What is the evidence that sound travels as a wave? qs1(f, y3,-thaf ny,jwcn.q w

What is the evidence that sound is a form of energyr58h.y,kpg l z?

Children sometimes play with34rgy3 um 97-3j: kgx6 vtcpjpf 9ymih a homemade “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 oth6 7cy3h pfxpti vkj4ymrg:-39 gujm93 er cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you.cumg1ujh ;0j :wn:k1dz;sl 7 ncc:wg expect the frequency or wavelength to c;.:c l1ujwm1s hn:k dgz0u;j gw7:c cnhange?

What evidence can you gl)tb z(svw; t9r,kym,ive that the speed of sound in air does not depend significantly on frequenm(lszbt;y )kt ,wv9 ,rcy?

The voice of a person who has inhaled heoij2 e1x7pw5g lium sounds very high-pitched. Why?

How will the air temperxz(n6*0(mc5ybllwbg2 gv*a .h (mtw wature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduf093r hfpr r1wce the amplitude of sounds in various frequency ranges. (An example is a car muffwf0pr rf 9h3r1ler.)

Why are the frets on a guitaoncqj ,ck*h if4b e3.2r (Fig. 12–30) spaced closer together as you move up the fingerboard b3*cn4. j2hikf,eq o ctoward the bridge?

A noisy truck approaches you from behind a building. .6d i5)njlb-rp1* kcu t7fyqmcd :lz9 Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectu q c 9-ipdkb:1l r)n*tj6z7l.cfmyd5ion 11–15 on diffraction.]

Standing waves can be said to be due09aw9 0krkpnr to “interference in space,” whereas beats can be said to be due to “inter99arkk0w 0pnrference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lob2 xfz0zim9h/wered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer 9zb0m/f i2zh xtogether?

Traditional methods of protecting the hearing of people who work in areas/ 8g .pkg)v oh.(ktfku 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 whift./.kk( ukog gh) vp8ch detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thou4)m3 b.yx8 v(qmqg 4k:f lpmajght of as a superposition of two sound waves with slightly different .mb4agvx34m 8k qfmj )yp:q(lfrequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the gftmjr kildnd ; rwj468:2.h5same direction, with the same velocity? dhlrgt4w 85dn m;r 6:ik2.jfj Explain.

If a wind is blowing, will this alter the frequency of the sound heard b4oxn34 a:v2h / japcn8k3hyj ny a person at rest with respect to the source? Is the wavelength or velocity chanhxhvon4/ a4caj nn28:jy p3 3kged?

Figure 12–32 shows various positions of a child in motion on a sw6g 7vbb1du ;q5bxik7 y2t vkw-ing. A monitor is blowing a whistle in front of the child on the ground. At which position, A ki 7b67-vbgw v5qby2txk;u1d through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for vl1ua9q9m2jg: gbc.p the echo of her shout reflected by a cliff at the far ejmql91:2bpv c9gua g.nd 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 sidoap 2m+9 sinybi-u6l,e of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sou2s-lo9n6b , +iuymaipnd 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 ra6q 4yfc+m;5f,vbazl( n- zy 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 jvyp.qh-/m*c 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 elapse ./mcjhp-q*yv s before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking th/j /i)gh k9t91)0b ejfsleai re water below is heard 3.5 s later. How high is the clik) /b )eirhl1 ite/sjjfg90a9ff?    m

