What is the evidence that sound travels as a wj(wdg. d2em6wave?

What is the evidence tx 6i yqgthr51 k*7qy8vhat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching :k wx w.jxm0,da 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 other cup (Fig. d0:xw, xw.jkm 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 frequency or wabt +5 8dj nsuo und a6rhy;8itp1z.,*mvelength to channaho+ ru8*npd it ,s8;6.dzjbuy15 tmge?

What evidence can you give that the speed ofl4e x zez9f2a3ue,3 sm sound in air does not depend significantlyee3f3l s,x42zeza u9m on frequency?

The voice of a person who has inhaled helium sounds very highm1+d8p5y,yu wk vw2n c nl9 d4p9dh+hx-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipep2vu6km pt66gg7j o tcom4 5w1s?

Explain how a tube might be used as a filter to reduceg jcx;d ty9dqsskl9-8 -hkr(. the amplitude of sounds in various frequency ranges. (Anhdry(k xg scq-td9l;jks . 8-9 example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clor 9;vxe4q u4wkser together as you move up the fingerboard toward t u4ke4vr9;qw xhe bridge?

A noisy truck approaches you from behind a building. Initially you hear it but x*1nm;sl d(/ tteh os6cannot see it. When it emerges and you do see it, its sound is susl hn6ote mx*;(/sdt 1ddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beae8xt8oake2h lefxo o +*k019pts can be said to be due to “interference int* o2e189 ofa op8x0exklhk+e time.” Explain.

In Fig. 12–16, if the frequencywh,) ;ik ny(q (fldzs6 of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer toqy i6zshfk dn;l()w(,gether?

Traditional methods of protecting the hearing of people who work in:syi b j):qx*f areas with very high noise levels have consisted *qys:x) :j ibfmainly 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 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 thougwd an:o4c ttg*2 :g/ye,8 .qoaf6lp blht of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the tw qe2:b: .ogt8 *oaycantg l, wd6flp4/o component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if thjp qom(a49cl,9re;fw b ( ql6ja2h7mi:s olz,e source and observer move in the same direction, with the sam7rq(:zo6s 9q2i jpf, lc(,j lmw4ea l9mb;ahoe velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a persbymki gu su9678uw f4a;+jao8 on ;k uawfyja ou47gm89uis 8b 6+at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positig;v.zw1t8v5avz0 g5 rfs zx0tons 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 frz 8v;5z gv1.5trwa 0xvgs tzf0equency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ech /+9-kl ox d:8s nv*nv;odeaaco of her shout reflected by a8anc:o- a+sk 9nlde/ov;x*vd cliff at 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 side of his ship just below the waterline. He hearsfoi 8g ,z 3vsc q+vm3dgw7qh(*n(l-ds 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,ozd(cqm n- g f qs7vd(vwhgil+*8s33 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a*nrnap : hjwmck( -/.tt 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 ofv 0 w2tm9fzaeoh;aty) -u/8xv 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 (a) by ty9 wz;uat8h o-ev2 )m0tva xf/he fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikv2j8c ch r5 n-tiv:vt9j+g ;tbing the water below is heb8 vhtjiv:-+5c ctjgrv;2 9 tnard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge m wqou +fj04v;stone strike the concrete pavement. A momefv4+0ow; mjq unt 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 occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ove+yo6.ub.+xc2o e )o5noyig,vuis yn,r one mile of distance by the “5-second rule” for estimating the dist+ov.yo y6y+,nne uo)u ix,s5i2.gob c ance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paxcqq /ga2;1j1 dxh m vxg 9g22)h,gg;e gl3ioain 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 8,shx,kz1z ed whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired skd0 t s1x dw rjx.-8aurzk0e-0imultaneously at a certain place, what will be-td1u z0 arxkk0 wex8-d0s.rj the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from k/ s.czlp)0hcf5:d9ns q /z rcan airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]s)0zc 5h 9sd.:p/ zf/nrkcq cl    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dojq l1mmcj91yg:+ x+gwa1f ( yB, whereas for a CD player it is 95 dB. What is the ratio of intensitiegjlo(y cj9xqma11 fgm+yw:1 +s of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal convenqvt;(d dd0 g/rsation. Use Table 12–2. Assume the sound spreads roughly uniformly over a spher qnvd(0/dg;dt e 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 strik6h-. xi /xx ,kko9iqores 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 q wwoa-88 rh2eA is rated at 250 W, while the more 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 loudspeakeqewwao8 r8h-2 r 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 fro4byz6bet(;21qvu zs c8,ikq ont of a loudspeaker on thuo4 ,zve1s 2 qc;i8ytbzb6(k qe 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 of 2.0vy d,vz1+/qp9hr n( pv dB. What is the ratio of the amplitudes of two sounds whose leve(, qv/ny vz+vr91hp pdls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the i8.,8 uvlay lptntensity iu l 8avy.p8lt,ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudf 174lwh,:x*hpa rj bees, but one has twice the frequency of t jx hrpe7f1b,*4aw hl:he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave atd i-d1bim3.+ d e7tlin air that corresponds to a displacement amplitude of vibratini3mi-de.t71lbd + tadg air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thafmhq-98+u b s ,ptz4jjt has a 50-dB sound level? (See Fig. 129p8qf h-bjz,+u4 sm tj–6.)    dB

