What is the evidence that sound travels asrlt* rt5n 4yyc9,kt4g a wave?

What is the evidence that sound is a form of energy754my:fl zi za?

Children sometimes play with a homemade “telephone” by attac)d+iotjsi8ukqh,,ma jq4p.x47y w t ;hing a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heark7.mj4a p)qhqs x ,jtti4;ow ,d8 +iuyd 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 water, do you expect the/ot7gu4ije fd72 9)nj4c w xde frequency or wavelength t4gdxco77tjde e)2u4n 9/ i jfwo change?

What evidence can you give that the t;hsuxkqq5 ;we, fqp: :7;mfe speed of sound in air does not depend significantly on frequkwe7tp;q,f5uh sqqxm:;: ; efency?

The voice of a person who has inhaled helium s1**ot v: 1q wbpbm1bchounds very high-pitched. Why?

How will the air temperature in a roomrci:x:eb *fnml64-)cm gi1js affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundsg-1mb g4ckyf*t2jek.v .a72gupf ;p h in various frequency ranges. (An example is a f*gkpy7; . . g-4uf2m t1gavphb 2kecjcar muffler.)

Why are the frets on a guitar (Fig. 12–301 /g9*p:hmnxil4s h9sq its v() spaced closer together as you move up the fingerboard tol9ss4x sgtn( hq1*h/pvi :9miward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it buaf d:6end z(s3t cannot see it. When it emerges and 6:z(d sade3fn you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sa8gkr ewio.,(bid to be due to “interference in space,” whereas beats can be said to be due 8 .g,(krwob ieto “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers w p*0,)ygwo-x( nsrlzx ere lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together ,wnx(o)*y gxz-ps0 lr?

Traditional methods of protecting the hearing of people wrld se 8ne 4ge47oz1t7ho 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 ambient noise. How could adding more noise reduce the sound levels 4e71el8se47no trgzdreaching the ears?

Consider the two waves shown in Fig. 10jhpyxc9n/ou yu,be+2 tmmco- 4dna8 z (x;(v2–31. Each wave can be thought of as a supu08 udx,4 n -9ze(yy2mtco ;bcjxhp /n+ amv(oerposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourrb1fw/ 0cow- d47it sz;5swc rce and observer move in the same direction, with s/r107cio- 5ww d4c rtsbz;f wthe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sounya*7q58 -3e8p+ajhk xzm )wfdn nd +ird heard by a person at rest with respect to the sourf i8jxdz7d+a3*m np) n8yeh5w-aqr+k ce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moti3cm t8,3iwzs jdrr n)(on 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 forw83 n3)srj (tmrz, dic the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenivfb, ,3a+ gext*2cpdrh 9ob+sng for the echo of her shout reflected by a cl3 9bchav2 sfe rpx+,b,+gdt*oiff 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 waterbwt ls)1 8cn ;ad,:o5cxt5rtnline. He hears the echoc5nxbat :,wts8 5l tonr) ;1dc of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavejqb d amt, wd0fv,v94kbh1x*)lengths 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 foggy dahn 7cx2; t-y,9oby tkn67qdsp y. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfi,pd s9t62qx y7ycth7-nno kb;re is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash -3evm8sx(l xeit makes when striking the water below is heard 3.5 s later. How high is x s83mvlxee-(the cliff?    m

  A person, with his ear to the bvnliolayng;k8 47h.p6v2 :po;7lg p ground, sees a huge stone strike the concrete pavement. A moment later two s l6b2; h.87n:ovganli4ogl v ky;pp7pounds 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 ov3l- iyf nddb xf4m,))der one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if t xf)b4ym,)f3d-ndldihe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 yj *ja93 u1jojdB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity ial )e*;ur 7zxern ulm.,xc1o,xtrz 2, s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously a 4r60.kn6gmzbxx6t cqt a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’xnb kz.t406qr6x m6gcs.]    dB

  A person standing a certai:vjyx :h m2v (p1bxjs9n distance 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 experience if the captavxp(sjb y9hx:12vjm : in shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wed yz535.ojd2m q msm6po ao4/hereas for a CD poma3qmjzd5s6yd 5 4/o.p mo2 elayer it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of souo+q1trfntlru v n36eam) f1tq9 t:/c6nd from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ovcvnq qrutf: 6tfen)tr 3o/6 l91am +1ter a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area idy/jkf zn/)u7 *jols- s $5 \times10^{ -5} m^2$ (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 mo e- bbn+qg kwh,q6sxhp -gtz+hab)86,dest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you woulzg e6phwx)g, bqkt,+ qhnshb-6 - ab8+d 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 regig 5 gyav zi/u/q 0x9)p+1kfa)zzwj1 acstered 130 dB when placed 2.8 m in front of a loudspeaker on th0v9 zw+ zz51)pagfk/qg1 /cjuaiax y)e 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 difen8f:bjs 5, igqn:8aloe+k,e 4 whg /bference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whosefieng,8o,sl5+4a en/q:w:b8 gj kheb levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wil5znta.jyb; 8g l ;j)drl the intensity in)jr alz;.g;jbd y5tn8 crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplituddgr5bn2m.l qpt b**z5es, but one has twice the frequency of the olb**n2mbztp r g 5.q5dther. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a soundznapy. ): ihji m.k:tt85 sd8j wave in air that corresponds to a displacement amplitude of vibratingia.z. 8sj i:hy5:)dkj t 8ntpm air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound ; 4;aqtrer4g wdb0r8v level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 124arvet4qg ;r; 8bw rd0–6.)    dB

What are the lowest and highes(wer5t v08i- 7rzuhb1sfg;li s w:r0v t frequencies that an ear can detect when the sound level is 30 dB? (See rw:lfh(i0v b-e0utv7wiz5 sgrs r18; Fig. 12–6.)

