What is the evidence that sound travels as a wa/gzf7v8vu*k( il3zqbve?

What is the evidence that sound is,+oqgc rh9bn9/ khza wpj*mw,;l t**x a form of energy?

Children sometimes play with a homemadet 7;b;pme kl: v6tseh* “telephone” by attaching a string to the bottoms of two paper cups. When thl6ts ;e et7*;kh:mpvbe string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air-mghqq- oag/;+ u, ewh into water, do you expect the frequency or waveleng- wheqa;/ o-gqgum, +hth to change?

What evidence can you give that the spatfvqwm *2fiprex 5y);d7 p1.eed of sound in air does not depend significan 7;mppyq51e*).twdfi2 fvarxtly on frequency?

The voice of a person who has inhaled helium sounds very high-piqxf,hp, a+:ur wt*h(;xn l x3ptched. Why?

How will the air temperature in a room affecbj3x9) uq4u(i u cd4ry+4 hg,kd8g niut the pitch of organ pipes?

Explain how a tube might be used abo+9mu7qo*1k ;fa ew hs a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muf97qk+ ew1 uobhfm;oa*fler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move h) qp.9(- r4ii pfhmwhup thep r h pf.iwh49mqh)(-i fingerboard toward the bridge?

A noisy truck approaches you from behin.6oxm .qox j82o ybd;bd a building. Initially you hear it but cannot see mo6b; 2.y8ojb dq o.xxit. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas 6 l gkb p:08j1llozg hsi el 1l5uud1rwd(+k52beats can be said to be due to “interference in k5gr( : 8edku12jp+1 loidluw6lh 1 g0lzsb5 ltime.” Explain.

In Fig. 12–16, if the frequency a; e m9x0z-b)(3se6ifvccmxtof the speakers were lowered, would the points D and C (where destructive and constructive interference occur-v6c9 ;cx0 mt zs(iaxbe)fe3m) move farther apart or closer together?

Traditional methods of protectib5bkgyq 4m r ebd1khpe,+:81ing 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 hek1ip8mb,b+d4 egk ehb15y :rqadphones 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 ta;eisq/ :iyd* rlv zow .0m(q:q b;0qahought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In wh(iz:s/ ;wraym oba*eq0lqdi:vq; . q0 ich 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 mz7)tpid xm gmq 25pt-.rvz9n) ove in the same direction, with the same velocity? Expir7 m p.2-qdt))zpmtnvxzg5 9lain.

If a wind is blowing, will this alter the frequency of t9gm2or1/ ( :ynu ;vmdx p*vxawhe sound heard by a person at rest with respect aro; xnym/xd(*u9pv2m g1:wv to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a seu1pqz 7b/qh 53ha;h 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 for3qpqeu1hsah;5/ 7h bz the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of1m h+.jj mc.hgedmn:m2xl.v ::7jtd k her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0mvktm :cj 1.:.2hh:nm+gjl j e7dd.xm 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 rr d9-tva6w s)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 the6a sr-dtvr 9w) 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 wa*dw/t n 2ci17nq tejy86qoy+dvelengths 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 dril)rh:v tdibrap q1) d7+2dc h7fting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before 7d2hdvrd+ ti)cb): phar1lq7the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when str uo t02org3z c(u5qa*h2p*vm :ru1rzr *)pkzp iking the water below zvt kq2z0:ohopr*pcr1 rr 5*u)g(zpu*2m3uais heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stoxz ywwheqc3 y o6/ -no+7zo,p;ne strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did theooxw/ qe6nyzp,hzo7wc;-y3 + impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error m;/ fh (n9 itsay93qlpyade over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if th; nhqlpy(fat3 9sy/i9e temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 12k( +vv nwcm4bqfi(o 7.0 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 souz7, f)5t yzd:vh)mg ignd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB ;u3q, z) sj x;jmjuwn*when fired simultaneously at a certain place, what will be the sound3 u;j);u sjjn*w zq,xm level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certcr68(uzes o, 4v .hu wpu2f9glain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level w9c gf2wup (e4,lzu8o 6rvhus. ould 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-noise ratio of 58 dB, whereas for1ae+et o p+(fi a CD player it is 95 dB. What is the ratio of intensities of the signal and the ptio+ ee( a+1fbackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from(ktflg-hg * ggcu +d34 a person speaking in normal conversationhlgd (- u4fg*k g3cg+t. 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 strieym ox.*i2m9o2hpa33b5mxrd *aoy 9skes 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 modescr9gn 15t,r but amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.,19 brgr c5unt5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB, e z) k.:oi ti(ffh ry1yjmma,+x3o3v when placed 2.8 m in front of a loizr+. 1ajim kh y3v tff, ,y3omo:)(xeudspeaker 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 typically detect a difference,be )xa (gr e(6xk*vuj in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by )e (v*gxxb k,( a6uerjthis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the te--xu* 7szyq:p pyd6 h 0xo0zintensity increase? Increase by a fac 6- 7ye *h0:oyzu-z0ptxdxps qtor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equ 9e2icnn/;c t3l0 pk0,y)mmhd6 xxzrral displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensiti/ rmi23z6y xpn c0; 9eknltrc,hm)0dxes?   

