What is the evidence that sound travenon z,csl,c*5o ;;sgrls as a wave?

What is the evidence that soundzc 8u0jq6qeorf e+.x/ is a form of energy?

Children sometimes play with a homemade m 5* dniaq3rr:“telephone” 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. 12–29). Explain clearly how the sound:35qi*d rrmna wave travels from one cup to the other.

When a sound wave passes from d.*f zi,y oat)ivxw a79 ig.(jg g/u6nair into water, do you expect the frequency or wavelength to cha d)g fng aoi/.ajt,yi*x u.7z(wig6v9 nge?

What evidence can you give that the speed of sound in air does not dependq j ,)p q.q)s9-wj f68vejfcji significantcw,. pje)s i6j9fjvjf 8q-qq)ly on frequency?

The voice of a person who has inhaled helium soahl:a7xh5a mvsa;r9.1xgy0 a unds very high-pitched. Why?

How will the air temperature in a room 98:)wq/9bdvrw fq r4 vtvlvs2affect the pitch of organ pipes?

Explain how a tube might be used dl8q sl4kri/ 5as a filter to reduce the amplitude of sounds in various frequency rangk/d8sq4r lli 5es. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethe-ombxc0l+ 0z cr as you move up the fingerbocc- xmb z00ol+ard toward the bridge?

A noisy truck approaches you from behind a building4 f-ru 9qiukcb.6u nhcy (r)p4. 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.bu y (.9 6nki)cp-cu4hrru qf4 Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferen*s 84osdl e-g)kj:mzsgi .*ncce in space,” whereas beats can be said to be due to zl gm)koi. s:-8*cnesg4j *sd“interference in time.” Explain.

In Fig. 12–16, if the e vu6bbidq6bzv 1g./4frequency of the speakers were lowered, would the points D and C (where de 6vu/zg1.dq4bei vb 6bstructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectingheh9gi;p; f szc:c.yr2 5i fd* the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reachin;hp2dr*.fs; c zf9ghyi:5 ceig the ears?

Consider the two waves shown in Fik gkvc)r+n)w7fol36 0g twa; xg. 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 the waves, (a) or (b), are the two component frequencies farther apart? )v70w36 +n; grk gwaftlkxc)oExplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in th) 1uqn fybme:6e same direction, with the same veloci1bnefm6y q):u ty? Explain.

If a wind is blowing, will this alter the f q2hdb,a; hp,wzb.b1 mrequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocit1;b dm2 h ,pqzab.,bwhy changed?

Figure 12–32 shows various positions of a q uuz+l80h( ekcp/f4w child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, wuwk z lqf8(p/c4h+ e0uill 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 f3e8ly8a ph5kt or the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the8k a5p 3yhet8l lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of n5hks97g2:rfxktu)u obgw.pv 83e t +his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly b.39+x8:hfk) ubvwts2n75gk tg pouerelow 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 yed333gz*q: z35uynkrl x )to$^{\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 driftingq-bf/1c zl-q:uniw-j)mxqc8 just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awayc m--: j/qnq b 8z)1xfui-wqlc (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(/::wsv hl lap.:;qpdlcd ii . of a cliff. The splash it makes when striking the water below is heard 3.5 s l ld.p/ :i;dqs :.pc (v:ahliwlater. How high is the cliff?    m