What are the lowest and highest frequencso5 w,q*,kok2 m c.vpiies that an ear can detect when the sound leve q,*v, o.p5 kowmkci2sl is 30 dB? (See Fig. 12–6.)

  Your auditory systemwki 3+ toddr6. can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity a6d3+kroid .wtt
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has 7 l64h2(kyelbo w(slrp3pkk y6 8(cbma fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Un 6k(mbyb68shy(7cp kl 2kopw4le3( lrder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the funda6lxpn)ejqx55kqp,8)ld, -l lfhkl0y mental and first three audible overtones if the p,lllnkqj-)d,eyf xp85l k0hq5lx6) 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 frequenc) c3 6wu:uxm ,;o6hc uakxih-my would you expect from blowing across the top of an empty soda bottlei6)mx,uhcc 3-kma :o;ux6wu h that 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 range of hu01xn0jgeb x*i man hearing (20 Hz to 20 kHz), what would be the xbe 0ij1xng*0 range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its wz)-3ivnyg m)a-q( obu;q. mdthird harmonic. What will be its fundam vq a-zdw;.om(-mi3u))qb y gnental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strin 1s k2lnkcrf(h7 ubbi+6hw6(dg is 0.73 m long and is tuned to play E above middle C (330 Hz). chh1bb2 fd k6(+rns (uk7 l6wi
(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 pv;x 1k1d) ;xj zggutx,o(mx -open organ pipe that emits middle C (262 Hz) when the temperature i-1u ) vmgxjxdgk;,(x z;px1ots 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 aw61,/vfkmq+sdgo ;) w r0as yk m9yg+ut 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thexl3d1z i 1l9sf ya+-rs flute in Example 12–10 should the hole be that must ifyx szll-1+9 r31sa dbe 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 264 Hz, 440 Hz, and 616 Hz, but not ;hiwonzr4m u:2dn.:clk aq 6*)-nd tfat any other frc-* .6)hirow:qt24nmkdan:;u d nflzequencies 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 long is open at both ends. It resonates at two (g1ufgp)wv2d successive harmonics ofv2gug d) f1pw( 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 cm b0h*x2tup(k5ya/ f $^{\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 pr+ifbo-id8uoaswd x1q pi(t6076cn :d esent within the audible range for a 2.14-m-long organ pipe at 20 6-qo1b6ao i(id0fsnux:7wc p di8d+t$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. Itwujayuzujusp)9 q45,cb:m t. 0gm:g7 is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer bu uq0m wgyjzu4,:57ms. t)jcu9g : apto 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,0.r*(f6 *+a kzcfbuildm ge. t one of which is sounding 440 Hz. How far off zlrgd + 6fm.*ubc*ka tife.0(in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) un/s4zv dc 1e) njvbc48 ri0f;xi7;sl and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 ksn no 0;9p bsgt3tx(x)b4lhe)Hz, while another (brand X) operates at an unknown frequency. If neither whi9xlgsbtn 0;)e )sh3otnxp4(b stle can be heard by humans when played separately, 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 tuning fork and s1y(1wz o :(cutne;5flj +-uyk xjn1j9 beats/s when sounded with a 355-Hz tuning eluo:;jf1jj(xc1zs nky 5+wyu- (nt1 fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to(ffo 5ch6-ew m the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the bea wfh5(m 6eofc-t frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes,f8ojc9plnak2l97 , e ,jh9t)ihzb on each try to play middle C (262 Hz), but one is at 5.0°C and the othe jh9,iko9n7f b lhz2ptej,8a,c) lo9nr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz *(hoxd mm l;s978fcjr; when A and B are sounded together, a beat frequency of 3 Hmjs(o ;f cmh*8dlr79 xz 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 from one speaker anm0-o-tx qns0 v;4g1bb 8lkxmousbd66 d 3.50 m from theog00bsxxduvq1 n 6mt4bl- - bsm8o; k6 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, but k 3 g*-xi kx7wd57meqrayg38 ta piano tuner hears three beats every 2.0 s when they are played together. 8a7 d r-kx3m37iyxwqektg*g 5(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. How many beats pers pnm2(. pcrn5 second will be heard? (Ass.c2pnn pm(r5 sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certso ,, 8gayrb: rhi/9n,ydl ;wlain fire engine’s siren is 1550 Hz when at re ry ;,:b,n9 ghswoy,dra/li8lst. