What is the evidence that sound travels as a wavig:x9b 64gbx x/bo+ qfe?

What is the evidence that sound is a form oqblgb 98n6rjh;o;s .cf energy?

Children sometimes play with a homemade “telephone” by attachi; 4s cg iek,j+njg0ojt;;qa +nng a string to the bottoms of two paper cups. When the string is +; a ;eqjng+tn;o0 ,jkj igcs4stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into watersbmi+ j2fl.ek yfi u2*elo2. 6, do you expect the frequency or wavelenbef62lmo.uk. yi2f *elis+2j gth to change?

What evidence can you give that the speevcp rj3,*viv rox23 cuhg /s,7d of sound in air does not depend significantlxv h ,osuirp,vv *cg733rc2/ jy on frequency?

The voice of a person who has inhaled jdy (k k g ;*9cogx3yn*t2kd7ghelium sounds very high-pitched. Why?

How will the air temperature i.cwj y; nay.d ),n.zkwn a room affect the pitch of organ pipes?

Explain how a tube mighp;+3cvly / sgvt be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muvc3vp/l+g ys; ffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer n9.dl f/7avvitogether as you move up the fingerin.9/dvv laf7 board toward the bridge?

A noisy truck approaches you from behind a building. Initially yo jcqm dx62 viq/(flo glk *oop3.lt+70u 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 Section 11–15 gpdt o ic7jfx*0/k6+ 32q vll.lmo(qoon diffraction.]

Standing waves can be said to be due to “interference in space,” w eg6(s :vxkup:.xl)w3txg f 8ghereas beats can be 3lxwvf:x up6k8g:() gs txe.gsaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thf8 l.vx/l se+rsrg* 4 tp 8kai9sn+0ife points D and C (where destructive and constructive interference occur) move farther apart or closer i +il40spf+ 8t g/sk8*r asfr9.env lxtogether?

Traditional methods of protecting the hearing of people)s u m71ez :fzxna sts4j36 l1/hz*ggw who work in areas with very high noise levels have consisted mainly of efforts to block or reduce nshu f*3m sx6gawjz gel1 )nz:sz14/7 toise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be, sxl4ux0kuot9n, t; rfc r9g+ thought of as a superposition of two sound waves with slightly differ94x,tr+k r su0ofn,lc9t gux ;ent 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 obsenayxx-r6r g -;rver move in the same direction, with the samexy;a-n 6 g-rxr velocity? Explain.

