What is the evidence that sound travels as).ihv lro ;hhs;i70mb a wave?

What is the evidence that s8zd;exg)k.zztfash,.w +*ar2z i c 5dound is a form of energy?

Children sometimes play with a homemade “teyy2ijkn6jg2:(l)ao hvq /y/ flephone” 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 heard at the other cup (Fig. 1/nqg(y:2il6 kjjhoy fa)2y /v 2–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expdrle 2s-53gqryt5 jg,ect the frequency or wavelength to changr5 d e,rtq5syl3gg2j-e?

What evidence can you give that the speed of u. w)3z+:4 qsreljmww sound in air does not depend significantly on frequew j:uw) qs+m3 4.lzwrency?

The voice of a person who has inhaled heliu,pt1i6p g5kup m sounds very high-pitched. Why?

How will the air temperature y6qn w0jt5 z9m0q+nr jsjj2h/in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filt h/g5td4cf3 y,uf- yvmer to reduce the amplitude of sounds in various frequency ranges. (An ehcv3-y tf54md f,ug/yxample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog:x /hylnr htd352nkpxv) ( hk:ether as you move up the fingerboard vkn: px y(3hn rd5k/:2lxhht )toward the bridge?

A noisy truck approache2 rij* -yv/;oa),9n knsqlz wns you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectiw-2ns,ljan9*z qivr o/yn) ;k on 11–15 on diffraction.]

Standing waves can be said to be due to u9uyep1y-hn 9u meh2 ;q6-yml “interference in space,” whereas beats can be said to be due to “intememy1p9--y 2lun6uh ; u9qeh yrference in time.” Explain.

In Fig. 12–16, if thlr/ t6; x3 e,g;s r*tnqpqa6yie frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fanqr* /6tq;i y lsg xra6p,te;3rther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas witec9b du )(fqfbk 3b3(m/x+c qkh 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 ix3bk3 q) mf( (b9+ecq/bd fkuct 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 wae(2tfqehbg ,(8yt 90 ydr4ucave can be thought of as a superposition of two sound waves with slightly different qye ufbdy4h8(et9,(t 2c0grafrequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move zk0 :f1 wjh xk3gt*t/5yj6al5bosa f )in the same direction, witw x1 /alf:tbzsg atk y 5of3h6j5)*k0jh the same velocity? Explain.

If a wind is blowing, will this ajq9:g3e0b wkx lter the frequency of the sound heard by a person at rest with respect to the source? Is the waveleq0xk3 gw9j:bength or velocity changed?

Figure 12–32 shows variou pt:n04, gqhac.d7kh ps positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the groah d k.p0np4: ,qhgc7tund. 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 ej:op tuh,txxxkb.i*1c2p/ (of her shout reflected by*i(x bk /ut2,op .h:1xjtpce x a cliff at the far end of 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 jhe ;eic.7ac7 fust below 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 7f.iec;a che7in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength4*ubqn r-e5o/wf8 wivglcn 73s 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 foggy d9kwk ab1c c: ,p /hplw9hq,nmr:ti1c.ay. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. ,p9qkbm1h1 :w can 9pcwi/rh k,.t:lc12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fromj6uig 0imm x-dmje0/ 5 the top of a cliff. The splash it makes when striking the water below is heamgi-60mmj 5iej dx/0urd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sbcx vv))8 ko 6z pn63mne9i(vmees a huge stone strike the concrete pavement. A oe )nb vzim36(np986vx mcv)kmoment 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 di h+l6 g:hj70m/ gnmxjrstance by the “5-second rule” for estimating the distance from a lightning strike if the temperatn0/ g mghj7jm6 +xlh:rure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of fo94n-v0)dw g pgoa:ca 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 levelus63kqyab2 2uw jp1i7 of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously aqz 0bx +;yjm0ot a certain place, wh0bxjyz;m o+q0 at will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain din 0sirvauv2/fh3v 8r39,jl lystance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain i v2 ls3f9l0rj8v r/anv,hy3u shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of pv2. qjb z83sqx*x6ih58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bac6vqq z2x8hj pib. sx3*kground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a *6 unr/dm ep js2f;q:cperson speaking in normal conversation. Use Table 12–2. Assume the sound sprerfm :; cnpd/*je u26qsads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wh0*gwm 3hyc*cnose 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 amplifier B is ramur7v5k2 xy8u ted at 40 W. (a) Estimate the sound level in dm5x2ukur7 vy8ecibels 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 registehk4j4cl s q;5gred 130 dB when placed 2.8 m in front of a loudspe 4 q;54gjklshcaker 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 divp j.tn,7; wqjfference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hjp wqv, n.tj7;int: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inte gmh6pt,y5 m4a zwm2l: 7oado7nsity increase6ym7ldmowmt zp5a2,go4 a: 7h? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tbx*7d uls c drigz9.*q2 31qwghe frequency of the other. What is the ratio of their igqwrsg l.i71c bzd9* qd2x*u 3ntensities?   

