What is the evidence that sound travels2ii9nw-w zr.pq iou 6.be;x (s as a wave?

What is the evidence that sound is a form ofaws 8ndp. s6tlazpf.1cg /(y4 energy?

Children sometimes play with a homemade “telephone” by attaching a string to cm( hud; ex1.mthe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the(m1 ed cmhu.;x other.

When a sound wave passes from air into water, do you a0l*io gtq7 r3expect the frequency or wavelength to c7lt3oa0qri g *hange?

What evidence can you give that the speed of sound in air does not dependjei(.la- n9(ih 9k yby significant9ii.9y( h(e j-nal kbyly on frequency?

The voice of a person who hn4gwb., r5uuje )dpi j 765czeas inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room ac a r3fo.cy9.wm,o .iug4d f,tffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of solq6gu -94sow (nnau( t *v1trdunds in d*9 -w6(nouvgta s 4(lunrqt1 various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mobx+v*c -gy;n meq4ejc/ q7sa0ve up tbvycqc s-e+ mxq0/;aj7e*g4n he fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially youti+;t p b )fr6owpu(( 8abqkuums+a -3 hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of +-qb(os fmaua8 pukbr6puit;)w3 + (tthe high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bokbtalx(rm fr 9*p2 7k 4t:i1deats can be said to be due to “interference in9alfmt(dx27kt 4o: kb r*r1pi time.” Explain.

In Fig. 12–16, if the frej3o7mi l620mwj k xq8lquency of the speakers were lowered, would the points D and C (where destructive and construct6lmjjk7 8xil0 wqmo 32ive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with hd 6--ps/3fenubi/9rd xrunpv u:t ;2very 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 a/r2n;i/ p-: 6s uuuxden3rhvdbp-ft9 mbient 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 showbxh5k3 njkt,g62 )zpk n in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies g k kj5hn6zxb,)3k2pt, 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 moveznq3 oorrx1b 5;f)-ku x+(m8m mrdz0t in the same direction, with t)(1rn5r;mx m 0d+ q 8ufzkzroom bt-x3he same velocity? Explain.

If a wind is blowing, will this alter the frequency of the soun.ei e8ffri qm-39 frcx3cz;ap/l8p5ed heard by a person at rest withzpi f83.qf-ec 3 mrp/ ei 8;5x9lecfra respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. ymnxuo gmtp4 v:4 y4gs+q(+l (A monitor is blowing a whistle in front of the child on the ground. At which position, A through Epnms( x(:gt4ly+m4+yg4 q uvo, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines thed njofj,u ab-+ztin5 ub(3onpf)y ,+; length of a lake by listening for the echo of her shout reflected by a cl otjbn)fap,oujf 3y +d(+-u5;n, n zibiff 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 just below the wateb9)jd/ony ac:g:1rap2cj c: krline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How da ccog 2dcj)ypanbr :1:kj/: 9eep 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 id p;.xt1 q 1.sjfeupd,n 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 r9mwe5p k b6r/just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses b9k6wre rm/b5 pefore 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 when3nq aze:i.b-b.px / as striking the water below is heard 3.5 s later. How high is the clifp ai. b s-zbe.x:a3nq/f?    m

  A person, with his ear to the ground, sees a huge stone strike n/h elgv;27,,f zlw4hpyp 70v5rsi yvthe 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 12 vz7hyi, w5f/ne r,slh 0l4p 7;yvvpg.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error m,hjz1/ zakiojt gh+- x-n2lw 5ade over one mile of distance by the “5-second rule” for estimating the distance from hjt,kz2x5w-ha-g zj /oi1ln+a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity 5aady2 mb-.cyof a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a g/mh17 2wmvg bs*o4w tln-s wt2y xr57sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wh)aau-tk20 t8mr/q;mbt w3x el en fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add int2)qmmltx ab teu- kr;a8/t30 wensities, not dB’s.]    dB

