00 m/s strikes the ocean. Determine the shock wave angle it vb39z*x uhyw :1n;wi fproduces
(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 y,4 a-xp /vpei$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhatdg0 q5 e90,vz3l ryvead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic 9 3qvzd 0gtyv0elr5,aboom, 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 20,000-Hz s;ohxm2yfa vxszkyoa6ty121g2oc6 6o u*7bl3 ound pulses downward from the x;6xbso6mvzahoyu1cy23 7o 2tao fkyl16g2*bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves art8ksyqst7( ;45zjs zm e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a ss up aeghyaz:8:l(56,n;czj mewer pipe symphony. It consists of many plastic pipes of various lengths, whichl zjcy 5 6:aen8s(;a,zum gph: 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 frof9l+b 1)d yfshck3u 6hvr72mgc*x:itm a person makes a sound close to the threshold of human hearinbic9tvy cfslf6 ) 1+u3*h:h gxrd2km7g (0 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 snz1 wq,bsf fm0hw7ic86ph 8m- ound are heard simultaneousmc i1 fbfmsp- 7zwh6n ,q08hw8ly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1p; +4hfjizgxpw 2m4c .05 dB. What is the acoustic;h2zf ijmxwp 4g c4p+. power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops a wj831,(knlzt 7besdq;5wqc by 10 dB at 15 kHz.cq5qtnbzd 1 w(,; 8asj kw3e7l What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovey o+g,/ bauem+6k+ lkrr their ears. Assume that the sound level of a jet airplane engine, at a distance of rk +/o6yla ugkb,me++ 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 communicaj-bc/*ihpk;6m.dso ytions 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 tuney wa2bedf5.vze;le 3 7d 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 bet;kq*c-at 4:v .q7 qeq8nd y-wp ccxq/hween fixed points with a fundamental frequency of 440 Hz and a mass per unit lenk 4/v:yt.qxc*c--cw dqaqqep 87 ;nqhgth 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 tub) 9xfmap+4rfue 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 thepmf )9rx+f 4ua 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 thab9 cy+g *gjmzg-:gnfx31 .fv5ac oh*at is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resgfghy n **fmj5- xa.9za+3bg:c cog1 vonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lo v/xl )u(ua1juop ($\frac{1}{2}\lambda$) 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 comzi4)g sjf5c34vulpp,l1-qe6l)kc1r ja ) yaking from two sources. The sound is loudest at po)u i6lpvz5 -aqp y4jgr 4aejl fsl1,)c)31ckkints equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary1h+(1mkc 2mjt jfc5d q. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train apprj kq1h1(c+t5 cmm2dfj oaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches youw h1 1mn2qk9id is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?qidm9kn1 2w1h    m/s

  At a race track, you can estimate the speed ot :pprg7j6gdy7p pt(4 f cars just by listening to the difference in pitch of the engineyg r7t4:p p dptpg(6j7 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, sounding together, produce a beat frequezdgu3 f+of 1f a-2 wrm0;qguh7ncy of 11 Hz. The shorter one is 2.40 m long.;g1-ozru0mdfgw27h 3+aff qu How long is the other?    m

Two loudspeakers are xxr;wr.ncjfqc 5 c4+970afj fat opposite 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 sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he liste4.c7cxnj0q+ 5fcwjax rf9f;r ns 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 blouv 7olkso4 47ood flow in the aorta is normally about 0.32 m/s what beat frequency woul o7kols7ou44 vd 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 sp p,px5ern4 : ;utrnlm.eed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat en;.r p e,: lpr5mxnut4mits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches y24 qt,fy jso*a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next cf*q,o4yyjt2 shirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals zjj1mk ,mkox-f)z 0q2 from one Alpine village to an0j, - fz2mkz)xj mk1oqother. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening cq11g frs3(m 8bofzo.y,0 cwkzan be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frq fz oc(ok3z8b1y.10,rgs m fwequencies 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 aluminz c-6,o -yujalag;8 +agivelk*m gv76um rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, t c8v-mo ajizkg *;a-+u7,lga6lvy ge 6he rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequenc.7bcn6l uo, 0wgt i3rey of abou 63beotgwun7i.,rc0 l t 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at xm; *)qav;xthMach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altituv hq;x*xam);t de?    $ \times10^{4 }$ m

  The wake of a speedboat isne(pac rq)0cf ea5:e( 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