  A person, with his ear to the ground, senoxspqxo9 (b3iu td 24r4:5ac es a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? Se9r u:x5 asnxt23io do4b cpq4(e Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent errosbxj)r 2 e4zl w 9+z+tdw0dom6r made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperat6xzz2 wr wdosl49+ejtdm+0)bure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitd7z4ztxdy4sv0p j jhk2e2 x-9 y 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 levelucue s sst;-(x ;7ou;o of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 97j yvva9f-i:i 5 dB when fired simultaneously at a certain place, what will be the sound level if only one is e ivjf- 7iv:ay9xploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally*h7hi5c6ofg u65zz ch noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if th75 ugh5izco6fczhh* 6 e captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 s,.s6nw::0niesqxk 4sdce /p 8q2oeg dB, whereas for a CD player it is 95 dB. What is the ratio of ixseoc k8.qdws26: ,q0g ne4/ne: ssp intensities 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 pi:dr gnviokr p5e/uvw +4*6 (cerson speaking in normal conversation. Use Table 1u *r gwdo5c : vnie(vkir/46p+2–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes adki+3k tt6izo0o1i9 gm if8+kn eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, :5dqk3e;.oo mor1mfz while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poin.o:m ref3 om5ko;zq d1t 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 r a s2owfekzns((mwrn2+h0d :,egistered 130 dB when placed 2.8 m in front of a loudspeaker owrsm k0fw(a s(e o2:+,dn 2zhnn 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 differeh9a 68se 6cc*r(ad k.oel ub/znce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:8ad9r(/h6 u a6lec*o.kbszec See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilaa2zo hq :b:;z(c/l )f7wa qyql the intensity increase? Increase by a factobzq q2h:(al7 fa/c :qwo;)yzar of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amxl+ fj :.w(i .e+0o fbqxoao-hmsd:t ,plitudes, but one has twice the frequency of the other.+0x l qo.:mxo .- dhfis,w(:tbf aeoj+ What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds to 2mjw(kxks(k0 a displacwm2jxk k( (k0sement 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 loud as a 100-Hz t)63ltpneer ( tone that has a 50-dB sounde 3(6)lntp ret level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can 3nu9hmxl9 n lp u3+r*odetect when the soundlx93 n3mrnlu+hpou9 * level is 30 dB? (See Fig. 12–6.)

  Your auditory system can 5 /nsr5v4,nyr5e 5go ut wo-viaccommodate a huge range of sound levels. What is the ratio of higyuov4svtr,g rn 555/eo wi5n -hest 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 viixkk*z16 k iz. yg l6j3m9s,jiolin has a fundamental frequency of 440 Hz. The length of the vibra6z 1kz*g3i,sk jix mklyji96 .ting portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental andd fb9k/prq5ds66 .hdtj9 zr /c first three audible overtones if thh5sd9 dkb/f pz/rdq6jrc96.t e 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 the top of an regka0f(humz v63 e1 2m3o )hcempty soda bottle that is 18 cm deep, if you assumed it was a closedauh10efz3(c) 3vk2g 6eohrmm tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a p4sa owd8e)n h5yz2e2sipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz) 5o8) yea2s hwsend2z4, what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz af 1 gz9bnniu+a6/eb)qo,3xx is its third harmonic. What will be its fundamental )o9innxbqeb3 g ,61zufa+ /xifrequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar stu*fyhg93 4h v (lqnher)xa-,e ring is 0.73 m long and is tuned to play E above middle C (330 Hz)x e3) ye, *ah4 nlhuqhv9(-frg.
(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 or(aaxf+cqnd 0o j rts(,b89gj4gan pipe that emits middle C (262 Hz) when the temperature is 2j8 d4 r9gatb+(fcj qs (0xnoa,1 $^{\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 av/3p:p n4iezt t 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 should th7 xv-n(w*d 0)lfooz4j c d/v fcl-tn1xe hole be that must be uncovered to play D above middle C at 7* z x-dn jov( /ff10xllv-cwdo4)ct n294 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* sd3suqyqork+:* ;d j Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wy*d j3q r+:us qsdko*;hy this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It recebux7+:oiv+m nj 6 z)sonates at two successive harmonics of frequencies 275 Hz a :n cij7e+o+vumbxz)6 nd 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 v*yphl -1e6a(-psav a(* jhra$^{\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 fo/4mpu9v gfij(s mz p1(r a 2.14-m-long organ pipm 1 imz/g(s9uj(4pvp fe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is usu)01 7dopkbam )7ueapproximately 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 b71uueso p7)m)k0uad 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 everq01j : d/ r3ub)hwryynx0 0sxmcrr)5gy 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How fahw: 0 3qdr)0)5xyynmu rxjgbcr 0r/ 1sr off in frequency is the other string? ±    Hz

