What is the evidence,88, 5hss5 tx;a 6vwrfvgulh+aa5qnq that sound travels as a wave?

What is the evidence that sound is a form og7w5i0k8yb nq 3yrowc n9.0iuf energy?

Children sometimes play with a homemade “telephonexp4m *48xo 3r r*xphvq” 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 other3pxh4 m*xxv*rrpq 48o 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 expect the frequenck7cpp; a:ar.q ,(nkc uy or wavelength to kpp;qc(kc.ru,n7 a:achange?

What evidence can you give that theu ort+dn 4)z0mjqs(od ,cg(/z)f* xwp speed of sound in air does not depend significantly o) wrjut * dnf((zp,0)oom+g xc4 d/zqsn frequency?

The voice of a person who has inhaled helmf12 j sfdkx.tw ;0 jwx.ok4 l5s)5tpfium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipepwy(ho8 l+g 4yh tatub- /xm(.s?

Explain how a tube might be used as a filter to- aip22us 1dwwh21a 5fk;jz uj reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler. u2k h5; p2wjzd awfsi2auj11-)

Why are the frets on a guitar (Fig. 12– b93.wjsshdm530) spaced closer together as you move up the h.9mwjd5 s3sb fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you he -5nsaa-/ /mvhurywx;fes: 5rar 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. [Hes/r5f w-rsxu-yva:anh m;/5 int: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas7o bhf-f u t91dj:1( zlcn,ojd beats can be said t ljzcf1 hodt 7,jfn9d :bou-(1o be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were 0lwmnu,ph7 w+ lowered, would the points D and C (where destructive and constructive interference occur) move farthn ml+upww7h0 ,er apart or closer together?

Traditional methods of protecting the hearing of people who work in a5ddkj ncpk. rka)-6n1reas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn16krd)-ack5pd .nj kn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of a,z:mpttyh8u*m .0 rn0x 5 do2nd/ bwrvs a superposition of two sound waves with sn0rty 5dpxtvz0 bn8u m2*.orhm /,dw :lightly different frequencies, 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 observerhg sbyshf -e23x,zu g2*z1o0g move in the same direction, with the same vel 2 essofyz,g*30uxb1ghg2z -hocity? Explain.

If a wind is blowing, will this alter the frequency of .pxd ;f4k3pqd:u *rmv the sound heard by a person at repvd.3:kxf dr4p; mu *qst with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motio4/k1d3 mfku h03lay wy1pg6jdz5bqk5n on a swing. 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 frequem 35hafg0j3wp1kq5dk 41kbd/lyuy6zncy for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengthksko1f7* ze6e,(jzam);xd ye of a lake 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 ko z61e yfse dk(x*7jem)z;,aafter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ecpbn aa; ahx;bfs +gdaqzq5: 9+-.x)qvho 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 12–1) and does not vary significantly withhb :q+x;nzd5)q +;aab 9s.g-vpaxf aq depth.    $ \times10^{ 3}$m

