What is the evidence that sound travels as a wav7ye8.f.g 8d(q9ulu , bhj q9icr6cqkme?

What is the evidence that sound is a form t/obr4jb:1f oof energy?

Children sometimes play with a homemade “telephone” by attaching a st fcjd0(qmw-)u:i;fv rring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can bew:i ;cujq)0f r-vf (dm heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes fq8m6qswd g 3 8ypis5l6rom air into water, do you expect the frequency or wavelength to ch6ws l y3q6pqm8ds8gi5ange?

What evidence can you give that the p:jc vys 75/r+eeii,u 3 9wpqospeed of sound in air does not depend significrsq7o5,i p9j v+:wec eup3yi/antly on frequency?

The voice of a person nv obm4q;3g- indjj+6 who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of or 5ei3hd-h(wox g :y7ndgan pipes?

Explain how a tube might bcxutqfz m81 93e used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.9 qcz8utxm f13)

Why are the frets on a guitar (Fig. 12–30) spaced closer toge/)kqz: ow;l.f-: wyp uuh q0ngther as you move up the fingerboafh oz0-gku)lw/.qyq w:;u np :rd toward the bridge?

A noisy truck approaches you from behind a building. Initiallu-u(rnv.w rnxh8o4l mj 7(rl(y you hear it but cannot see it. When it emerges j(-vml ln (wh(o ur u48.nrr7xand you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due g6-soo qqk1b2to “interference in space,” whereas beats can be said 6qs oqb1-gk2o to be due to “interference in time.” Explain.

In Fig. 12–16, if the freque9x yihkl7u c.wok35n, (oqjw* ncy of the speakers were lowered, would the points D and C (where w o.9n3*l7jcykxi,oku 5w qh(destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of prot9 : nnapx4*wwlecting 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, inp:9 xl*a w4wnnverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tyr4go-(.e odthought of as a superposition of two sound waves with slightly different frequencies, as in . 4r- dyoo(tgeFig. 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 9cmaq0- 2rk)d xt,qbu0xx3 szif the source and observer move in the same direction, with the same velocity?b0tru x 0q92xkx sdqacz3,)-m Explain.

If a wind is blowing, will this algb2f jmtcss6k(e:hyb;9 m (d1 ter the frequency of the sound heard by a person at rest with respect to thdbs( bjftg 2mcesk(:y ;6 91hme source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swin6ges ;ef.mf0kf5 (glx g. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of th fmg (ef6lf50exgs.;ke whistle? Explain your reasoning.

  A hiker determines the length of a lak8mt .x d1k l:q5yyc1sne by listening for 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 lengtsdt1ykc1 nl. yq 5m8x:h of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears2)oe0p/ uqikf9 k6 pxv the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12pe6kv kio/p 9)2qfu0x–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at.ta(y) k gqb 6hac+hklc3 0dr3 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 da) -qfxjlbs3a :y. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the b3:ja)qsb-x fl ackfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the tolyl6y7y1 d s yqj4*/1in-yualp of a cliff. The splash it makes when striking the water below is heard- /isyd q 714ljyn auyl1*yy6l 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stonk 2qdbpbtw/z2 0)(nqwe 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 fb /kz()20 w wd2ptqqbnar away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of nc wp:czzg rp(m)q*,-distance by the “5-second rule” for estimating the distance frgrcpwp*):,qcz-m n z( om a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the p1:qdaf7s yxtmh)*m b+ain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound hdwb5v gssc rbc,aw kgs7k 932o4;95 bwhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously a6h8a30ktzpr+ hko 3 zxt a certain place, what will be the sound lev0h a6z3p 8xkrozh3+ tkel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a 4ydlr,*gh1xx:g.o1h vy x1 nfcertain 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 experiencen o:x1yydhlvr1 41hx,g*.g fx if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, who)62,3 z fwjro vr/ nhurk9pq.ereas for a CD player it is 95 dB. What is the ratio of intensities of the signalo.own9khpj r uz/3rr )62vfq, and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outp 8p5r n+ wadx*r 4agm2ud5lmc5ut of sound from a person speaking in normal conversation. Use Tabler5m48 w+d ucxr5napd 2a*l g5m 12–2. 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 an earfch5g+c w yzg. a2(gj+drum 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, while the more mod7spmg , 9gb,wqa:0l6evp 9 sqkest amplifier B is rated at 40 W. (a) Estimate theq mqsaksbvlp6e7gg9:w9,p,0 sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frola.n+c jj,o. op t(c0tnt of a loudspeaker on the s .nj+oaj.,ocp (ctl0ttage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What isfks6wy:0leg: 5 b4epv the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secti:s gb56 yf0k4:ewlv peon 11–9.]$\approx$   