  Your auditory system can accommodatebde.ih s38 wwql(gl5k6 zw4b ) a huge range of sound levels. What is the ratio of highest 4wbghkws 5)lzdwl3b( i68q . eto 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 length q0y7jt89 mz2 z z*o azq2:o*f bsl;nkhof the vibrating a 0f9q22; onz:h*zl7zt yjz bos*mqk8portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audn0)e0 5xytdm :u*e:cnm 67hwsgnl6r oible overtones if the pipex0w : elmd 6m7:ye5n*cuntog)n60rhs is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from bl 0hd mr8rf xx:2k0c:2o wqs2xvowing across the top of an empty soda bottle that is 18 cm deep, if yourm0x:hxv 2:fwc8r d2 soqk20x 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 h n).u-slq1quthe range of human hearing (20 Hz to 20 sq)1qnu-u. lhkHz), what would be the 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 kz08t ou;r t 1rl*cd4le(yby/03diyras its third harmonic. What will be its fundamental frequency if it ist 1b0o 0(lyi;yeuryrc* 4kr/ldd t38z fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m l8pzrbm 9 +0ttge+ ksr,ong and is tuned to play E above middle C (330 Hz).trg+be t,k0pr8+9 zsm
(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)h)4gjt gktgn;,: klh open organ pipe that emits middle C (262 Hz) when the temperature gtlht4,nk) )kgg;:hj 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 iizl0mz og**( at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpie ,zgu+5leu )g0oe6k,xhsgn g p8etg./ce of the flute in Example 12–10 should the hole be that must be uncovered to play D abovee60 o/gzg,gsx,)eehp.n t ugk5g8u+l 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, b+zgu*/tm9u3huelsep / i q +n*egkm;3ut not at any other frequencies in between. (a) Show why this is an ope 39gs+*/lmhnpei;u*qgzu+ / te ku3men or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1sz,bxj:llr5- km4 6bx.80 m long is open at both ends. It resonates at two successive harmonicl,b-jz km:r6x4bx5sl s of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 c :n0c.nfwxdjpq 2*x9$^{\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 presuih .5rn 5b-zbcp ln)3j l(zm:ent within the audible range for a 2.14-m-long organ pipe at zuzr lcn- 5):(in3bbhjpl.m 5 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately c 7 1v.gx1 mm 7fbone ku/(*yu)lc,sut2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequk,x b*1vos( .f tl7guu ey17n mu/)mccencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one e2 sxaw;z1 +jns rg(8f jtz o;t:d*tm-of which is sounding 440 Hz. How far off in frequency is 1z2w*e -fo 8dsnj+tmst :txazj;(rg; the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzmea.1ckq;.0oq + akmu plvl* *) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates atq, aa3+yy (+cf 7rived an unknown frequency. If neither whisty+( i+ ac,f7v dqrey3ale 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 whenr/cf j88 (iadr 5mwfy6 sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Expl8/68cmi (fjr fy5wrad ain your reasoning.    Hz

