What is the evidence that sound travels as a wave?,ge qda 9esqhrq, h4 qws/3**t

What is the evidence thatutkwih dt(+ to b:r309 sound is a form of energy?

Children sometimes play with a homemade “tg 6)js0v7m r(gpwv1a gelephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one 61v gmr( v)pwgas07 gjcup, 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 pap+vge; 3rxe *lsses from air into water, do you expect the frequency or wavelength to change?l+* epx3gv;er

What evidence can you give that the speed of sound in air does not depend/y h v:7v.1;ifwf cs6-snf aru significantly on frequenc6: c-vi.7n fhf1usvf;w yars /y?

The voice of a person who has inhaled helium soun c1 9xvzqg3nj9ds very high-pitched. Why?

How will the air temperaturymzr z),ek. )oklm,c s ++-3qimt6ovu e in a room affect the pitch of organ pipes?

Explain how a tube might o9di6;p8d* img ub 0si:hrvx6be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufoi x6rg8:*du d sb6mv9 ip;hi0fler.)

Why are the frets on a guitarik6x0n - rq+7obaftgyx03r 8lijto n36qa4 (d (Fig. 12–30) spaced closer together as you move up the 8niqk jlobq -6a0f t3a4t6g0+ ndix7 r3rxyo(fingerboard toward the bridge?

A noisy truck approaches you from behind y2f36tzdj 3vv r2zjl4 a building. Initially you hear it but cannot 2v4d zj6rz3 tfv3 jy2lsee it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be b jd)wy l5b9m6due to “interference in space,” whereas beats can be said to b6m5d l9)wb jybe due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the spe(yu6-p5s yg)h9 yeu xeakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togethux ) -eug5y(p69syhye er?

Traditional methods of protecting the hearing ozbwfonl *tx u; f,6ofd-pr ;;-f people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in adzxb n fo;-6l; dr -wfofupt;,*dition 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 ca vty2z 2*s:2 qcz)yfynn be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the wavesnyf v*)t 2sz2:2yyz cq, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourcdx lxo,lb 95.f2upx 5ke and observer move in the same direction, with thxl lb.x,f5p 925 kuxdoe same velocity? Explain.

If a wind is blowing, will this alter the frequencyifr lff v(khu +:s)y.3 of the sound heard by a person at rest with fsl() iyu .r +f:kfvh3respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a gw* awnjdg5d j( 7r)9gchild in motion on a swing. A monitor is blowin(w gdj9g*w 7djnr5ag) g a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ecmdist3 23kqc6f 6i/jwho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of skc3/2 it6q6ji mf dw3the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his /g-n qckccq,c6je8 y 0j63zhwship just below the waterline. He hears the echo of the sound reflected from the ocea80 jc je/k3qcc -wnyqzh6g6c,n 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 wa/krd9b d:kow,(sh-wg8 h sggd z0m6(c velengths 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 abovd-co.o3ev: (o; tht qse a school of tuna on a foggy day. Without warning, an engine3thso .vq ceto d(:-;o backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The spla uq3mqqn io/7f+ c.u2q 1stuw(sh it makes when striking the water below n2wq(us t3ou1 q q +c7f/miu.qis heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grou- xhyr3k7t12b /gh qzind, sees a huge stone strike the concrete pavement. A moment later two sountk3z2-yh1q7 g/xbrih ds 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 over one mile of di-z+1/oki u ywaj(1 lgz,wtjc;stance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a-w ; z uyago 11t+k(lic/w,jzj) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at th):p hr,(r pyrpzdr1; ajp:i7*nhbdr -w;eiy1e pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity i 4e )lz7m8 v4rbts)jews $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of m+q3knpm(ive4yk +k- 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, no3i ye(+k qvp4n-m+kkmt dB’s.]    dB

  A person standing a certain distance from an ks6 aqv) fm3c( mk (yt965x7 jda8pgcgairplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level qs6v 9 gg5m7a6k mc)xa3p8jf(dtyk( cwould this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is saxlgdo3/dvo/:erw 4 g o 7xrr;+(eas,qid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of theev xrdl 7/o/+,oe; 3r4(xowgrd:asgq 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 conve1y28sp5btaq z(mt(gj,v 2uyy rsation. Use Table 12–2. Assume58yg (jtp,sm( uztyay1 vqb22 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 strikes an eardrum whose area is see8 : juynt7qia 1a24$5 \times10^{ -5} m^2$ (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 mow 349wcp 0m* bnyo/dlxre modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at dl 0 w/wpmc39yb*oxn4 a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of(/thoa u-1ni2wfu nh0 a loudspeaker on1(wh nuf-o0taui 2nh/ 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 in sound level of f:m 5y4.k73 gf*+t zbmp hauri2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amountfbygzi5m uh. +tp*af k m73:4r? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (ai1wb39f nn d :1eprp*v) by what factor will the intensity increase? Increase by anpb*r e dn19 vpwi:3f1 factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equalv dw 6eups-(kym f(i4. displacement amplitudes, but one has twice the frequency of the (v 6 i-fp(sykd4wue.mother. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspon6c la9mp)4e+ 8z0er 0-t5khr nzupwesds to a displacement amplitude of vibrating air )u0z- prc 0km8h6n+l st94 5ep ezreawmolecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hazm z0.jls+z9;iy * anave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6lay z9nzsi+zj .a ;0*m.)    dB