  A person standing a cert3oknrf- wl vep8dg .c;:xk94sain distance 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 shut d-w893r klo; g:psxc n. 4vedfkown all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to- upuz2 m.07l1wrz/ nhinoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background7n1 zuplmiw/rz0.h u2 noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from f ;;d(,htlkkt ,3 n+f ,gkmvqaa person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a smqdk; f3lghakft+ v,k(,t n,;phere 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 area qke73/dwz-vb nj 7 jq::s3zay 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 og g9q)hra4 oi *:2gzkA is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound grg4kg*z9h2qa) oi o: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 reus (rqierz/j /78sd,sgistered 130 dB when placed 2.8 m in front of a loudspeaker on the strq7 us8/,sz ij(dser/ age.
(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 dec8eoswb4el 3xz5(kj9oj or / 5tect 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 Section 11–3bw8ej5 5c4o/skrzolox(e j 9 9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fascop9lm:-1r s masfl. yp0 /+octor will the intensity i lm-c+0fr /1lpm.s paoy9:sos ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitud .houvpa+x. *ges, but one has twice the frequency of the other. ouap*x+g. .vhWhat is the ratio of their intensities?   

  What would be the sound level (in dB) of a skv oc,m/i/f6lound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 cl,vfki6om //Hz?    dB

  A 6000-Hz tone must have what sound level to seemqg 31idj)8zyv as loud as a 100-Hz tone that has a 50-dB sound le jiq 3gd)yv1z8vel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thi s( omgozu.4oy d9)0kat an ear can detect when the sound level is 30 dB? (Se d4z)ougmso( i.y o09ke Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levelsev vhu 3o936b,dgy j-r. What is the ratio of highest to lo9bv6oe g, uhdr3-3vjywest 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 fundamentak r3mxc :cytzb:+-v t6l frequency of 440 Hz. The length of the vibrating portion ivby6x cttr+zk-m:: c3 s 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 and fz s4 qn bv.d5fzup1r(*clf()virst three audible overtones if fpr* 4s. c(v bl1d v5qzzu()nfthe 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 p he6og6l.c2c 7qt.. h8nz9k ddrbc2 ztop of an empty soda bottle that is 186nzzlch co.db.9ck6g8t.qehr 272 p d cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe o,tayn flaetl ;q4 m(76w/bci 0rgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the ,0yw/m ;t(eifbtlc qna764a llengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmon4ma- l*krfg4gic. What will be its fundamental frequency if it is fingered at a length of only 60%mg-k a4 4gl*rf of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E b noym4/a aup6 :p.y4p w3mq6xabove middle Cwp4 bpy mpmn6a.4q o6a3 u:y/x (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits mid 2(v; g)h-kt)bmchth5 tdm6a rdle C (262 Hz) when the temperature is 21 (t);t khm d2h-6) 5vr tmcghab$^{\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 20mkh,sgdr27 nm7f9 i8 a0w3ssc $^{\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 kcvg (jeti*mtuf9) /+12–10 should the hole be that must be uncovered to play D abv /(j u9keit)gfc+ t*move middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, 6u:05asy )bqb1m ugjt and 616 Hz, but not at any other frequencies in between. (a) Show why ths 1bb a5yjgu u)qm:0t6is 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 opevx;2 ld0bf6 93xodfpen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 62xl9f3;d ebx0d fvop330 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 wg6gpadnwd z.4jo gz;u7.7o/*elz :l$^{\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 witdeuz7 0pgx+ iy9 evjda.o0xf7:5-x amhin the audible range for a 2.14-m-long organ pipe a7xfxd- i09ve+a 07p ga mu. e:oxz5ydjt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsid0nh6y4ve * vuie 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 ini4e huv*6 n0vyformation 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 trying to adjust tw+mal:d; s p*tmo strings, one of which is sounding 440 Hz. How far off in frequencp;a m+t:lm sd*y is the other string? ±    Hz

