What is the evidence nv y1-8oubt wn5gj4q/0k-e nl- shi4mthat sound travels as a wave?

What is the evidence that soh3 rm8r a b1ua:. 4s6hrxdp9bsund is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a st9 w;i+ i0h,ubk zat(mzkd1 fh3ring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be hem1z3ik, z0dit+ka fh (hu;9bward 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 fro (amtvf+g.czn7 l+9zom air into water, do you expect the frequency or wavelength to chaglz.mtfn9c+ 7zvo(+ange?

What evidence can you give thav/pr*l xy jzb0n(x b7jo.cp70 t the speed of sound in air does not depend significantly xcbp /p lz.*nxvr007yjo 7 (jbon frequency?

The voice of a person who has inhaled helium sounds verz 5kzr jkopr:nv za56mb1a s2u,5y s*3.js*zwy high-pitched. Why?

How will the air temperature in a room affeohbv130w lg +no9hn:h ct the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude ofi04)so kcq5b o sounds in various frequency ranoc)b 4sio5k0 qges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer to f6cdsyje89rh* dqv a;o: so-6ki:6v agether as you move up the hdvseq*9a 6icdf-8:sk6jyo;ro 6v a:fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you h)a0l,vmjs vn * w4sfys 6nm6q;ear 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. , *f sm6vas;snjym460v)q n wl[Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be dhd6xsw4:c28l3x,co+ b/rza2 wwdm mrue to “interference in space,” whereas beats can be said to be duwd2d,xolsac246r/mwrw +: z38c x bmhe to “interference in time.” Explain.

In Fig. 12–16, if the frequency ofjm+fj rs )b3l0 the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther f+ 3j0lb)jm srapart or closer together?

Traditional methods of /5 tc9tr aj pc.6-p y+a4xhhxqprotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambit t/xc q -h5a y+9xrapc64jh.pent noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31.k6l0 90vmncljp)umgn*7 ; fph Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as ip;ncmnpvl 6h) m 7*9f0u0gk ljn 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 same directiof(vxe(uv2ozq h7z z 24n, wit z7 4(vx2(2hozqzufveh the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by ay.0o)brjm1t+;d- x k oxwj)ml person at rest with respect to the source? Is the wavelength or velocity changed? yojmk dxwbt). r+10o)x-;mlj

Figure 12–32 shows various positionugd nw :zjwcr;.5d1b:s of a child in motion 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 frequency for the sound of t n;w1gdd5w:jc :u b.rzhe whistle? Explain your reasoning.

  A hiker determines the length of a lake by listek ar.ivw(7 3rxgo7jw89dq 0uc ning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s af0dcur3ra7ow kgj 9v .7(wqi8xter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shirk)yg)pm/y/* a/ sgd vp 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 sound in seawater is 15g*//) sm vy)/ygdr kap60 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths sjgoz8p l2 ;nswso3y.+)n4hl 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 n vz q a,i)y8/mmt+;kjfoggy day. Without warning, an enginem/ij ,8;v)aqyn km+ tz 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 of a cliff. The splashi6 w0v8* zaupm(oci)0p y-cbm it makes when striking the water b 0iypwc a0c8ov zbpu*-im m)6(elow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike grpf;4a )rb r+ u0cw9wthe 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+49)wrbfwup; a rc r0g. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distanci m8elqfu n:ghc s/rf.(6a6v/e by the “5-second rule” for estimating the d l a:f8uh(/qrse c g6.fvin/m6istance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun7ge*q eq,c l7jd 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 sounb/sa4 (i mmn/x05o fhad whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound l30 vgx;z5 wiigevel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? w0;i gizxvg3 5[Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane withlvx. 7yp hpijha--t2- four equally noisy jet enh.pah lt- iyv-jp7x 2-gines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person 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-c h,xhb/drstg-4 jz5 0j-wb v*noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the j -bwbhx,sh dgz 0v/-*5c4rjtratio 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 nori7 jy8;bw,z1bl3 c poomal conversation.jo l;3 1w8cy,z 7bpboi Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strgr4ke 08 *okgkikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B ikwmb9v4bem 4j; unn( +ss ,nv:s rated at 40 W. (a) Estimate the sound level ib:ws+mvmksj b4 ,nn9nv ;4e (un 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 meg)f5t h6q5b0-gi u rau5ka3fy so11ii ter registered 130 dB when placed 2.8 m in front of a loudspeaker5i-af) 5g1r o1f ti k ib0ag6uysh5qu3 on the 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 typiuobzbsd 7j 886eq4 ;eocally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amo so6zoje 7 bu4bq;d8e8unt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, 9.)/mr.zdip skv r g vky(-)xb(a) by what factor will the intensity incxvrid. k(9/)y )z-mgpksvr. brease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice th;8zhprgv511a ,cg y ohe frequency of th,z; ogga 5 rvph811hcye other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air1 .lhe3ob0h1jt9 qzvg that corresponds to a displacement amplitude of vibrating air molecules of 0.1h z0 gb19th1jlv. 3oqe3 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound loc) (fxan7t:srb2w ie)*h.rvm+uyt+evel to seem as loud as a 100-Hz tone that has a 50-dB sound leve7 tb vafs(t2mw )u+y :r)hn. *ioex+crl? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ld .hm.uhsz c+j z,h-5ear can detect when the sound level is 30 hz..jmldzsc-u5 hh,+ dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hunq xy.;o+,nc vge range of sound levels. What is the ratio .xo+,nv;ny cqof 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 frequency of 440 Hz. The lengthzk/:mq x wz+g0 of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string b m/+z:gz0kqw xe placed?    N