  What is the beat frequency if6k.qunlfb0n4(i3;xvhxw ) bw 09 oaw a 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) et t*p sy.10xx:a5dal operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine yp:xt5tad*1a x0sel. 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 s2q -7fcqe g;(;xgqr glounded with a 350-Hz tuning fork and 9 beats/s when sounded with ;legqf(2;q g -x rqg7ca 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to40w:,jy hm o.cignqh: the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playe :yj4h:, .ohgnq0m wicd together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twokkmkoc5(8 k rr,* 5qdi identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othe58kk(qi* dr kckm or5,r at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; owzfix6pn3 -nr01qe 0when 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 frequencies of A and C? What beat frequferonxi q 16 0zpn-w30encies 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 speakp2 (cki0vsdgs1 j2/q cer and 3.50 m from22jc(d/pci0sqvsg1k 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 2fg)so8 lab90b yaqlj h9 9m0gHz, but a piano tuner 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 g9 as )byg8 902ohlqj9bf0mla the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many nq5a8c7o/ na9z -jqt pbeats per sq5qzctj-on/ np9 8aa7econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a5ks-buzabjj:r9z0pu e4 7g5g certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect ifgg5a5p j9 ks- jzbu0e74zrub: you move 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 if a fire engine whose sira2xk nwc2e v 4oh,eawa :6k:e/en emits at 1550 Hz moves at a speed of 32 m//h2a e2:k4 :ow,axvkaceen w6s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcxrppufnz.w7 3-z f8y7 e is moving toward you at 15 m/s versus you moving toward it z78.rf7znupp- xf 3wyat 15 m/s Are 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 same single frequency hofmx bp(51xmm. 68wos rrn. 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 of5pw(omsrm x 6b.8 xfm1 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultr pmef.07fecb) 9e go*xasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fce*9 xo0 fem ef7g)b.prequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall a 3;ud4n 4.gi krs jq sq/d8nxn/nx*,pkt a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freqk4 q njrkx.4g/8s nd,;/n 3 *xpnsudqiuency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubas99is ddnhq4e/kpf voye 60/; 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 railway station. What beat frequency was heard if the train car approached the station at a speed ofkd6/9 qs4 p/d h ofieyve0n9s; 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measu9- ig6) ;nerb7nam)+o w, 0z, d0phnfdloykuare blood-flow speeds. Suppose the device emits sound at 3.5 MHz,; p)z w9e6)+ ndaf0 hd7b 0gloni,roa-uyk ,nm 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 using ultrak*w b,)i u8jh mep1dy t44fh7asonic 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 of frequency 570 Hz. When the wind ve+a4aav0* bhf tlocity is 12 m/s from the north, what frequency will observers hear who are lft+0av*b4ha a ocated, 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 49fr)*jhzhoqx.jkp 4if 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 whli 3qh uf278cbere the speed of sound is 310 m/s (a) What is the angleliubfc8 h372q 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 planet where the speed onsuc5a rvh63pwa5d1 )f sound is only aboutuwac5 hn 3p)rv1s56ad 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/h985t, rv euees strikes the ocean. Determine the shock wave angleeh8v u, ee5r9t 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 k93c cndwe-53c3i wm9xtdik5$/theta$ 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 exactld9fs:tumd6hk5tbh j09 h.j9 o)nk (+r4xm r way 1.5 km above the ground flying faster than the speed of sound. By th.9m ( rt9mw: bdux9)6 j5tjhha f0+noskrdhk4e 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 sonar device that sends 20,000w(kz+v6ttitv4fqe+ o x j 74;r-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimurit7o(+qx+vwv te4fzjt; 6k 4 m time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rab:-v2jmgx(po-1 fbf ndts- x(nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dispd 75ujtu q8s u47.v x7iymv:cp 5cef,ulay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open onvscfu8u5pucm7iv j4 :uy5d,e q t7. x7 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 t* iqhn +y cq6h-80ljyeo the threshold of human hearing (0 dB). What wilye0h- c8q yq +nj6li*hl 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 are h4cf9h3+qa cbqd /l -+u up4z)rf7qrcpeard simultalbd q7 cch3pq4/r zc9p) raqu u-+f+f4neously?    dB