  What is the beat frequency if middle C (2t( pldcgmf* p+i.9 ,ru62 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 7 z*hl+rrcbw :23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle c7rwc*: r+lzhb an be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soahk+ f m63;gs djsdk/ zw3+i s7kir3x:unded 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 reas/rai7h3 +x:s km3didzs+3jsgw6fk k;oning.    Hz

  Two violin strings are tuned to the same fre+n6ouc7s yoou;ti9k c8z)4kfc qs77 6 o fvx-zquency, 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 played together? [Hintoc -f; k nu7i)s cosk7u7cq46689ozxoz yvt+f: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical7bk; 8(s:e m f6,kobigkbxa)n2 c/rew flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 b2km wrfies( : 7enc) bgo,k/6ak; 8xb$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frex59jabcm65 ,sl 1 drbequency of 441 Hz; 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 frequencies of A and C? What beat frequencies are po b9ed1al5cr xs,56j mbssible 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 12f9zdw-r y u,m.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from-,2wmdfyr z u9 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 us+ utwk:de; ;g *3pvglje:: ea piano tuner hears three beats every 2.0 s when they are pve wp3sju:e :k;ld +*e ;:tggulayed together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many* z n 0ik:-bvgd)sdi0l beats per second will be heard? :b*igd0 sn 0-)ldv izk(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when atd,k; -qchcc5 e rest. What frequency do you detect if you mov dkce q;hc5-c,e with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fuu d6(inhqrn e59 v3w:requency do you detect if a fire engine whose siren emits at 1550 Hz nv 6(rwn5: q9euu 3dhimoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000jxlfhq/p4 + 9r-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are thrl9f4hp x+/q je 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 equippeda7m v61 .vjbbo with the same single frequency horn. When one is at rest and the obvj7.o1 m6 bvather is moving toward the first at 15 m/s the driver 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 them roq 4v 7:-r4tl-*el dy4brt,slh xze)seturned frome-q bh*rol-yx)e:sl7 ,z4 4 dl4 vtstr 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 speezj,exwj0vjp h3w9j4 s :-pw)yd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freqhp xye,j vzjwp- 9)0:s43wjj wuency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played0 n* 5w.2, jioorqifcz 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 freq o,5*r wicq izf0.oj2nuency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wa;6ri yq2 obi 7rxlfa*(ves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the roqy*fbirli;2(7 6 axspeed 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 ultras9):v aa* j v vhur2h22orcpta;s5h3yjonic 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 velocity is qv)2+rq .uxzy gfe1+imw;d (m12 m/s from the north, what frequenx ;mdrg+ iezmvufy2)q.(q+w1 cy 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 moving on lan9/q) d:;+p vpa+o)m* php 8gmkxpgtxvd 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 nakykruq z* +ck55sdww249d:m/s (a) What is thed+k ns4kc dw 5*5aqzky :w2u9r 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 atmosphere2 l -p uj+k fpllytlw1p* /o,p1tm(a6r of a planet where the speed of sound is only about 35 m/s 6,p ppalmlklwfyu/ pr(j2 tl- * 1to+1
(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;mo+hnbc e9b i2amg ,9 wave angle in b,;+ch 9b ageomi2m9t 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 ozj )w7a *u(eeadvdi0 pkc0wa23)g c0$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grou:nn h2xnx a8nk+r* p g6w3dmt* h5ga0bnd flying faster 6 n 5h * *mgha+xnpdat8wx b3kn02g:nrthan 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 sonar device that sends 20,000-Hz sound puls 7iia(lgjset5pgy 1,hpnr483es downward from the bottom of the boat, and then detects echoes. If the maximum depth for which itg h n1sil3t(ygr87, jeip4p5a is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangk(wyx 0xcd;mwq3n v5+e? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called zry 9xf0ebz f(p0mq x)mu29o)a sewer pipe symphony. It consists of many plastic pipes of various lengths, wh)qfxr (90xpom20 uz )fyemz9b ich 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 oxv ijrf o1-:/5 amq0xuf human hearing (0 dB). What will be the sound level of 1000 such xv1u fjarx im0qo5 -/:mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87uvb g(c1ia0 )gw5uw*t4yv 3ax1 ndtz3o9qi,s -dB sound are heard sica5 wgt1u)v9vs 0 n3g yaob*id(31t ,4izqwu xmultaneously?    dB