  An organ pipe is 112 cm long. What are wm/7m 6 l+uqh+/v*hv fy-vs7;itjbndthe fundamental and first three audible overtones if the +fi vj*-/vn h;yqw+ / smthdvu7lmb67 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 freb:noun cj0am ;;r,r0f quency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed ionf;;arbm :r0 0,cnujt 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 pipeseb(k auy::tllp ;/ *-vtaxi3xb*zho/ spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengt(:ibo /auxelhp3kyl -xva /t **bt;z:hs of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of - r,jqb0zl .ib9t ad(p540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length oza , -lbiqt.dpr9(jb 0f only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is oavuvzahox :y-cf)k02/ m1) y tuned to play E above middle C (mfuok)v-y z 2:ha0xc y)1/o av330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middoke 0 -b3co4zdle C (262 Hz) when the temperature isoeo0 z-ckd4b3 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 ato9ba7xa+vr +d1 e,ilw 20 $^{\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 hole1v l;ggfo3e-q gsoh/. be that must be uncoverege- sf vho1/g.;qglo3d 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 pipgot/ 9;x;ad 5jcxoec1 e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) S5 x 1coj/9etd;xa;gco how 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 open at both ends. It resonates qxa)xb2x)r 6di5q+owat two successive harmonics of freqxxa+oiq52) )dbxw qr6uencies 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 ) ju4t yz3h(eb ,-sdja$^{\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 p xt- /w:arfd*eresent within the audible range for a 2.14-m-long organ pip:*/rdet-x wa fe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximat( kigeezf-iy/ u9r 52tely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your ay-i /kg5f(29zr iuetenswer 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, one 0 e4 qkz .ij/17f4wmpkeb8e h f2tesg2of which is sounding 440 Hz. How far off in frequency is the other string2 2ke8 k q1gmi4h p4j w.tbz7fes/0fee? ±    Hz

  What is the beat frequency if middle C4rw, k*po0dgq (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 operat w onr0p:90b9mr6gq mees at 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 pl6om90 wqbgrer 0m9p:nayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning forkg:o9yp u12sx,l )2o todljr9p and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoni9p oo: r2o9s,tldu)gl1 xpy2jng.    Hz

  Two violin strings ait+ lws1-pz 1dre tuned 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? [Hinp1 +dsizt1 -wlt: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fi x3q:m5 lzm;mlutes each try to play middle C (262 Hz), but one is at:x mi5m3q;lm z 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 fre+(3:w+ixc l vpb4/,fk 2 qavtiokc ra8quency of 441 Hz; when A and B are sounded together, a beat frequency of t av8cwl2 : oab,r+34ckfivkx+(p/i q3 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 person stands 3.00 m froma *zmkujr3 6/ozd1wd( one speaker and 3.50 m from the ojkm3* /d1o6zr(awz duther.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tun)9bg 4rp v1b t7cwza*ner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must vtr* pac 9n14b7zbw)gbe 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 2.64fm3x jk8)dp8g1. )ui )zpymqi m and 2.76 m in air. How many beats per second will be heard? (Assume 88xumy zd)g 1if) ) 3kjpmipq.T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency o *8pvwug4jgb n./q7 qjf a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect /4qju. * gn8qwb gvj7pif you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. 4b db )*dxqjd:What frequency do you detect if a fire engine whose siren emits at 1550 Hz m*dbjd b4:d )qxoves 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 sodg t,ou) 0fmhgur06k:-d hdpbi+p+v ,)i w5d gurce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? A0d- o)+pd5)uh kdid,m ,f:br pgggih0+uv6w tre 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 b/zc p n r.d,wfit2o6/with the same single frequency horn. When one is at rest and the other is moving toward th.z62wdr,/btp c onif/e first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz andw;.2 *xw 0o3egpl oxwp receives them returned from an object moving directly away from it at 25 m/s What is the receivowxe0p;2 g*wl .po 3wxed sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speh3tgu(3)tvugt7 mq 9bz,yu4p ed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fre9pg g(yv4 3,7uu tqu)zt3mhbtquency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mozzn39l88qe/d kid u4qving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while qnz9e l/ud88dkqiz4 3 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 ultrasound waveo(hgt6h p/-n i aon9ot8zi.-hs to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency iohnn- too(6zai hp9 h.8i- /gtf 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 frn0o0 qcf*fx/mequency $2.25 \times10^{ 6}$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 570acy w5ed.0: ff(gxm,g Hz. When the wind velocity is 12 m/agcf:(g,d5mfxe w .0 ys 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 land if its speed abo5y z(blib,q m/ *yjt 81ap,ct 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/hjfr+ gt +,a4+hcl rr,s (a) What is the angle the shock wave makes with the direction of the airplane’s mo+ rjh+ at,fg+4rhr,cl tion?    $^{\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 sp) ffj ;t;dp. zi3v:by0mr k;spkt- i5geed of sound is only ab- kvim.kzf:;)g r tjdfsy0;tp ;pb 3i5out 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 bl2nw2.l u +wx x4p7x b.nugc5the shock wave angle it produce bng 2xuxn l.cwb5+.x7pu42 wls
(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 (a4plnm. 0wd y$/theta$ 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 *0c+3hyc5e oi aqhz.j 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 oaq*c0 +5ozjhei.hcy 3f 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 gnrhauccl;-(htb8irqo39 rd. o7/s 2 sonar 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 to work is 200 m, what is the minimum ticha7h9 t- .bq l;c/orsoi u8r3rdng 2(me between pulses (in fresh water)?    s