If a wind is blowing, will this alter the fjm* )ng2 cn 6dsq8a,zb1fkp f5requency of the sound heard by a person at rest with respect to the source? Is the c8)q1kam,6b fz 52d n jg*fspnwavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a *uqogt .5hcm f ;5ms.jswing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child heufmhgs5m5 ;qjtco*. .ar the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by list. 11i8dzm uccw))geyr ening for the echo of her shout reflected by a cliff ac81 ).y )cemd1 rzwigut the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sh0* q nzgzlvn s;h0)o c jkavyst(.*96ide 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 de;hvt)h(as non ycj9zsk gzl6vq.0* 0*ep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wav1ah v ni8y4jy8elengths 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 school of tuna on a fs7: s46 6ov)gwzg womcoggy day. Withou)g7gow6 zv: wmsocs64 t warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top o(5d o7c vxs4i,r7arlcf a cliff. The splash it makes when striking the water below is heard 3.5 s later. od7csrvr 45alix, (c 7How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike th6o:pnsf.q v/0gfzh7/ o pmfp ;e concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact oc6vzs7f/0p: pqon; / fmfg.op hcur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dispbz ds*b)2.pitance by the “5-second rule” for estimating the distance from a lightning strike ifzisp *b.2)dpb the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain-7p3dgcs1q pm 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 who e2qqzes xp3)mn-:7,gf 57 w blaq(vjtse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wh6.abndw-9 twe emq(4f+vft5b en fired simultaneously at a certain place, what willf4-t 6+(twmfbb.enq 9 awdev5 be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain disj :bua4fkw*orl-b1/ uih w;4 ctance 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 huw1b; aok :rui4-jf4 *cbwl/ 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 sif1 k2(fudav; dgnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio ;(ad2 vfu 1dfkof 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 x )a/wr hhax/;3w, dbvnormal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere ce3 w,xhx) /a;/ whbavdrntered 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 bj2o)zjrv-: fbr vnl v ,2vy21eardrum 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, wgag-bd: oeh t5sw- 7ci4p71grhile the more modest amplifier B is rated7 pshe -ct:grgibwadg4 1- 7o5 at 40 W. (a) Estimate 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 fr x(h*fd que*/-yn(5b a5o8y xyvq8 cjib-s0ulont of a loudspeaker on t/of*qleyu8vn(5 hy8 *d -x a ujysqb5b-(0xcihe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level o9ghb3,z ;obvh+ m/s uunt 14znf 2.0 dB. What is the ratio,/h9;shmvuztb+gu3zo n bn 41 of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sounhuwuz+p 7,34n oiy +b3lu/exk d wave is tripled, (a) by what factor will the intensity increase? Increase by a factonx ,7ki+u+w3pe zy3u4ou/lbh r of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displace9ntx97tprw4gr0xnzn, z9 x( kment amplitudes, but one has twice the frequentx,(xg pzrn9rwn9t4 7x9z0 kncy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds toe 8i0:-vobmiz27c gwu a displacemeco : i2-weg7i0 8vmubznt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem dsv,;ih k(r .vas loud as a 100-Hz tone that has a .d;ih (,vksv r50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ead/.r0zx8c om wr can detect when the sound level is 30 dB? (See Fig. 12.rocw8xz d /0m–6.)

  Your auditory system can accommodate a huge range of p*dqmf zkk4/7ojgg a:1/ uv*rsound levels. What is the ratio : mr /qk 4d1jo kv/a*upzg7g*fof highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequencysn3 xd5t*)q 3baniy r( of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Undeib xa*sd) 53 y(nqtn3rr what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wh8s hhg fapfd6 q 9y8:gi,p;-xrat are the fundamental and first three audible ov,a;hpgs di6 -89qfyp8 fr:xh gertones 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 frequency7 v1l/gxo7i6xv 7std z would you expect from blowing across the top of an empty soda bottle t1 t6dv7isxozlx 7v g7/hat 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 open-tube pipes spanning the rang7k-q1xl gi: mwur39im e of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requx iwgil9 uq3m:k-mr71ired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fre8w4he h7fbemuj w)/7oquency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lj78) ew hh uo7emw/fb4ength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middlt-9h x d+cev)qe C (330 -v+c tdxh)q9 eHz).
(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 le(ygo: e fddq25v b*fl-ngth of an open organ pipe that emits middle C (262 Hz) when the temperatu-fv*g od d5:(elyfq2bre 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 20m ic4qg,4: ugb $^{\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 the hole be tha e y*1e4f,2agisx jw4dt *fi ydje2 g waes41x4,must be uncovered 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 264vhy1nliuo97) 5hy+ (/rx eax -mre,te Hz, 440 Hz, and 616 Hz, but not at any ot(o y7iev x/-+hml,) ea ry1tn9r5uxh eher frequencies in between. (a) 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 lifv +;q-+k3+x pb uws :j0 kmfdr2ka8nong is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is wqkk32;u:d va+ksxji8 mfr 0+b-f +p n
(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 nqo.4)is ;xo 7 fyx2wr$^{\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 orga dzt1/:y +thvln pipe ad1vyz+/tlh: t t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the oujqu x3m1te;+t g 2c*nstside 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 information in the graph o u x2t;g+qn*se1mjc3tf Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears owaosr46jp8d-pex 9(+ ;jrro mne beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othxr;ro (4-o wrjde+9p6sm pj8a er string? ±    Hz