What are the lowest and highest frequencies tiwjqq /6+q umxb b)5o6hat an ear can detect when the sound level is 30 dB? (See Fi 5m) /ixq+6wbbju q6oqg. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thc*4 oz yzxs4pa-v2w +dk8k s9he ratio of highhzxd*oy9 z-442kacs +8vw k psest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin hathj cv/v2hwiw8.0 mo( s a fundamental frequency of 440 Hz. The length of the vibrating portio/wow. chvh2i0v j8t(mn 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,8 ztxl+e974)m f)gyylpm tsf the fundamental and first three audible ovs my9 tmt,f gyx f7z8)l)e+4lpertones 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 you expect from blowing across the top of apy,3-f dwu5d sn empty soda bottle that is 18 cm deep, if you assumed it was a closed tuw5y-pdud f ,s3be?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with opena +dew7hoq57 m /cqky lez68 a5ir:5oe-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), whatz5hiyc el: mreq5e/a78 w6k5+o7 aqdo 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 u8juppwa 05 iejwx:zf-+95rlits third harmonic. What will be its fundame9 5if lzupar-wjux 0+5p8:j ewntal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m loze8q( 7w .ud nmd)jog4ng and is tuned to play E above middle C (330 Hz). )uo 4mw(.dejgq 8zn7d
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle .,yz*wlb l2orC (262 Hz) when the temperature is 21 y z.rllb 2*,ow$^{\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 rvd xgkx d+eir085t,:at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–1ryqic605 vlvv:s sckv a v38+0r5kco40 should the hole be thatvc 0lysko+r8viv :v 550 rck4c3vs6qa must be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate xykb( 5mv,wm, at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thiy,vxkm b,(wm 5s 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 1.804,ru y02izct m m long is open at both ends. It resonates at two successive harmonit2z0 mru,yi4c cs 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 42u sn.ij+ tk .bcz7z(uz+ ,rx:kkrzq$^{\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 bc .n(, p7ui os/p1hplrange for a 2.14-m-long organ pip(o/ upl,sp7 nbic.ph1e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open :k2zd) .o6jxhz i)bgb to the outside and is closed at the other end by the eardrumjg6z:b b2izo.k)h)dx . Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tri6 t t:,x-ku 60agun72hlvtq iying to adjust two strings, one of which is sounding 440 H62,vt-0 iq 7 kua6: txgtniulhz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency0rf j;bi6qn57bdg1q hv y3zk ; 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 whistlef+mhx4wt36 hzewb c(- operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously,4hcexh t(+w z-b 3fmw6 estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beatsoyvmm/:k x1,p2 ub: , gvlaf8n/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency o/ u mbfg :oa8x:2vlm,y1nvp ,kf the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency fz2+hh6 .w+x*k/y9mmgb cypk, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togethermw*p.zxy m/yh b269fkhg ++ck? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to icn 7 c8s6f.18kcg6yqwxwxp8play middle C (262 Hz), but one is at 5.0°C and the o1cs6cpgf888.k xq6win 7wyx c ther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a)5w1am,*duxva ero077 c xvxy frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded togetr*y7xvdueam) xwo a70cx5 v 1,her?$f_A$ =    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 3.0::cdgs0o x7 b* i-dqz:-ba hpbvn 4an*0 m from one speaker and 3.50 m bgdznho0d- bv:b 4p:x :n-s i*qc*7aafrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibraif qk+y2c 2bi7- rxr*ee4.zjqe.jlf8ting at 132 Hz, but a piano tuner hears three beats every 2.0 s when they ar8q2l yrr fj+qc.ii42-z.kx jfbe e7 *ee played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Ho*v(z.q.ghe k nm1nk;kw many beats per second will be heard? (Assume T.;(nkvhg1 meq.n*kz k = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fi: t/ 4gtafhm0zz+hu0 nre engine’s siren is 1550 Hz when at rest. What frequency do you detec4h/nah0mguz: ft0 zt+t 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 detect if a fire engine whoseb/r+d)bi. wl5 ,cbz qr siren emits ad,ib5z qbr wl/c)r b.+t 1550 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-Hzx qw 9z/v8+ql71f u4:wpqc rt h-:lvg8+ gwdmw source is moving toward you at 15 m/s versus you mtqpg1lq wv:r+lxuh+ /w-m4 87w zf 9 gd:8cwvqoving 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 equipper3::ovx (nv3ds 2hzpld with the same single frequency horn. When one is at rest and the other i(srzo: 3vd:pxn3hv l2 s 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 ultrc6 uvnau 0ome 9,bf3 ,3wcbgv0asonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s W0u on awb,g6,c3 vc m390ufvbehat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fli(8rf2 tb7tf xhes, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the 8(7ft 2bfhrt xreflected wave?    $ \times10^{4}$ Hz