  If the amplitude of a sound wave is tri9ii bnupl /4 1vw1u q/d-ek/wkpled, (a) by what factor will the intensity increase? Increase by a fac/ ki 1w/lq1en-kuu/4wipvb d9tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal d(v,ln jox-8c5aibf 1uisplacement amplitudes, but one has twice the frequency of the other. What is the run(- ib axf15j,lo8vc atio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that2c1q (j)1gzbplx5lg w8l bw(r corresponds to a displacement amplitude of vibrating(xpblc ) br2j(lgqg1 wzl81 5w air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whateg rrn 0h;y4uxlb :yeoo :59:-* pzngk sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. nzkp 0-he* :yn:ur;o 4gxy o95: elbrg12–6.)    dB

What are the lowest and highest frequencies pkl-jh5 c4v9nthat an ear can detect when the soundkj -c4vpl59nh level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range o8nl da(x)c 4jq0 wfnu4k l(fly+03,wkct h/v lf sound levels. What is the ratio of highest to lo0 a,fk8dn0yw)(wltc +(4fhq/vnxkc lullj43 west 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 freq(gmgc6f5b iw::j,+h du5g cwquency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Underf,gi:5cjg:w6 dc wgb5mq h+(u what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three auvo dwnd.dr:v*eh 78/kdible overtones if the pipe .nv7dwvd /de: *8rhokis
(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 wouldv,pv lx*/- xi6b. e ;e+vwhfjb you expect from blowing across the top of an empty soda bottle thaeixpv*vjlbh v xbf6e.,w+; /-t is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with ftwde(d83 if1 open-tube pipes spanning the range of human hwfdte8 d(3 fi1earing (20 Hz to 20 kHz), 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 5400ihru3/luffc;3 ufef . 1x v/m Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original l /h;rv 1f.emf/33fcif0xuuul ength?   Hz