  The sound level 12.0 m from a loudspeakert6)a r5lbg y4h, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?bra56h ltg )4y    W

  A stereo amplifier is rated at 150 jt3gyffjvhnpb k*6 tv9m6+1+ mco4+qW output at 1000 Hz. The power output drops by 11ct+b3jv nfy+h pom646vkfm9tjq* +g0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wc*btm/;b ure (ear 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 ha*brec(b m tu/;s 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 communicai b 6v-y+pq *q.9ueuc,0mo zhq3oiv7ztions 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 tuneww/) w2sv1nh5 w n*luid 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 fixed points with a fundamental0dpu/rwiurm.6,bb g5 / wwe2 u:x) wzt frequency of6wmu2 gu :r/brdxp/eu 5.iw)0,bzwtw 440 Hz 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 in p: eafsji07w6to vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again w6i7sap0f :je at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mac 6sllrr-s- b65uzcaxaw3 z(zdi0 9pbt lu)(2ss 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmou(bldr--bx(zslra9pcuw 6t zz32l 65 asc)i 0nic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsewm ,smnw73r3u z0j c ivj90ny;rved 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 t.a4w4z0wh8enj 2 acd/o;dt w:g;csw jone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exacej taw .aw4482cwo/ wd;d:ng s0 c;hjztly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the s:ly(,1syjgfk fnw r()tationary train hears a 3.0-Hz beat frequency when the other ,:(y gjklry1w( )fnsf train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam tracnbq(l0f ,ppmnrb-,+ uy0) i/y du3mwin whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume/(0pn ymrm3ulqu d w0)i-pb f+b,,yc n constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenh;bcqjz ;mc +-ing to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops b ;mjhcz+- ;bcqy 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 freq8i.9/mpm1 cd 1a xkalluency of 11 Hz. The shorter one is 1m a19.xkpd a lml/c8i2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of aq21w1,fey4gu+ ur cdcdqp+f( 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 between the speakers, at B, and (c) he hears the speakers after they have passed him, adwq4 ydf rpc fug1, +u(21e+qct C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beat fkr6 awj* rpzi3 b9xp,s mi,jo/g+ ,9dfrequency would you expect if 5.50-MHz ultrasound waves were directed along the flopw+igr3 ipf 6zkmj,9, x 9sr,/bo a*jdw 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 0e);xiu ,q 4yub :g mgrp)jk0fwhile the moth is flying toward the bat at speed,uym))pgq x;:f 0r0g4ijke bu 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses a,s;d-ghzf ) grs it approaches 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 chirp is emitted? fz,dg;rsg -) h   m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Ao kgecv(q)ksj8 zfpi9. .lu h 51rrh(*lpine 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 mos85rgk*e(h) ps ..chkqlfi u9vz1(roj t 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 lis4e.aa0) b ghcgjza. /ptening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at tgcgbe.ah az4ap/.) 0jhe 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,” ing;d jx ,n ws),xwy3fzf o76rr5volves 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 practic36x n wrfd7syzgw ) jxfr5o;,,e, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold ofpzs8p3* k-n pz hearing for the human ear at a frequency of about 1000 Hkppp8n-z3s *zz 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 2.0. An observer on the ground hears the sonic boompn0lhr v47 cq; 1.5 min after the plane passes directly overhead. Wpn4cq7h l r;0vhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iupcsq,m5vngnhm )mcz (4 0p+6s 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