  A person, with his ear to theqt7o h;c *) 1htvb wyn-1f9afe ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travelsf;w 1o)bchyta *h9v7ft n1- eq in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent +x lvl 9zlrk,t w (pp rqk0.054o.lzjferror made over one mile of distance by the “5-second rule” for estimating the distance 0k ,r+ l.lkzovpf rpx.(5qtzw 0llj94from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity o .q nlfvt w)1*ehs6r2f 7/kucmf 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 sound whose intens znko.t6ccl:; ity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousz9jisgh:b*-g :z3n j mly at a certain place gbi*zj: 9nsmjzh -3g:, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from avp t cv8,c;q;yn 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 down all but onvpt; ,8qc vy;ce engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise n eif )m;n0j nax;x/7qratio of 58 dB, whereas for a;m)/ji ;xenxnqaf n0 7 CD player it is 95 dB. What is the ratio of 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 person speaking in normal conversa:+bp ob qxi4j5;stpm(j +thr:tion. Use Table 12–2. Assume the sound spreads roughly uns4p+xhb;+ro (:ipqjmtbt: 5j iformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whosedv0h;a7rj ;m. dar7ta 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 mopomwyhl r1*+7 dest amplifier B is rated at 40 W. (a) Estimate *rophy7mw1 +l the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in 8l/voca39+ onzjn)3tdqv 0 bn front of a loudspeaker on the stage.t vaocn+ 3 9qd3oj08nzb)ln/v
(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. c/ncijg:cctfv7 n+2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by tc/nncij2 fc tc+7v.:ghis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will thiy.r,- gr+b lfe intensity increase? Increase bg.f-lrr b,i+ yy a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one ovs9x 01+drcshas twice the frequency of the othe xr9s0d1sv+ cor. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wav :*8 zmko )sb p7jdpr0g:v)kc*j rcqc*e in air that corresponds to a displacement amplitqrm j*k*pok)c*scbr0g j zp7d8:v: c)ude 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 acuajzrn 0go-7.nu99 us a 100-Hz tone that has a 50-dB sound level? (Seo.-nuau09c7rgj 9 zune Fig. 12–6.)    dB

What are the lowest and highest frequencies that an(zxwrn,w 7 v*w ear can detect when the sound lewn*rwz, x7wv( vel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What isuqv:s2g0 .2o:tymavi the ratio of highest to lowes:i0 2yvu:sovmtg.q2 a t intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 4i3; b qms7+njl40 Hz. The length of the vibrating portion is 32 cm, and it has q;j+ 7binl3ms 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 firs( l6(0 ijfuouet three audible oveiu lf ej6u((o0rtones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect f.f;fmaw,3vcoi k/c8 qb4bby0 rom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed c. avoyb b0w438kfcmf;bi/,q 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 opec q hy30*ymm04ic)csa n-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range o*hai3smy 4c cq0m0)y cf 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 as its third harm5 /i44u 5hb5gp xkglrlonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orixk5/g 4u5r4 pgl5bhliginal length?   Hz