  An unfingered guitar stt6blih p6ke15ring is 0.73 m long and is tuned to play E above middle C (330 Hz).k ebth51 6il6p
(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 th.da.xoyj k;i, at emits middle C (262 Hz) when the tem axod.ikj ;.y,perature 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 208;dmvv at t.( a2d curs2+7fl-wp2 bdh $^{\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 19m vk:v0/k*mjpov0 zx ;qjxvi.dua412–10 should the hole be that must be uncovered to pxjk .m9vk *a;upivq m:0zjvodx /41v0lay D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and fwq2hr) 4,6jtg janoo 0b. /wk616 Hz, but not at any other frequencies in between. (a) Show why this is an open or o0 jbkwtgn4)2. h,or 6fwq/aja 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 resonates a9) g (oaz+izqjbof -3jt two succeso(9 zjo3 ijz )qag+-fbsive harmonics 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 l-t em(fve8v;$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orgaz )zeg824kgvqicd ,(wr ag;n* n 48 g (2qzd; )zg*,cigaevw rnkpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long.rc s3xc7:m,el 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 inflm,x :crs c73eormation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat evehk +:hft*e qb(ry 2.0 s when trying to adjust two strings, one of which is sounding 4h: +tf*k q(hbe40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if midd/ctko m4,h;10udqt u ile 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 (bynk6)xpp(5; .uq9wv mjpt2gogt4/i2ow l2 cwrand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whinen tc2m wo 9o(j wq5v.;p6kpxpu2i24gyt w) l/g 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 sounded with a 350-Hz tuning fork and (ic/i jp+lle/9 beats/s when sounded with a 355-Hz tuning fork. jili/l( pec/+What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tefk7kaz fqv54d* ;mn0 lnsion in one string is then decreased by 2.0%. What will be the beat frequency heard when the tw0;ml nv k57afqf 4*kzdo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each 6l8uqd* ct e bm/*mlb5try to play middle C (262 Hz), 8u /mm 5ble6l* bdcqt*but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork 7mj4ec( ugp: ss5i d8pB has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and Cc85 spgu 4di ej(pm:s7 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 n 1hsd7n.pvd kwkzwcw248-n /one speaker and 3.50 m from the other. cn1dk p78hwn 2vwsw/zkd-4n.
(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 ,l;v(d:re,qnm; t* kwy fo;tj 132 Hz, 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 odtmre(,ktw ;; ;vfl,qyo:* njf 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 o 1yx+/q 5,r8- zdhomg)b ipjwif wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T =b5 yj+zm 1)giiwr-/ph8qx d, o 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque.us xfjff2e r rojj) 7db-)4p4ncy of a certain fire engine’s siren is 1550 Hz when at rest. What4uf b-fjpxoj)r.f4)d 2 jr7es frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stillb/w5m2u )/cq, z ,iodhswz, uq. What frequency do you detect if a fire engine whose siren emh c/uiowq,, /sb2m qd,w 5uzz)its at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moxt w slw(hy+q2s 19q8vving toward you at 15 m/s versus you moving toward itq9y sv 1q+w8s 2xthl(w at 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 s3vptyc9 ,i5bn ame single frequency horn. When one is at rest and the other is moving towpb5t nc3iy9,v ard 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 themb3 22 aszok1 ag(zrtd4 returned from an object moving ddbrz2o4t(a2 s1z ag 3kirectly 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/s A t exuz sl3:u*n0ceha,*6 i;qos it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wlsh:a t;n *uq3o*0xec i e6u,zave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat 4v;k/wh:hly iekc8g3train 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 approac4;l3gcyhv:8kh e /ikwhed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-7( /el xfvdwfnk280aiyq u3. lflow speeds. Suppose the device emits sound at 3.5 MHz, and /k.lqav(w 73x2 yfe0dlinf 8uthe 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 ultrasonic waves of frequeaw mkod9 5st;rs l:kflm30d)qi7a00j ncy $2.25 \times10^{ 6}$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 jktm97(f fk 3be 0d3ehkgku73 of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequf gum0kk 73e3d 7btkj(3keh9fency 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 objeccfv/f7gtkd/5r -ov5l t moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Wha(a8t3j3lm o8m3za uvtkn5k-at is the angle the sho aloa3vt 38 8jmt5u (m-kkza3nck 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 23rjyn) gss.tthin atmosphere of a planet where the speed of sound is only about 35 m/s y)j3 .stn r2sg
(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 strikesgn qy7 *md*s/x the ocean. Determine the shock wave angle it pr gy/n sd**7xqmoduces
(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 xp 849dd(odyq( kts0f $/theta$ 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 abp s7um u6yfnm zemt7zyw*0+ge:cj375 ove the ground flying faster than the spzy7 6n jte*usmz mw5p3:mgfcy07e +7 ueed 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 pulses downwarduj1h- a/.a -uvdryar;p/omapj)x 0 if(g0v p 2 from the bottom of the boat, and then detects echoes. If the maximum depth for which it is v-0prm oji.f2dh / 1ua(y/ jaapp;rv)axg0-u designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves amd4 ygavwo aa*1*- r4zu67hyere there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonw3 h-ihgp:b zabk k-xj7 8+ff+y. It consists of manyxj p:+w bfa3gih-8b-fk+ 7 hzk plastic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m frompfqc05,- ld s h:wb6tb a person makes a sound close to the threshold of human hearing (0 dB). What will be th-b:c ,qdbwht l50pf6s e sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87 wu9q4.xnij33skf5 g y-dB sound are heard simultaneosy3j9.q 3w5fxn 4uikg usly?    dB