  What is the beat frequency9hy abzw f3m8.6*;aa otkk*r s if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates atavop (k*r3 e,x +j0rcf 23.5 kHz, while 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 s,ac3(x0 + keo*vfprrjimultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string producesnog5u* ee ,j8s 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s wosnu g,eje*58hen sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tunpe+z2sxgw+x/k*8rh. -y ic ql9azs )ged to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: p-9l *a2/qsx hx8+g .es+kgzi)wzc yrRecall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try ts: 3)dgtxd rj74s4u boo play middle C (262 Hz), butr4tu:o7 jg4d x 3s)sdb 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 B has a frequ9 j*4y4pw6cccy a9dd eency 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 p9cj6pd49c* yyw4c eadossible 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. )jv05nzto9,;d3 uct gctk8:uk a p1urA person stands 3.00 m from one speaker and 3.50 m frt9 kcda 0r5;:j)u utt v31uzogn8 pk,com 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 a tk,kavcy dk4h/5pxn2w0:;o i t 132 Hz, but a piano tuner hears three beats every 2.0 s when t/d2:4t,kk0xw;cin ao5 pyvhkhey 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 fz+: o9q aohek5qe,-y.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 ,eq 5k:zhqe9yoaf- o+$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f o)*x.26td j ft tddl+a 6k:ovcod)o9sire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of jcl+v todax*62ddsod6t t. 9ko) o:f )30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detecwal ;zks nr09j-vv +6zt if a fire engine whose siren emits at 1550 Hz mw a9 nv 0;6zv+klzsrj-oves 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 mb 9clf/5 7d.ek*mhxulqm (qt,oving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Arlt. kquhl7(cq ef 9xb/d*,m5me 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 them oi:gm c+a41a same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beatgi o 4aa:1m+cm 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 am91emy 2x)j d+o q+h+x hkff6jt 50.0 kHz and receives them returned f21d+yxmkj e +9o qh)xmf6h jf+rom 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 speed of 5 m/s As it flies, the bat em7ldm6,qwvmjo w5fx 3(its an ultrasonic sound wave with frequency 30.0 kHz. What freq j5m(xo,7dm3vfqlw w6uency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doh ;soc2ajc(q ;dnwosl ))8djbkv.*8 nppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and).j2ssdkb w;lcq(av)d8*;oh co jnn 8 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 u u.soec(3j a +bt)t;xof7q ro.ses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in huma;3 c .tooe+jrous7( xab.qf)tn 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 freqz+u .*bpnjce .n2zr 90ukb+y fuency $2.25 \times10^{ 6}$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 570xf,*z lqb.ir asd14,n Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, rix.dsf 4z,q bn1, a*lat 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 lu/viwmb; wb9at:*zy - and 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/6d7 9otjs a3yl3p5 fi zyf1hr*s (a) What is the angle the shockap*ofyt7yf51 3si6z rlh j9 d3 wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of be1xayndh:p ji0/q6;, 8w zi 1wpdbv/ a planet where the speed of sound is only apay1nb1// bi:dpze wiqx 8w d ,0;vjh6bout 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 ocean. Determine the sho9o7wzqa(f 4f a.3auomck wave angle it produces 7auqafa 9fomw.zo34(
(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 f w3*4gze+mb6my:q l w/qs/fp$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and s. 3x l1p1 j3-ruuzb r5wqbk*puee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 1wrb 51 blquz3uxkp1u* pj-3r.2–34. 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 souniirx:* f )tcf wu*e5pf*lk3w5d pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time betw3f kiuw f5*rtl*:pifx5 ) wc*eeen pulses (in fresh water)?    s

  Approximately how many octaves are there in the huma 6hg; (l+w rw6xvm6fvgn audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calleu+l9 rkvu .e*z7y* wojtp f9x:d a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both*+jvro 7 :e9*f .u9uk lywzxtp ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound c.gk wsio;l01fpl-ede(r hq 6yy9 02 2n;zruo wlose to the threshold of hum swo9g0p2i(zryl; lko ;6 q.yehdw02 feu rn-1an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB ep7,-wue+ 6-t v2yqow5tr z hfsound and an 87-dB sound are heard simultaneou7-pfrw,zh q + eowv-tuy25te6sly?    dB