  What would be the sound level (in dB) of a sound wave in aibn,xfivkm1://8bwk vhc c +: gr that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 3k w,ncb/ mvi:xf: bc hv8+1gk/00 Hz?    dB

  A 6000-Hz tone must have what sg k 1) f j1*0l+7pztxqk+rcqynound level to seem as loud as a 100-Hz tone that has a 50-dB sounq+ t7)kzp1nkg*c1+l fq0xr jyd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an em ,l wulg qw(q9y8*e/mar can detect when the sound level is 30 dB? (See Fiw e uy9*lmgq,wl8m(/q g. 12–6.)

  Your auditory system can accommodate a hugy(i qqoqcl tmkb,k 5-8*) 2umpe range of sound levels. What is the ratio of highest to lowestqq)b,ik5o2m8 u(l kyq-m p*tc 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 fu fq2.8af 7:uea:jrw;i * ceqhandamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be plaqcua 8 e.:a* fw:erjf;7iq2ahced?    N

  An organ pipe is 112 cm long. What are the fundamental and fir(cu +w xb)p:d ufwjsq9ax-9m:st three audible overtw: w xsxqdmp:j9+cfb)(-au 9uones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would youm76/*z1 ilufxh (nvtr4ao6 np expect from blowing across the top of an empty soda bottle that is 18 cm ip(vr6xn17t4 6z lm/h a*uofndeep, 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 t1pi rrn/ 60qpjge:a8go :d y0whb8ku 0he range of human hearing (20 wrphn1 d0ir::o806/ y a0eg jgu8bpkqHz to 20 kHz), 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 as its thirdr4agl,e3w5w, kdt op x8wf0 6s harmonic. What will be its fundamental frequencofl0gtd365,wr84 ews xp kaw, y if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lo0:mhmki: 5nf wi dk*;1hxp cv/.bgc7l ng and is tuned to play E above middle C ;k7m h xp:v/:b0ikmgincw *1 l.f5dhc (330 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 organ3mt4+e zlw ) 2jkm4xnw pipe that emits middle C (262 Hz) when the temperature 4m432ewl+mtjxwkn) z is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at g6hpu8 01t rtc20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of v3 66zujs+m*wjgui .oq gv+7bthe flute in Example 12–10 should the hole be that must be uncovered to play D above middle C agmqv3zv 7 buujw6o+ + 6j*is.gt 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 Hcgpz*c xxjb/ mn 77tf4 9s2fg;q:y6loz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a)9* m4/cj2c 6:fb7oxf7qtz nsg; lygpx 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 oayox4z* j7v+vvv( dg5 pen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hzgox v+7dv y*avzj5v(4. 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 8 5yc)e+otsa 1vif-fbx+ 9lys$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-qzmgqpdvcset* /)b0 0qqjzj k m7-0. /long organ pipe at 2)z q*0jtsdcj qgvqzb70/kmqp0 . -m/e 0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open/,adx6 4d*vu k dipv6f 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 eav/f i xdvd6 ua4p,*6kdr 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 adju.f*uw, tu314szo5s3jk6pa b -csmv bust two strings, one of which is sokvu fbc*b 3 u3u56jswp,s-m s14o .aztunding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequenccd9drzd +s g/7y if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates vf4i)zrew*;c 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 oze*fiw4r)cv; f 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 35osigl.gs 5 g lvr +4ou(3tnubhkb):- 20-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning forbi+rsngl.-bgol 2 o54 ugut3)hv k (s:k. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensi:.vhx m zvud(:on in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together?hdx:u(mv :.vz [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be y(/fd /mpekb ;qu2eq5 heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ke y /;fdqem5(q 2pb/uother at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fr v4y 9tjj67kbccdrd:; equency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When dcy4t9kcj7vj;: r d6b 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 1.7.nb:7ivcc co h3u-x1 ykqz7l80 m apart. A person stands 3.00 m from one speaker and 3.50 m fru7o7 zyx3-q c:n1ickhbc7v.l om the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are vm+xv +f qlu7ws3kn ,(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 anlm+fwusv(3qx ,v7k+t 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 q*))q)pi i8 v2qtlqu sper second wiivsl)u tq)i* q8qp) q2ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s 4oh4fu)ai bl/ siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s /a) h 44bioulf
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequen2yvwd 6n)d/+4fgxqtncy do you detect if a fire engine whose siren emits at 155nny64 x 2wgd /f+dtvq)0 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yogum 7th 5j7m *jxi:q;l+;phdz u at 15 m/s versl zm;px+i;75qj :gm7*d hjuthus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whena 3o6orm2 /58 yufmc/e8mwb ssdgq5k tp)6la( one is at resaa oy ogf32r5mwq5l / sbum 86dpsm6 t8)ck/e(t and the other is moving toward the 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 and receives them aep)nsy3c :(k returned from an object movings)( caeynpk:3 directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sperf 6wdkqn236:o ;et pyed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat he6;3wodqefr2nt6 :py kar in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler e)65suv+kcta n xperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second iden tn+c uvs5ak6)tical 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 ultrasou9- zhiu bl*gati42wr zyi )v61nd waves 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 )i-i2w gy9zlr 6ztv hu 1ai*b4frequency 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 freq q- khdxw6s; r7. 6h9gcb gfgu/isd9/duency $2.25 \times10^{ 6}$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 em1lel:amv lra3b,+tb 8its sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obseb,lm 8lb:a et3lv +1rarvers 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 landscxsg 5a*k(/ hb2y+3zvsm u j9 if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (aj6 -b r,njoz0h28gfkrki, /xc) What is the angle the shock wave makes with the direction of the68ogr,h0bf/,i n rx j2zkkjc- 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 atmosvo)j1r44a atkn; g8yf2 k m4mdphere of a planet where the speed of sound is only about 35 m/s rkd);tmg4a1 k 2yvo 4famn4j8