  In one of the original Doy;arj.cv9p 3eq wsz e:).; nqyppler experiments, a tuba was played on a moving 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 he9qjsp 3 vnzy w;c) qa;yr:e..eard 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 gbtfr-.4jl6qj v7 0sa-flow speeds. Suppose the device emits sound at 3.5 MHzj- r 4flg6. tsvba0q7j, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usik3vnn. 2n4 olv03 colr9jp3 d s5cdfp4ng ultrasonic 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. 0lms54ueoraw;- o 0 pdWhen the wind velocity is 12 m/s from the north, what frequency will40wdalm5 rs0ou; oe-p 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 lang drjg0m .wb 04gy9x:ud 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 (a) What ishad( c yqc2g/e8;e sd2 the angle the shock wave msy c(8dq ;eed /hc2ag2akes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed a i::k.r ,- ygkmxga(tof sound is only about 3t-ar.y am:x :gkki( ,g5 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determinet n8kn+yq49sl the shock wave angle it produces9nn 8 +tl4qksy
(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 . 04s /rmlpz1hf;kpbl$/theta$ 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 ground fmj8xk-gctrw8)c6 fp + lying faster than the speed of sound. By the time you hear the sonic boom, the plane has t8 mp rg6kf+-xcj)ct8wraveled 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 that sends 20,000-Hz sound pulses downward fr/gghxtll; 8m0iwe-g6sv6 u6q zmo6g2 om the bottom of the boat,q2s-gl6gm/068gvlh6;x iumeo wg tz6 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 audico9(y tuognp 7 4e6.-,chu 9v7) stukere 1cghble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cos aq,b/lo4/ro nsists of many plastic pipes of various lengths, which are open on both endlsrb/q4ao,o / s.
(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 htbb+pis+ f)i2h vc3.person makes a sound close to the threshold of human hearing (0 dB). What will be the+i)spb h fh+i2b.tvc3 sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level wqw 1z;/gor(uxhen an 82-dB sound and an 87-dB sound are heard simultaneously? o;qz wg(/xur1   dB

  The sound level 12.0 m from a loudspeaker, placed in the ob) i;w00xa0,n )srtpj j* zurrpen, is 105 dB. What is the acoustic power output)irb ,tz sxr0j*;)u0rjw np0a (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 output drops 4 -nj,5lg*csx pmwiurr m.5z0by 10 dB at 15 kHz.5.rmsw5lxgn40cjp, *- i murz What is the power output in watts at 15 kHz?    dB

  Workers around jet aircra(uc rzq8/.2k4jjq 8(zj-slf34tfhpgphj;rb ft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine,;4jcrqjf3gs.u4lh8tbh 2z(frp j p8 qz (k-/j at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemsi v9u0x7gphrj5g1 i .q, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequenhd:9iik.30qbs 1doem qxl8 n *cy 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 aiy 3tyjc: f7z) fundamental frequency of 440y)z yct3f7: ji Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verticaj 8+uoon0n6pk im0m* fl open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water leve*i j+u086mfno k0opnm l 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 tubekr: orr :zz55t that is open at one end and also 75 cm long. rrzz:5 r:o5tkHow much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was ob++xvo*a-n( vl (cp bk0 o)bzblserved 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 78qy 1nnon+zd coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactln8 nqd1ony 7z+y what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statte *01qyqgx2a 8 6tvztionary. The conductor on the stationary train hearsazyx16ett* q2q8t vg0 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 whis,9-dc9 vvj. qbnkfh h9tle as it approaches you is 538 Hz. After it passes you, its frequency is mqv 9h-dvhf9j.nk9cb ,easured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of c5x+j07p,yc e 0ykgrekx.jds 1ars just by listening to the differenc es10.c50ykx e+7gpjkrj x, yde in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency o*7sx cv.z(k:qn zha3l en:,pof 11 Hz. The shorter one is 2.40 m long. How long is theq nn:cokx7(zhl*: s,apv ze.3 other?    m

Two loudspeakers are at opposite ends ur8ciz9 zv)1a 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 )zaz8 9iurvc 1frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0zvo69psp yr ,-ge:vi9.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the9ipo9v-vr ,epy: zs 6g flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth /psfrf;j 00ep is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequ/0fpf0jrpe;s ency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series *h 9u5egpoy;lhk iy+ 2of 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 the next chirp is emitte keg l yh59;+oiuhyp2*d?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from*zhv eem /)b8x 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 8 vze* mbhex/)long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence o,j.udwn94 r s-rvypbz.+mm:h ch3*dnf 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.n.hcu: hr,j p.-zd3w*vy4r d9mb sm+n Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, cavznou u5 b0gk+ 1v:qu261l bdwlled “singing 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 cl buwv+0zo bql1v n26k:dg51uuear, 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 at a*ix:a03ui1s l axbj .u frequency of abo.sa xju 1:ix ia3u*l0but 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 uc.qpx(:cu+x the ground hears the sonic boom 1.5 min afte.pucc:x uq x+(r the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1.esr b1b6 rkn2b+elz5c; ux8x5 $^{\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