  The sound level 12.0 mf t2ff(upt dxw*.)q n7 from a loudspeaker, placed in the open, is 105 dB. What is the (2)df7*xft. unwqfp t acoustic 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 dro- y;8;e e0gdxnsmt3ptdb7a h4ps by 10 dB at 15 kHz. What is the power outputmyna x td;g-4;dts3 8pbe70eh in watts at 15 kHz?    dB

  Workers around jet aircraertwa6 3 jg.boi8ubhf5u+ 0 (mft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engj fm.ao35e8bu6rg +ubht i0 (wine?    W

  In audio and communications systems, thfr;pwc :va7n n.f-s,kpt-g q3 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 is -ut)kppy,x f-1/wf h vtuned 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 (a*qt m6k)vk+ qi)ouo 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per uvm6k)qouok* +t( ai)qnit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above ld+;nwz+ hb f(d:j12g gdxu5ua 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 at 0.395 m. What is the frequency of the tuning d +gh ufgz2bwj:5l (;+dx1dunfork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that iseq:9w4,ev; 7 fljna x0v ,khpw 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 79hp v0qwee fl:4;j v,xn k,awthe third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as oneuvnn-kbq.5e7axi4pj /55 gwq full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in o):uu6aecp j 6 h0 y)gkaa3lb.the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is tubhl0j.yco)k a):a a egup663he frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Thm.xvx53/ngm1 zwb x-ce conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is thwxv1z3xnm -cg/bm .5 xe speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 d- zfbbv+: 8a/r,czdxn x.j 8uHz. After it passes you, its frequency is measured as 4868.:djxx8ufvz/dn bb r a -+zc, Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dimhm m((4s8i ocfference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on4o8h m(( cmims the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding co/w1 tw/v kt7uxdf(-together, produce a beat frequency of 11 Hz. The shortwf totvk/w-uc( 1d 7x/er one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a;n+ee a* ya;pb railroad car as it moves past a stationary observer at 10 m/s as shown in Fig.a ay;+e*bn e;p 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, at C?

  If the velocity of blood flow in the aorta is normally e7fyh3- j,l2w v -1,q:.ij1ocdemqa ax3a d cdabout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected fr1-3amvya. cdif:dh3 ,d ,x-2ql wjeca1q joe7om 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 mu wv8;wslwso)uu .j 8scp4 ;a78bjyf5 /s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kvy7sjw a. uus8o5 bp;8f4ws8jculw ;)Hz. 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 fremf,o8 fpo3rv.-ins, p2 h*a+ 1gknipbquency sound pulses as it approaches a moth. The pul.g3okbrfm1i p vhasi,8, n 2nfpop-+* ses 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?    m

The “alpenhorn” (Fig. 12–38) was once used to send signa+8 nc+amff 2dk 9b*c4adviv4y ls from one Alpine village to another. Since lower frequency sounds are less susceptible t4ynfmbkvc894 dc dfav *ai+ 2+o 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 can be compromisg7w ,j,io:+ t1bas,9 ukz pcxyed 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.x, o7yk tija+p ,b9zuc1gsw,: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, callepn- naue c5l4qc84iife 8p76zd “singing rods,” involves a long, slender aluminum rod held in the hand nea4c56q8uep 7lf4i 8ie-azp cnn r 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 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 ear89z*4lmlv0nkk8 q9pb t na+rt at a frequency of about 1000 Hz 8k8p0t m*kvar ll4 bnn99t+qzis $I_0$ = $1 \times10^{12 } W / m^2$ 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 ajsv4 2o6pcu,ln 4n zo(t Mach 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 altitude?( ljz,2soo 46 p4nnvcu    $ \times10^{4 }$ m

  The wake of a speedboat z.y fk9a. s79ppvvmbir/wl95is 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