(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. cpvwkrh+)5 rp mg zmi;ba)t)8b ;,8xiDetermine the shock wave angle it produceszka 5rvir)p tcp+)i);wg 8mx;,hbm8 b
(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 3tg pd 8e;c59q9kx djp$/theta$ 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 exadfpho/*j6a we6 g-eg;ctly 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 /*e6-p fah 6jgdwo;geof 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 sends 20,000-Hz sound pulses downward ((w uc(.( anoyraycso 7s oc80from the bottoaor(ywsy .nc(oca07c o(( s8u m of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human auyeoun+ d-s1 ;edible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dis7dpxg 9f.h augpar2 4/bboy/ +play called a sewer pipe symphony. It consists of many plastic pipes of various lep/a af+ gbx7g2. d49rb yhpou/ngths, 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 threshold ofvf v2g 45ot*iik0ua3p human hearing (0 dB). Whau3 akiv 425iv*0o tgpft will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level kf5,/j ha4uz;.yrppni/mx36x ruak;when an 82-dB sound and an 87-dB sound are heard simup rn4af36xax ;pi;zjhk ,.r/u5uy/mkltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. nao0)b rwj26 p plgo+x: 59wxoWhat is thwr90bop oa:owgn 265xpl j)x+e acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W oukoxsb9; . +ys26x5 gz4utskj ktput at 1000 Hz. The power output drops by 10 dB at 15 kHzzkbk6o2;yx .xss us45j +g kt9. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective d*hbq:kp;7:0lasg bnk hpf7 x8o/ h(idevices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 p g:7( lxi 7qh ;k/:nhkpo*a0hbfsb8ddB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemp2qre, 4vg uk (koo4c6s, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned toeu-wo:p+ mi0l/zh itk)( qy ;y 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 fucxq) .(n ;szijzt: /o2d(v jjhndamental frequency of 440 H)j/zn(c(t :jvhq 2;idozj s .xz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration aga9p .hhkgu/.bove a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the kpu.g/ah9 hg. 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 q qu/p /hul:m7string of mass 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 itsulu7: qp//hmq fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsnwx1uz3 7 ,,q9pcmoeberved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range conn, q75j-k23yf uptvvming 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 anj qn3,2 kfp-7tn5vvu yd finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cozm aqww /4e 1*xll,a x5-w3rlcnductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spe*a -l4 31z/cmx5laql, wewxwred of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After v0 .p ,zkkuqd;qu-*upm/lfe2it passes you, its frequencq*e-0m zu,puk;v2 u./kqdpfly 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 gsst 3w 0,obc+o7cn i2just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a cert 3+ncg sco0w ts7,oib2ain 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 beat frequencyd5i6jr4ej6em vz5 9ir of 11 Hz. The shorter one is 2.40 m long. 5j6 jd5e4evi9rz ri6 mHow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past e in n -k*g53g97dzluka 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 g5dn gil 9zn 7e-k*k3uof the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m chj7ic9/m 4ry/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? j/ hryc imc479Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth i kz)anwuf vkfeg;e)m p) 84j,7s flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of th;jn48)awekvp g7zfk)) ,u efme wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of hi 8u*. keoctd sl5yda-/gh frequency sound pulses as it approaches a moth. The pulses are appe -/csku.*dy58td aolroximately 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 the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpil -z/bl9r tr3ane 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 olz9/a t rbrl-3vertones 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 can4be;va zkg :k+ be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a l4+gzk ka;:vbe iving 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 “* .yt,kziy)w v 4hue/qsinging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. i,utewy)zq*v4 yk h/.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 for4h a4je8fbr4*psen - gmh /mfde85n3s the human ear at a frequency of about 8ne 3b d 4fegsp*8 jsea -/4hfhm5r4nm1000 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. eec3kycvn(*20. An observer on the ground hears the sonic boomvk( 32ccey*en 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ikm5*a8 njj hs2s 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