  The sound level 12.0 m from a loudspeaker, placu/,vc4+k 3b58 a-fv z1tr hkp0oxsyev ed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assumin5fakze130pxr v/ t -,+co8 kb4vyhvsug it radiates equally in all directions?    W

  A stereo amplifier is r usi4wl 1-1iojated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpu-1i1 wli4jsou t in watts at 15 kHz?    dB

  Workers around jet aircraft typically w- zgqims9tvg: ( de:(wear protective devices over their ears. Assume that ezd igv-(:tswqg(m: 9the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications synz4js,wqag 4 (stems, 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 tuned to a freqi0zt:fx 8 t87ex8w kmihn lz+y 7qw,/ouency 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 wi,btceg1x0qr i;1ysxl,1r 9z ;(hxl gk th a fundamental frequencex1zr rkl;,x(1s9,c1 lx tq 0iyggh ;by of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set i v)r1vin 033 1ktw8dlawrlvld0hi 6d -s*er3q nto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening toi tw0dq -l3nw8v3k*a1r3 ev1i dh0vlr d rs6)l 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 of mass 2.10 g is nea)4x : guu se;q( -nn4zjj.+lyvor6osnr a tube that is open at one end and also 75 cm long.n ne4(so+ qn4zj6-ur sgvoxl;)y u:.j 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 wascjv2r4tsasg iht-04j0;a0z cp m4 e ) 8tywq:r observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1 rr)t:c73g7sqgx a7ro 000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exaa7x )sg7tr o73cqgrr :ctly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train wu vbzzhrd p,7t1 ;3 pb3e*5pmis stationary. The conductor on the stationary train hears a 3.0-Hz beat frequencv* pd;5pb h13,rmutb 7p3wezz y when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistwl-sl. ,zs8l.)n xm9z kp7j wsfbk) .gle as it approaches you is 538 Hz. After it passes you, its f. fjl.))w zb,sz8.x g 7wpns9kl-sml krequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spe 5akvpcd) j7m tzu b.n*))nw7aed 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 drops by a full octave (frequency halved) as it goes by on the straightaway. kp75t v *mu7)a nj)wbz)n .dcaHow fast is it going?    m/s

  Two open organ pipes, sou,x eqskgz (a.heg. 48bnding together, produce a beat frequency of 11 Hz. The sheh,(ezagq4x k..s8 gborter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s( o+7atkzwc /jtationary obj + ac7kt/w(ozserver 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.-i*e4vlhp1mwhel 3v the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the r-* v1phw.el hmeil 34ved blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the motwek 85cma ,89i2jlzllh is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequel 9lzwe8l5,ai8k2j cmncy of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mothk/b3k /0fywhx . The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo frombywk 0/3f/kxh one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–3kp62vh*m o2p oh/x d3hq07p a s5smp-e8) 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 fundamental frequency of this horn, and wasmo kh-d2mop qh e p2sxpv/6hp7035*hich overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can fou3nzkav4i(y 0, omjy 7a7x8be compromised by the presence of standing waves, which can cause acoustic “a3xiyznjo kmv 7 0 7a4f,y8uo(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 frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” fge1fem s.m/;z)za0t involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the o z; m) .ee/t1mf0fzasgther hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the him 0au3sq zata thngq7n03ct)8e*4 9numan ear at a frequency of about 1000 Hu hcm8*) qiaa0nn7te9 nt3azgqt340 sz 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 Mzw1j;zt -ldc ce3gop ;ije28;ach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes direc jzodc- ilzwj3 2ce1e; ;8tgp;tly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboadf wy;1wa 8 ax:o0yh*v jq,u7bt 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