  What would be the sound level (in dB) of a sound wave in air that cor*w2 e5xz wh7/ 5)xw.jhh97/g bbpxnr9 wrfaov responds to ow7bn9. j )aw/5wgph59 7/2hv*exbr fxhzw xra displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lxt8emai.(y( d92cv z rm 2rnb8oud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–bv 8c(yz tr2x2(n m .dia9erm86.)    dB

What are the lowest and highest frequencies thu()fe tz 1kcc6;yhjypy( w6*mat an ear can detect when the sound level is 30 dB? (See F;(hzm6 eykfu 16*(t)p cwc yjyig. 12–6.)

  Your auditory system can accommodate a nv h45 f:1roo+0ro duuu pho2xr(/vi:huge range of sound levels. What is the ratio of highest + vuv4r ux5fh0r oro/1p ouhoid(n:2: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 frequency oz +ivl47o8f2pbln x5 kf 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what to4+iz8bf5 2plxnlkv7 ension must the string be placed?    N

  An organ pipe is 112v s ef kgjc3w 66 f4(u.- 14bn(nkqmkb70fcdtm cm long. What are the fundamental and first three audible overtonkmf1f cjkk6b n f3-bw d mnv(t6g4 .qc(7u40sees if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across t1md d1*is+6cx(diq ozn(ax-lhe top of an empty soda bottle that is 18 cmni-d(1lx c a+6xm(*dz1o dsqi 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 spanning the range mir*a, dnrviegt5 53(of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requt5v r*ai3gi5,(e dm rnired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequej uefz tj+(dnj/3ep 5g,e gv,1i k09vency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of f (0v/en 3pj,gzg9t ,djie kvje5ue1+only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tu:o(r vyld12l hned to play E above middle C (330 Hr h:2(ylldv o1z).
(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 org m;g/;flzz rsd,er oc;i e:9m1an pipe that emits middle C (262 Hz) when theiz;zgmlr :9 c o;efd;,ms/e1r 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 )/nh ygp(*jjv1az5kv x-d4bf20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece 8 5t+ j(cneszuof the flute in Example 12–10 should the hole be that must be uncovered to play D above mij+t 5 csu(e8nzddle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hzni+xc5 o7lvqijq . b8mp51:qi, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open m c niq jb:+i7li.v58qq1xp5oor 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 o lwr8qg;,,(wjr w 0awppen at both ends. It resonates at two successive harmon;wlj8w(g,wqwr ,r0pa ics 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 ,pve 4ow2odp)$^{\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 arokj4 px*i*rmrnr8m 8 (e present within the audible range for a 2.14-m-long organ pipe 4kr*r 8(mrjxpi*mo8nat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal nsxdxpdbssl(kc be 7+7,-/(pis approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the informat(b7bpdkx- ,dsls x pcn/e7s (+ion in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one bego5/x0n0 or+ sw4 knkdat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is thes5n4 xk+wnod0 r/0gko other string? ±    Hz