  An unfingered guitar string is 0.73 m long andwp ;k/eq8nmgye. 52u y--v hio is tuned to play E above middle Cye5 /uke -y8iopm-;qh nvg.2 w (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 op rsbx2 1ddjg:1 twj1l gydp9(2en organ pipe that emits middle C (262 Hz) when t2wjdj:(d 1ytd2g b r19x 1plgshe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20-y,l44 1wni4r 1cjdvel uj -xs $^{\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 12–1x( mzgu v1t7z60oud.z0 should the hole be that must be uncot70gu (6umzoz xd vz.1vered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 H6y 4--*v (ngvo,7fz ra:7m j a/k vhktuqpceg.z, and 616 Hz, but not at any other frequencies in between. (a, ao4.f7 ptk6h gg q- :a7zv-c(/ynjmv*vuekr ) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is u. 5x9vrt(a:;z h2ax u:mjxzm open at both ends. It resonates at two successive harmonics of frequencies 275 Hz a(vu a: xzua5m t: 2zxrjxm.;9hnd 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 wghp.tiv/0d+r.p eaw j6 7c:g$^{\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 wig2 ts3 t8ucvg3p 8znk/thin the audible range for a 2.14-m-long organ pc8 /3uzps2g8kvtnt 3gipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lrmv :irlv3gx4a7cl(nd5z- a) ong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in t:7n-z5vricaral(3xl)4g dv mhe audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tr(efdrttrlj13bsn95z qq w 9+v74rfuv ht 8)+sying to adjust two strings, one of which is sounding 440v z 5hq dvnts 1rf+7r3)j9fut 4lq9br8+tew(s Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middjn rqhy5ucm*-27,hm x-cx v / 4jhl0llle 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, wh )s *5-qqqgoplm )g1lgile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneouslyp)m5g)o1 lsq*g lqqg- , estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-H6 rx 4:f8c)nkulrh1l /tt7cuvz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of theu8rvkl4 ncx 61uh):r/t l fc7t string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 d9gej2, qq z.bjc+s8aHz. The tension in one string is then decreased by 2.0%. What will be th b e9dcqj+sq2,azg j8.e beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to vm9telg3*l0 l 84x quoplay middle C (262 Hz), but one is at 5.0°C and the other atmlxel ou0t v9l*3q 4g8 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzmwx /z s ddtu w)t6:xzi0h*0zmp56n:p ; when A and B are sounded togetmd 5)6izm6ndws:/u0t:*wxhz z p 0tpxher, 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 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 pers4n(.n 6 -wifwyuw9.jq dvbv- jon stands 3.00 m from one speaker and 3.50 m from the otherfnw 69 v.d.wv niyj4- wqb-uj(.
(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 vi ( zs 11gt8ybg:fbjen/+oiij 9brating at 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 of the ot:1+f 9nsgio1ybj(eizbt 8g j/her ?   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 ah k4 s1c+le503s-cbsndo c+ghnd 2.76 m in air. How many beats per second will be heard? (As s4bslec0n+h ohd 1gc3- sk+c5sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a c1z vi6 -nrr8lrertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move wi 61nriz r8rlv-th a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freque)i0mgk2t/t,fo6a(g yafz mxsq c2 o+0ncy do you detect if a fire engine whose siren emits at 1550 Hz moves 2gg+tm6oo2 zqaiaf c/0)tyf ( m0s,k xat a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward youj/g )5 xh,e 3i/a(tj a1nrdt 4imzryr* at 15 m/s versus you moving toward it at 15 m/s Are the two frjhxdnia3z/() ,jtra/rtyi5 m4 *r1g e equencies 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 horn. b*,5hnis n5jmWhen one is at rest and j n5s nbm,5i*hthe other 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 rcpmr *6xf39t p43* w yligup3ultrasonic sound waves at 50.0 kHz and receives them returned fpi6xltpw3rf mcr 9u3*3gp* y4rom 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 atf9t6*aw6p zdw a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz96p 6awwtf* dz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movp,ybbowfld i.p:( v;j 15n6oqing 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 b y p.:lonji bw(p1,f;o6d5 qvcar approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blo3o9o (om,cfx eod-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1exo,moc39o( f 540 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 ultrasonic2s3e2 sm-oql2l y oa5c 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 wjzr3.1k dq, xv2qqiyc1uu6-v ind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, 2iqux.d q,zk1v u-jy3q 6vcr1
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speedx0 cxg)x 4u gy/aez:p3 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) What is)b9gz c2 tqg,8sfn0 kr the angle the shock wave ma 80g skfzg9tq n)bc2r,kes 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 of souz2j+ct 9b w7hhnd is only about 3 7wc bt+j9hzh25 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/s strikes the ocean.hr(m /v4o jndfmn9t, 6 Determine the shock wave angle 9 t 4nfd(r6v,mh/njomit 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 :/4j zmexn/xs+ fgt7b$/theta$ 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 gbc ,1n/9ii/qb ss2 vlbround flying faster than the speed of sound. By the/ s/n,b1 iib9vsbql2 c 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 thatl:8xh rv4lcso5 vfj.1 sends 20,000-Hz sound pulses downward from the bottom of the boat,v8.xosr ll4vc1hj5 :f and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are th)m*,hpor 2ic4tb9 vmew :j/xf1 ms8 qaere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Iuu,b);hyca,b++ yokxg9c 7d et consists of many plastic pipes of various lengths, which are open on both endy u7d,b +9hg y)x+,ueko cc;abs.
(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 thy3jlkanc 5xmp3x;5zd 7 5k3ifreshold of human hearing dpcn 7; 3kf5l3kxyz j5mxi a35(0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound ;-jmi74c ebjoawn0fg81y .pj5i4j.ne ezr4 b are hea7 j4en ei-a44 1my.b zbewin5.r jgcf0;8poj jrd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1 t2q*gk;m 7flhmmwv1.05 dB. What is the acoustic power output (Wq lv;.*1mwmm27 fk tgh) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated fdlxdr/3 r9wsjlvm +1: kj .b(-n8mek(j-eng at 150 W output at 1000 Hz. The power output drops by 10 dB at b -fvk8s lj.lr(3em9/m- (wndjdg+xe rnk j: 115 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typic/vpp2h f++pgmm5t l k5ally 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 gm fhl/ 5v 2m+5pptp+khuman ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, th6f,.a 1hbq2ypzoqv 7se 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 tuned to a ,yot l90aidsu5x8xn, 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/uvwam+ij:z;ac7; ev with a fundamental frequency of 440 Hz and a mass per unit lengtjv/;avi uc+wa7 m;:zeh 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 openj;q :m;qqhv:bubh )ao6 6tu8t 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 au auh; hb :q8b6qjq6t;vo) m:tnd 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 nearx - 6;s l;2ey:z0+xeihqdyk su 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 harmonic in the t 0x sd;le6xzs h:e-y2q+ukyi; ube?    $ \times10^{ 2}$ N