  Two violin strings are tuned to the svc43e-6xs r zcek6ks8 ame 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 playek4686rzx-k3scve c sed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mipy i sug61 4 fx4sv/tg hobmy0*fk-y;9ddle C (pyg hfikf *u;6xtgb-m140o/ys y4v9s262 Hz), but 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 frequency . o8*ahqy j5vqof 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B an j5 yv.qqo*a8hd 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 z)m )va*9hsgpm :,t 0mu) mqkistands 3.00 m from one speaker and 3.50 m from the m zp) :mtu)h)mis,qk9*vm0 agother.
(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 ard,+a8rob i6 +7mel+qiat mjr6e supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the,+br qdtmm6iliroja67ae ++ 8 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 *t k2y2iv-wjx2,fkkr l-85 g/ cjrzlo2.76 m in air. How many beats per second will be heard? (Assume T = 2k/r2*wgf -y, 5 kjic2- jvo8zl2ltr xk0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ocw)r3 12se u)z ztm:jqf a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect isz2m qu jc:rz3w1 )e)tf 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 de c7r4 u:cz.vmo you detect if a fire engine whose siren emits at 1550 Hz moves avmr4uze:7.c c t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving 3yxzh ofwifz -,2e6k9 toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sa 6-yzhfx,kiow3efz 92 me? 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 snb1m /n2r snz*q ;zdek7umb;hs67 c4p ingle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hearsmsbcsqe*mz ;n h27;6u71d4p kbzn/rn 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 and receives themhvq+f /*9(wvn wizwh, returned from an object moving directly away from( w,in/wf9 +*vqzv whh it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sp,uv b6d3; 5vw g(bqa9vps wgc2eed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in v (du3, pw5gswcb ba 9g6q;v2vthe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movinac o1,z dvwi pn0yo+vy0.*6h ng flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car apo0zd1*nowc y v+.0 ai6y v,hpnproached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spu hct5q/zsp v o/j-,d9cb),o7gb ptc,eeds. 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 expected7 , -/c/c9bg)zhu bto s ,p5copv,dqjt 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 ultrason9yybqrza/qslnj 82. 7 ic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. va , xwt.eu3(aWhen the wind velocity is 12 m/s from tu (e w,txaa.v3he 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+dm d(n0 pendij gplgp f+;gi;(w32o5 moving on land 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 whera79j flc-d dejw)k95 ge the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motionfwkej79 g lad9 5j-)dc?    $^{\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 bnel(5j* lcj7.v5z9omx+ l xza planet where the speed of sound is only about 35 m/slcevxl9jn*+ 5x 7(lzjzb . om5
(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 8,ha)m8/cgul6 3 ysqulok2 q eshock wave angle it prqm),8c gqyuo e2sa8l/6ku3 l hoduces
(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 r.mqqkw20 kgwget 6w af/ vn8tab- 9ez/404s x$/theta$ 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 zs sme8(v :+uwv;oabn/0 dy 9n(dpf5uexactly 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 ofs mw;:fo d(nyuzuvvs+da/( bp9508en 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 that 34iw)bp 5vgq - rfxe6rsends 20,000-Hz sound pulses downward from the bottom of the boat, and then detect)5xrrpev qb364fw gi -s echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in t blsl k)/a,.zj7j er*yhe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has as ai,k-v j8k*y display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. 8ij -vyas*k,k
(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 cavq0 nuig ik65 wn-*-klose to the threshold of human hearing (0 quak-knvi iw56-ng *0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are xsu( 8y1sudk.m0k0 ibgmz :mkhmheo72o+/x 8 heard simultaneoi10 xukb g (mh0hems2y7k8o/: us.x+kmd8mzo usly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105al,xawe o* .wf9*qr213tx swd dB. What is the acoust 3*aqlos9tw1ww adxx2.f,er*ic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 31;p1.crlw2uxmcsa nl ms 2+o1000 Hz. The power output drops by wn3m; 11lso+2clxrcsu2p.am 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices xu1; 4np1 k-e1wj;,i9hd dfzdgw w9ltover 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 effecdgp,; f w uz;t1iw91ew d-9d1x4hjlnk tive 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 communicat -4z6frae2aaly3-lh nions systems, 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 +/b;u7lpr dgxis 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 a fy5m,bch qt9dcf tz/2+undamental frequency of 440 Hz and a mass per unit lenfm2tt dc,9zc5h+/b yq gth 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 with wati2o eo x *3y6kjz2w-ster (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water lekweo s22 x-izy*otj63vel 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 massn.erq+2l.fg pd;eg9 xnh sv61 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the tlgg1h6+x2 ;e fpdnn .sqe.v9rhird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass walk 8k,r o)kz9as 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 500jld7 sfnm5l3-o0b0 ak +hr,tp–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 fin-ro+m0 d5sab0lhnkftl7, pj 3 ds 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 is stationary. The conductor on tij8j*ar7( +yk ehu r:vhe stationary train hear aeh8 rj:v*+uk y(jr7is a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches ydnq ha( y97y0w,5)r enaem0vvou is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast wh9y(, 7ne dvqa anw50 er)my0vas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars j8y q/hga hw/w2ust by listening to the difference in pitch of the engine noise between approaching and receding carhh2/awyq gw/8 s. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a )mwkpc. xqoc0e)4 m sz7hw:x- beat frequency of 11 Hz. The shorter one is 2.40 m long. 7sehk ) -mxo )w qpxc:mwc.4z0How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it m)0.vt *gojoprmlfb1) oves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers hp o j*rlvg.b))1f0omtave 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 bl+u zxbc 4 sz,dplani/+nl v;+,ood 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 cells? Assume that+,+; acu,+i zn/vx snbzl4dlp 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 wht /-8njrcqk+ hile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35+k8tnr/hc j-q kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of xbmh++t6uw:v high frequency 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 tx whuv:+6+ btmhe next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wa6m*m-zbtro qp, ck7/ts once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns/,kcb*6 zrot -m7pmqt were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can b,;rhw+ksgnt-spn ev(.6o s1lfb 9ti; e compromised by the presence of standing waves, which; levswrh gsiof9t,;tn(s1 pk6+n. -b can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calux sq+b; .llo(led “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked wsl+l b.(qxu; oith 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 ;c(b.l5tf6 mrg(cioc q2q iz.ear at a frequency of aboz qc f co.6qc5bri ;lt(2.(gmiut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground/ +bu kmmix66h:zx a+c hears the sonic boom 1.5 min after the plane passes directly overhead. Wucm :xb++axh6mi6z / khat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboaoip cj8(eg6vzdv0.k- j47h c r*1sasnt 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