  What is the beat frequency if middle C (0jh(5opf n,uv 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 whistl.0jk o yg2(30 uwcldlte operates at 23.5 kHz, while another (brand X) operates 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 operatld.l3 0ytuwk( cj 20going frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundeq:v4bn-h3 gxcp1qt 2od 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? Explain your reaso h1b43g:qv q-to2xpcn ning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Thewi :1* vmdm;xy tension in one string is then decreased by 2.0%. What will be the beat frequency heard whey1dwv;:*mxm i n the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identica8zi9p d,fq;zl l flutes each try to play middle C (262 Hz), but one is at 5.0°zqpdz lf98i ;,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 o ofq5ee6ati)p7q pwrbj *g9yk .x.4(ezuy f) )f 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heaeuw9jyyirg ( eo fe4*ax.q6q5t ))z.ppk) bf7rd. 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 spexe0ymnm))e8nw *il42leae uqj0 c, , haker and 3.50 m from thej 04,nxcny0*, 8l)m h2 iueel wamee)q 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 sl6x :q14 o)u)(ekcp9 sn4ybzh 9nejis upposed to be vibrating at 132 Hz, but a piano tuner hears threehj1ey)4n:()ul x4se noskbzp96q9 ci 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 2.76 m in air. How manqlz:27 hlwrr 6y beats per second will be r:qlz72h6w lrheard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire en n cjw-dyt5q:(gine’s siren is 1550 Hz when at rest. What frequency do you detect if youy( d-t:wcnj5q move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency8 ms5:0 tbgtmz5)awlw5ob03*j xw6zw.b o ps m do you detect if a fire engine whose siren emits at 1550 5b z5638mjbp bz5m* w0swatwmtw)s og:0l.xoHz 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 source is moving towa/bgzfjj ;q)cc1o*svrg4b. x9xf g6/l rd you at 15 m/s versus you moving toward it at 15 m/s A 41;c q jr)bgbgjx9xv/6.gz/f* ocsl fre 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 equippe;a1mt* 43* sfnpgz unqy:xbc3 d with the same single frequency horn. When one 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. What i sqcxgz13n 4up*m 3n*t;fya:bs the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soux 4oh ao-xj0s ge)ds,:d4esm9nd waves at 50.0 kHz and receives them reth -g4emoasd )sx:4sxdj0e o,9 urned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m//l*6gm(lr gcxs As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in themrl6g*xl/g(c reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler en9v.qeo9w v79 ( gpdknxperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba playeddk9(p vvwoq9enn9.7g the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure 4,f p36wixaldti3duc 4a-. q oblood-flow speeds. Suppose the device emits s ,df4.4puo-6 tiacxai3w q 3ldound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi+z c9),(vegc f r;jwpyng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sou 4ez 30c:w r8si6n,kobyy8 vele( u-xgnd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, cr l4ezyy,xngeb 68:u 0i-(v8so3e kw
(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 spee 0i*jzo,wxh54ie gx)y d at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Wh4;2 1rgs tturs ;f-mkoat is the ug4krro; s - ;12sttfmangle 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 atarjus(c w++m vb *m/ i+ pex4kmv;4do1mosphere of a planet where the speed of sound is only about 35 m/sb mmvx d++14 s ircup(;oj4av mk*/we+
(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 wa47/8e9(vvk p1yd+mvqougqy sve anglevs/1y dvy q4uqp89 v7mokg(e+ 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 dlhbmc f -2t-dpdi38 qqg7-c8$/theta$ 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 t uto h:w7v,-2iw udu6hhe ground flying fastu,w- t vhiudouh :w267er than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a f3xk3 id, k76 yu/1s dao7mhinsonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designedd 7ofin3i a7kk,y muhd/x316s to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are thervsb.-uws c4 e,e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewez67ht)c3 qy0r6 ;qj eojj1vn kr pipe symphony. It consists of many plastic pipes of various lengt 6h;eky0j)j6jrv1qq7ct onz 3hs, 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 threshold of hu:po- *8sn lf3bxyp 2i z bejs 0pxdt1t-*d4uy,man hearing (0 dB). What will be the sound level of 1000 such mosqu3s z f 0ns-udx1ydt*p8p*, jexlob 2b4tp:yi-itoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound aaqr:c yv eam a8e,4qc f1;b-6fre heard svey:emaf-8rac4 ;q 1,a qbcf6 imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, wot*p1e4fe *qiy 5 x6vgyi(3 wplaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all yv61gwexit(54w 3ofpq*eyi *directions?    W