  Approximately how many octa-lga9lpt )e*q ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calr* 1w;;, 7wk .b x *:u+ykvvt4r +nqzbhdnklsvled a sewer pipe symphony. It consists of many plask74,;y*un xlvzvbw+. h nkrrw;bsq1kd+ : *vttic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresr /pxfifj9i n j-y3md+.9l.uxhold of human hearing (0 dB). What wilfx+.mji9udx93 f l.-jipn r/y l 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 pbkk4t3 t:u*aare heard simultanp:*tbu4katk3 eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, 8 3mdslr 4axh0is 105 dB. What is the acoustic power output (W) of the speaker, assuming 4sl8hdr3m a0x it radiates equally in all directions?    W

  A stereo amplifier is rated ao .u,o,8n paypg1ctrz3.r z2 xe*uw h50e3dx xt 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power ourx3ox.d5pzup*y82 o1aw 0, cxreghze,3tn .utput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectiv9j 4;xuqiga2zcb l 9q)e devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a )4bgiqz2 ul;qa99x cjdistance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the g y4i huqyl/ 6xkx6o1)qain, $\beta$ 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 frequ jcl io/2t*ka-w a)s9uency 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 0rp hpw6.ke3efixed points with a fundamental frequency of 440 Hz and p.r0e p e6k3wha mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wmh,3) ,t fypq0pg 4e1lmy8y djith 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 distfpj 8m ),hye3pt, gd1l0q ymy4ance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open avlm (k0s654 /mw mzemat one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundwmkm0z6/ smmva5el 4( amental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to recz+fsoym tk 0;7at+h7sonate 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 sourcest x*b)de(e,i: mr 9a(1uewrgl. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one sourc r *91re(ab tmi:wxu ),e(dlege than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on t y tbqa18o58muhe stationary train hears a 3.0-Hz beat frequency when the other train aaombu5y 81q8 tpproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is ,xg.qnqr/g z*pgg. /h 538 Hz. After it passes you, its frequ gg ./.qrqpxh /nzgg,*ency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by o31tocz:tgvsbq-c-d fm 2nz 1 f.8i;u 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 (frequenc-cidg;1z 8 t.3uv of1t-bs:qzf2omncy halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The rfsh54-c0k/y ltq z6 awt)f m,shorter one is 2.40 m long. How long is the , zt4)hqlskfa0ftr5y c 6mw-/other?    m

Two loudspeakers are at opposite ends of a railroad i+be)ism3e q. car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–3bs)e .qi m3ei+7. 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 azk l0c6z1+ jsy-md5ko;s ited;vr9,yorta is normally about 0.32 m/s what beat frequency would you expect if k-zy s1t,rc+09klded6vsjo5iz ;ym; 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the mo ,s rr2mzhm0.bq5aa-zth 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 after that wavmasz5 m-brz.0ah,qr2 e reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it app bri3x v*r4( qi2-mhde ogb/0bdc3nusg,o))nroaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far a*umbrq 32vne- c bix3bgni()o)d h4/sr0o dg ,way can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to c+gzu ce; p+-msend 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 ple z+up+g;-m ccayed as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comprom2y+,f aovk 9tor nsw :9yjj6*by0ay-y ised by the presence of standing waves, which tafb* 9:n9joy j +6asyy vk -ow0,r2yycan 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 frequencies 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,s5cd*: v o;lyo6: yo gah/a+lh slender aluminum rod held* dv+/gos; alh5 6hl:oc:oa yy 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-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear ath4h6nju9 t)ga6re2 *n :5vw h9h lsxnx a frequency of about 1000 Hz hsx66ng 4 an jvh *9h9trnh2ue5):wl xis $I_0$ = $1 \times10^{12 } W / m^2$ 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 yrlxf:(tm ph /p(7,5ev(vj2xncx g(e hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altituly7 5v t((vg( xceefppj(/nxx:m,h r2de?    $ \times10^{4 }$ m

  The wake of a speedboatj1z65eyqfl2q/ad + uj 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