  (a) Calculate the wapylg7 hxnh8l:tq frr ,1.)m7rvelengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a schoi udgj nvyam -alid-zb24*866ol 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 before the backfire is heard (azd lyingbi 8- a-j66*4mdu2av ) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it 8i ..qgk 00 2ypu5ktqox uycg4makes when striking the water below iog04.. xyk giquq 80y t2upck5s heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strikeskp, 1 cfwv9dsxfvh+2 wty .f:r q7du,r5/1rq 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 th9tvw+,d 7 2vq d/frrfqwyps,h1:c.s1rxfk5 u ey are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by hqn36 .4n4z1ddv *7buf wzt imthe “5-second rule” for estimating the distance from a lightning strike if the temperatu.fwn4 z67d 4m3u1bvh *qtzni dre is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity o0+m id 9g)uam ybsi/+8wswy)p f 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 +r;xej0 c.ki8i r/shq whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce avy 3 p)8g33nz )c7btg8mtxobs9lg6z s sound level of 95 dB when fired simultaneously at a certain placz 6gxb373lbmpo88vy))3zcsn t g9 g tse, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance h; (55ljf p*pmnib6mt 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 ;mi5hj pb pft l5nm6(*experience 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 rati: -v6ctu zffc2o of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of inf6u cz v-tf:2ctensities 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 per835mb3e hi hvzson speaking in normal conversation. Use Table 12–2. Assume vh35 h38emibz 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 eardrum u9(dxyg- c6cgwhose 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 a pb e8c+y*o/1hcryt7more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in tyh8 +btc erp*coa/y17 urn 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 iwx tkmu06v l 8n.+gw)fczkg(5n front of a loudspeaker on the sta)g5v6f 0 lzc +(8umnw xgk.tkwge.
(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 ofb-,i(kzhngh +shi i82 2.0 dB. What is the ratio of the amplitudes of two sounds whos i,i(+nh bzhg8i-2ksh e levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,iki8t: 67blb q (a) by what factor will the intensity increase? Increase by a factor o6i7: 8b biqkltf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equc59i b8.f2o)rb 2jd hibpx+mval displacement amplitudes, but one has twice the frequency of the other. What is the ra+ib5v roc2hji 8bpxmf2 bd)9. tio of their intensities?   

  What would be the sound level (in dB) of a sounzu gp9syx, 7;wd wave in air that corresponds to a dispg zwp,s;xu97ylacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud 5fp jd7xurwi/td 70l5as a 100-Hz tone that has a 50-dB sound levp /0udjx 5d5ir l77wftel? (See Fig. 12–6.)    dB

What are the lowest and htr/x 0l1 u navaa31-oc8u9x zl0 soi7highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6 l-nuaox8roc1109huza xv7a/s lt0 3i.)

  Your auditory system can accommodate a huge range of s,7sty950hoobz 5u/.uj4 xzq 3csqrm cz z9hk,ound levels. What is the ratio of highest to lo4qo0ru c 3 9uzsh,bzz5sqho/5kjz xmc.97 t,ywest 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 440 Hz. Th4 xsqk8)ff f4ce length of the vibrating portion kc 8sf)q4ffx4is 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 first /sdkh1m6jlin3g26.u jvsk/ b three audible overtones bj/3d6n/vkj21usls . hkmg6iif 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 ex 0i6,v scobc*5yl7xrypect from blowing across the top of an empty soda bottle that is 18 cm deep, if you asvblroc,x c057*s6yyisumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the ranget 2aqi(ie mwqym+ gg2rv0v, 9; of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes require(aeq2 0mm ;2vyr +i,i wgt9qvgd? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has.j.5fjcl4 of)vzem 4u a frequency of 540 Hz as its third harmonic. What will be i4) 5j. vl uom4fefjc.zts fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to,fh8y/p2v /ve+h tfrj -lefg6 play E above middle C (330 Hz). +eh-8jlphfgy/2vtf/vr6e, f
(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 mid472 mmmh/bcmrub(i me,u h39n+ xbci )dle C (262 Hz) when thmu2xmm/ mchb(h7bc 4 m)ib, 3u r9in+ee 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 ar/6: b;u pobrts (( :*ul0m fu(zfyvd$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should lr0rx3) w ;3)arvpfas the hole be that must be uncorw)sa)xpr3r af3;lv 0vered 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 pipeka-zt-7ug.; m+k das e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or aag.+ez 7 ksu;tkmd--a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. Iju0s-em 1g)xjt resonates at two successive harmxe) 1j0jgs-muonics 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 46n+c kpgy8ab$^{\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 au r*mmy spd-95rg b.h57cbh0rx6 xug fgaf9,0qdible range for a 2.14-m-long organ pgbug0qff*,7bhr0xsardc -h.xr59mp59g 6y m ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelynzzqg8j -yv1 g 5pjv6- 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimav zgny1-qvj658 pjgz-te the frequencies (in the 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 trying to adjust two strings, fz fut jnd3*n 01/qab3one of which is sounding 440 Hz. How far off iznd*jqnf 3/1u fbt30a n frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and )2 (dnsrr+llb$C^＃$ (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 operate9a.hio z5mzm h ;/qii6s at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played .o59m/i;qz hm a6hiziseparately, 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 sounded with a 350-Hz tun* oar80)i /dbhyh5rzwing fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoningw80zibhra h5 dy)/*r o.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz.1m;fadcjmmgj56 ow2cg5 0p*v 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? [Hint: Recall Eq. 11–13.]owap2j * 05v;gg dc15mjcm6fm    Hz