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you de(r h+3 n n;;jwxkxyq(vtect if a fire engine whose siren emits at 1550 Hz moves at ( (xq;rj; yh3vn+kn wxa 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 2 -ad ;:kg 2f c.r5ctmbs0bnjfmoving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly t:5bfjcd afk. ngrb 0sm;ct 2-2he 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 frk:2fl6vaphzb, .pvonn3 )gy 6 equency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5fn,6.2vo kp) vg3 l 6bayzhn:p.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic so p o9y-6jni+racv you bd06c(6und waves at 50.0 kHz and receives them returned from an object moving directly away (vdc6y69oi j6cr-oa0p bu yn+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 flief/es(*nx-q 4 a*od huns, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the refle se n-o*hxad uq/*fn(4cted wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a m4fz5 usq0n* wz ba.zr4zx(7 smoving flat tra xfz5aq04br*sn uzws(7z4 mz.in car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Su wchxxo,g1:.r ppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s Wxrhwgc.x ,:1ohat 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 frequencobz laz)qznbw in:)7qur ;+ :n4bm44cy $2.25 \times10^{ 6}$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 th dh0eqjn3:1ef e wind velocity is 12 m/s1e :3 fhnedj0q 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 speem:+ ytfluo /g)d 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 speeh-h;i,xgjze) e / vov,d of sound is 310 m/s (a) What is the angle the shock wave makes with thoz;ge ,x veh-i/v)j,he direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the sjltk 2l xn.my :w z;2of*s-nw4peed of sound is only about 35 m/s ywn4t l*jzk x:-2o .;2l mwnsf
(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 strikw-sf;j u t) dyej8(oa3es the ocean. Determine the shock wave angle it produy-(utsa)dj;fojw 38e ces
(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 ymtqn14 vzbw6;ys)j*g zn 54m $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grouuy *zb l:ayjb1j qno:ukl w9m6u+5t8:nd flying faster than the speed of souqwmlb 1bly8yut:k::5u+*9 oua jnj 6 znd. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device tha.k(banbtcyyrr d01 4tv73 q2yt sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the .ktynqv 7y1yrct2( rb4ba 03dmaximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there inzfh(b4i r*o5e the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pi;cyt7p+xl8a h pe symphony. It consists of many plastic pipes of various lengths, which are open on7a8+p;th lxcy 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 fre77gz wx4y, y ;2wnamakes a sound close to the threshold of human hearing (0 dB). What will be the sound r77x4,wfy 2g nywe;z alevel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB 9ocpum*z2v g v5ie89pf 8f(hdsound and an 87-dB sound are heard simu v 8emig 9u9*co8p 2pvzfdfh5(ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed k jaf y2dhbe+xrjvh5 +ic- 6x;-8k.loin the open, is 105 dB. What is th6jj +5lcr+ 2a- ;xhifh.bv8k od- xkyee acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power o5b g;: ya6 ;v)v o/gyzgilsev,utput drops by 10 dB at 15 kHz. What is the power outpvlgiav o gvz:, eby/;s; )5gy6ut in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective y4ezze:bf1 7 fj)g.h1od4x pr 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 unprof.1hp o)xg 4b4 rez1:7ydjez ftected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications s8fdlnj2 xnbi+z/9g2r ystems, 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 iwxe o5,+: k;h bu8wtyfs tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with ri e)nt0 ylaffp+,t5:cmm w( :a fundamental frequency of 440 Hz and a mass per unit lengthf5e ytmmc+,t)(w0: afrlp in: 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 hps+ ty qsn 5czv8p;0;a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, thephn8vs;p; +zq csyt05 air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m 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 netn2: j5 s)pxis open at one end and also 75 cm long. How much tension should be in ttnp 25jen:) sxhe 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 t. )9+tq/ d- 2ggvabr iamc0xyhc(a lv5o 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 5w2ee zli :7 dh51*cm uilhd*cthe 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is mic e7u2ili5:h*dhd cwe m5zl1* nimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The voghl(2+;ir w)c /38tqgqq bw2 1edka/fy/bn conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spee 2gdiwrq//g8q+yqba(; lvkot e2wn/)1b cf3hd of the moving train?   m/s