  The sound level 12.0 m from a loudspeakebu7 rum* mcof-. o.0/i.yu zxlr, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker,o/ ixuu. *c0lbru.-myo f.7zm assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1+ a gl,ongf7 (2n6c9f /jqwe)0b pftss000 Hz. The power output drops by 10 dB at 15 kHz. What is b ggfs/fn(e+2t7 6plf ,) 9jaw coqsn0the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically we5c( oc9to(innar 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(oin(co5c 9nt m from a jet airplane engine?    W

  In audio and communicationrdzkq4 lf j kk/yi8e- g26 .ubuo2*5vbs 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 tucr4qy4t 05uuog tvf/8r vq(2a -vko ;jned 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 sx- 4/kc gk fwolm)y5 wk ;+il5.h7hsppoints with a fundamental frequency of 4+ h-7l;4kgw. kliy xs5cpk/oswf5 )mh40 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 into vibration above a vertical op+ 3 qov2l- o:2)n7kxgifchix8pttk r)en 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 watert-3v 7xnol8g+:)or tpii )xf2khc2qk level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a t (3xr, tfceyud97 m*(-klq thzube that is open at one end and also 75 cm longt3hfzkmc7 9x(e( -t q,lydu *r. How much tension should be in the string if it 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 ful1tw) t40unpb3 jp,vjgl 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 03,; myttbcwythe 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 personybc ytt3w ;0m, 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. :t0cdh,hrx ;iThe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whdhi;: h, r0xctat is the speed of the moving train?   m/s

  The frequency of a ste3ph*immr- kj ,am train whistle as it approaches you is 538 Hz. After it pas 3*m,pr mijkh-ses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the sp4mi sb,7xk. u(m fbm -2gutkz*eed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drop7 ukg(4m xmms* b-iz.t2buf k,s by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of )w1uc dz2lyf(iyxg yfr0;z6z w i55q*11 Hz. The shorg*uqi ; 5xl 0wyz )yr 6z(ycdwf51ifz2ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mo :bo kx7o dogs.tq6vcn69r9/ yves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the spevsx.:to /o b n9qko667ry dcg9akers 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 about 0.32 m/s x;ac5a:,ai78a 7ip2g v p(lubuzqyn )what beat frequency would you expect if 5,b7 uc (zg: p aa; uixli75apa2vny)q8.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mn;lr tx5ac,;v oth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound w r,n;;lx ca5tvave 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 ofgcd 8-mm-s 2v .(ormzy high frequency sound pulses as 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 th- o.8gm-mdy c(mrvsz2e echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signa /yn syxlb imy3ms.cn 00b2;.1(dstku ls from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sha ik0 m2. cny0.uby smbd3ss1tyl ;(/nxrp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence oizf7/,t ,jhurf standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodh,u,t i zjr/7fes. 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,” involvest 61ni; r+zfm.s9-kys:auh r 1vbol;h a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Wits .ysrfz 6rml i:;nktao+ 1hb;9v-1uhh 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 tzvgfek-7: f1 lhreshold of hearing for the human ear at a frequency of about 100 k7lvfez -g:1f0 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic bea8 y8clhagb2 z4a ;ffc.2ry3oom 1.5 min after the plane passes directly overhead. What igelza2a y8a b.yc3 48;2frhfcs the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1d 9od+m9 2 lzpf.3bbc2)afjhy5 $^{\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