  How many beats will be heard a9lwdjre5u s(;n4 *y*jegyd qo x96+sif two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C *weu;ny5 4as99gyo j 6* +rd(dqex sjland the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B 6q j)9wgkmi0shas a frequency 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 possible when A and C are soundeqj)0wkm6gis9 d 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 c 79 rq:h:me6wmhorr)stands 3.00 m from one speaker and 3.50 m fromh6rwoe)mmc 7:hq r9:r 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, jb/hy6;;in rj1 scac32 sva. vst 22fcbut a piano tuner hears tjftv1;y.3 6 isc2r sc2j/n;cbs 2havahree beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air.jh .9kcfor4fkf4a1l / tnhe3: How many beats per second will be heard? :1 hh4fk9ec.ftrjl4n foa/3k (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 151.yw gw.;pm0 b nkz1ls50 Hz when at rest. What frequency do you detect if you move with zw. l 1nmbpw.; y1kg0sa speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine wh wj)pzia47j.ff idiw53 4w2ii ose siren emits at 1550 Hz moves at a jiwf2 )3wf i4d74pw izi5jia.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 u-*vtq)ypy4eenm:4u2 qx9o v you at 15 m/s versus you moving toward it at 15 m/s Are the two q)4qmupe94n: tvyo u* ev2-yxfrequencies 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 hort. f,v2)hmayz n. When one is at rest and the other is moving toward the first at 15 m/s the driver at rfv,2ya).mtzh est 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 zz bvwc(xjz0 -l- ex38)e2jbzy:ymy 5out ultrasonic sound waves at 50.0 kHz and receives them return -ybej:(czw0 yzmyjx5x3e) -z8vbl2 zed from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spci7r**vix5vx fb 9 p 34x:k.yxnm :wmneed of 5 m/s As it flies, the bat emits an ultrasonic 7niv mx9:p4k:**r3mnbf5w c.yxivx x sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experim m 3:+um,lshpa,7ooztents, a tuba was played on a moving flat train car at a frequency of 75 Hz, and7o husol, +zmmt:,p3a a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ul7ctc az qp.x/n o:1ca3trasound waves to measure blood-flow speeds. Suppose the device emits sound at 3zc1aqnc c7ao/:p t .x3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frnz-imy-(65 lcvf 3sn xequency $2.25 \times10^{ 6}$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 wip 7aqek*e-uy2 y( w jbntn3-adx+ *a:knd velocity is 12 m/7auqn:tw edy *k axb-k3n* ay+(e pj2-s from the north, what frequency 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 l*oyv7sx gb(k79 h:uyland 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) What w2:g46fc gkqg mdkl: /is the angle the shock wave makes with the direction of the airplan klgk gc g:mq:4/2f6dwe’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 wheregma 0j cp9j)1m qsd k;zr8bkjs8;d*4 t the speed of sound is onj* ;c ;jkar4qjm8bm g9d)dstp8s1 0kzly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oc.sa:l*az18 d+mqh cxeean. Determine the shock wave angle it produ e+h .:s18xaaqz ld*mcces
(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 ( qop/7hqpz(:za u5 qe$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andtj1o :r2weefa3 mm i 6)oxmj+4 see a plane exactly 1.5 km above the ground flying faster than tawj: m6 3j 1 2rof4exi)temmo+he 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 5wb(z,jiwo ,b*ohhw.; *juk y device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed t** o,i5y k.oh bb(jju,w w;hzwo work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hs* sz1.b5fmmc uman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dih.5+cx48ac cco/tna7 lis2cw splay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. hc2/i nlct.c84c+s x5aowa7c
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of h 5vc10e n -yf16sitmzquman hearing (0 z5ei6 s1fq1c-m0 vn tydB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level j4s jlkro;cj5)a8rh2 when an 82-dB sound and an 87-dB sound are hea)a;h kr o2r jlcjsj584rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker,,gnrra:eo*qroxlx 4o ;uke ;71 0i d7m placed in the open, is 105 dB. What is the acoustic power output (W) of*rr70miee;d71 n;ogqx4l uokrxa,: o the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 15 v g+ftm21r9pwsg16 tnt1ga6r0 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15t aw6g91m v6+1pntg1rgtr2 s f kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears iom+yo0vs; 3i. 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 ;iivo smo0+ y3of 30 m from a jet airplane engine?    W