  The frequency of a steam train whistle as it app4 pesuf+v .hr,py9y+ kroaches you is 538 Hz. After it pa, +eyv9kpfs .uh4pry +sses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jucz)/lokw1 d0 vst 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 fd01zv)k o /clwull octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of iw(va+gi .hy011 Hz. The shorter one is 2.40 m long. How lon ahv iy(.i0wg+g is the other?    m

Two loudspeakers are at opposite endst3xp97yf o:ya. -cpm l of a railroad car as it moves past a stationary 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 t m py-3fo7y9lpxat.:c he speakers after they have passed him, at C?

  If the velocity of blozvqqa 9a,0:b temg8* a /ol(rcod flow in 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 red blood cel c8tb*/:re ,zg a al(q90qovamls? 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 h)*jbj kqk(b8while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wj( kk*8jqbh b)ave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freb7flw l +rz )qqkj1z/*quency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before )1kq wl+jzbr7l/ *zq fthe next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used p 3ipvd/t l,2a:bwsm p9n5/py 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 lop3t/pp 9sidw2l ,y/ :5ban mpvng, 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 comxm 5a :gqnzh-do6dso62:e1bgx ac) g (promised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundameng(:bzmhe- xgao5nq 6cxog2a 1:d s)d6 tal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calleqn 8-j)vn w,hhc(p xv(d “singing rods,” involves a long, slender aluminum rod held in the hand near the hvj,8q-p wh )n xnc(v(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 ae+.tv xqt jx-:5z0ru .(pjk hst a frequency of about 10 x.stxjer:h+ q.v05 k -tup(jz00 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 tml9( k)ev:uzv z3ov3ehe ground hears the sonic boom 1.5 min after the plane passes directly9)lov u:ze3v(me k z3v overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is5 -kyth os1aahl7 au*) 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