A highway overpass was observed ta :kim k)-l-1)mx*j i tdrymnrvf2* ;jyz5j)y o 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 tone in the 500–1000-Hz range coming from two osr)p4g/u0gfh2 k z8g sources. The sound is loudest at points equidistant from the two sources. To determine exactly what0ugg gko f4pzhs/r2 )8 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.pp0pv+h1o+* uv0vp4lu re tt is stationary. The conductor on the stati4*opupevph+pvrv01.l t 0 +tuonary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train v;nu v,(65zf;vz(ji moqlr yvy* ;4 mdwhistle 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 constant velov6(o4,jvyf *;vq m;(5l; zyd nmvruzicity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to *i r4u/vxk ng4g8i adsw :-ui-/z)sbrthe difference in pitch of thez-s rg)du -:rb/kiw4 vn/8sx*4 ai gui 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 on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundid9m;md;j qn.sng together, produce a beat frequency of 11 Hz. The shorter one is qn mm jsdd.;9;2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of 3my /l+jj(u -i8wijbia railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speuwii mj+bi lj -/83(jyakers 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 what of7g;gs6qcklf z--i u/nkt f9b+j,y )beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the wav9gt +-foj;fzfk, -ncsbu7iql/y k6)ges travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth oy *wuho9b85-09 wpguu7lu (ksvwn4t at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat aftew5vw7uo bput-u0(9u8nwg * ls o4h ky9r that wave reflects off the moth?    kHz

  A bat emits a series of high frequencyr -cha 95.war)l5djqy0bc(m j ya 57tayx/2qc sound pulses as it approaches a moth. The pulses are approximately 70.0rq2-aaqryb (5l a5a.0 hy7tyj5jxcdmw c9)/c 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. 12–38s mej- 5a3crvsgp6ip(q 31a -l) was once used to send signals 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 funda6-ejsl3 q3p g(ri5 m1vsap-camental 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 compromisnvq4e0;vuad* o .mp4zed by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental freq ou.mv40pn;q e4v*dazuencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumin6:mq7 ,c4bdijv o6vk pum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little 6 jpoqc47v:,bdim6 kv 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 o:c0c zw,l lj1 ahsymapm- /6/yf hearing for the human ear at a frequency of about 10m 6lc /pl,/- hwjs :mc0zyyaa100 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 a c7(chidqs)*1oy9ap ot 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 al1io d7asc oy9(q*ph) ctitude?    $ \times10^{4 }$ m

  The wake of a speedboavj6z7ys y1gb o x/) nzmh*e-*nt is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h