  In audio and communications systems,.;0u6dd ir 7p sthxjfh +kjn2: 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 tunsjxj oq /l r*smz26lvld1.44hed 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 fixedr.3ayo3rop,y9ppig 6 points with a fundamental frequency of 4oyr,.p3p op 6ag9riy340 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 vibra c0h*nj84d3 b3ca.vor :qfuwnw-;jzn tion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tub-3r8.4j hcjdwq0 un3* nv:nwfoaz;cb e opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string ofdlseeqkw*,: h ny ;3t7 mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much t, hswk3lqydn t* e:7e;ension 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 o m 2 by p.-9nnz)jtn5jn5 j:ut5ulbm1mne 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 tw (bhao0 48ppe e2ay/,-c lymxro 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 oneeam/-y2x8h,0 rpyleca4o b (p source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is station3t.(fz cyz/az ary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is tt3c.fyaz/z z (he speed of the moving train?   m/s

  The frequency of a steam train whistle an:t od)1rqelt 9ct0 xe(+/rlk s 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 velocity)? q 9e+(toklrnl/:extt 1r )0cd   m/s

  At a race track, you can estimate the speed of cars just bywjc2l9nlz wic/ h-. y) gr-x)q listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose / cj l xwy)rwicq-9nzg-)l2h.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, sounding nxc4ckg7(y6 k xr/t3ptogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How/ (yt34 7xccrpk6gkxn long is the other?    m

Two loudspeakers are at opposite ends of a railroaafw oxvd p2al hbzfb c+kd)5gw-s: ;(bg0.2/cd car as it moves past a stationarypd (0c-owh flvdb/ w2+acg2) kzsafg5b x;:b. observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m29m 9u*a6*z tbitisyst0w zo: z5;hng/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blo90 2;bsts z9g w*6*hztu nma:y5i tzoiod cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward thex. cnhn0c-;u d:dl d/k bat at speed 5 m/s The bat emits a sound :ln0x.; knh-du /dc cdwave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequpx/fuvzlq)4ks)80 nc 0 1*chnarp7sjency 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 that4f )vxcrcus0pzl a8n)n0*j17 k/sh pq the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once ophsn y 94ymijp+2jhw1 -:8dgused to send signals from one Alpine villag4mhi9 ynd12oph-: jpsjgy+8we 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 sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stkjfzekxc4gih2g )s7yr n/8 ;2ereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a h/eyc2;x k) i7fk4 gn g2r8jzsliving 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,” hz7a bt (qa.e.a8*ec ej9z*qm e9qv;6r9 oplr involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90- j r*t 6q arqlez a8p79hmc*(9eevzqob9.a.;ecm-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 ta 56in/c-r0bh2not rhearing for the human ear at a frequency of aboutt brt0o5h6ca2n i r-n/ 1000 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 t 5aa.k3 l3vwttc 2t7bhhe sonic boom 1.5 min after the pla aht5 w3a3ctl7. vbt2kne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 8t* q/, vez2i 7nuebxr$^{\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