  A stereo amplifier is rated at 150 W output at 1000- yvzi:6a0nyu jox(p )vvm*;l Hz. The power output drops by 10 dB at 15 ki:zx;(panv )6vo-yv y lm* ju0Hz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wearfk,z94h -,1oz d ltqni 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 the power intercepted by an unprotected ear at a distance of 3-zhqi ,9dolk4z1ft, n0 m from a jet airplane engine?    W

  In audio and communications systems, thurhdpk fznm21(*37 *jjhk vo2 e 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 kdd 58ovyrvva, x48u/is tuned 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 betwee m 6br;4xsy+.8siyxf dn fixed points with a fundamental frequency of 440 Hz and a msf+ sxb8mx; y6di 4ry.ass 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 rj ojqkf:y.5:4 cazww z6w)r9-g ark4into 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 forwj4r4 qkgy:rcj6zw5 zokf:.-w9a ar) k 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 5ib a6ut5bm( f*m/bc8 lo1dbya tube that is open at one end and also 75 cm long. How much tension should be in the string if it f/ bol bba6tm5mu cb*yi51(d8 is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one g c z 3)fid8y(d,rx;zcfull 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 ra6k9l/c,*j t wt)vhmbznge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the o/)t6klc, t9v z mhbw*jther. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statiouny:l :wa6c ./hdyay)l +mvo 8nary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the otheml6/cya 8vauy d): + lo.whny:r train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trai-b*aux1swm ; f bm(-fdn whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was t(wu m1f ;-bsmbfdx*-a he train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenixh kfq8rx,wa 0y*2zf(ng 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) a (x* frqk8yx a2h0wz,fs it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sou37ibl 7j acvr6nding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the7 lc 6iav3j7rb other?    m

Two loudspeakers are at oppos )al* lh1jzw pu/5qey.ite 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 listens from the position A, in front of the car, (b) he is betwe/ hajq w*lepz.u5) ly1en 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 ik9 yx 59mnt+47zpfkef2:f 4btczem*rs normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves t mfyz +*7b ft25c:49t rkz4mxf9pnkeeravel 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 t ;yfy/ xxjbm45q7es* ihe bat at speed 5 m/s The bat emits a sound wave ofx;i mxfbq4/sey7j5 y* 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 souni 4zxcg .t-qb*d pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and-q.icb4xzg * t 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 chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpwro5 a2e/0r+h7vu p y0s uyd52.ovzlmine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When playedl5so0 oaey2. uurzd ryw0 vv /hpm752+ 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 o+guht(iedd , j w4,k(listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Considj(e+,ugki 4o(, hdw tder 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, called7af/*kpnh 2o om8ce x(z9 nau aj:5;xcl :ks+z “singing 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,” or emit a clenpl ac mj axex2ck5o8 nosk9/uz:hf*az7;:+ (ar, 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 theu f b a0:3xz2yo 0yl,+zvt3ajq human ear at a frequency of about 1000 Hz 0:ty3a3 ,vfq0j z o+xlyab2uz 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 Mach 2.0gadzkpb 9x 6cb d3o;8n3(+gcq. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overheadd3z( n93 kqdagbxo ;+6c8bp gc. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboagoq4ssp :vma h/3v:p0. t jg5at is 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