What is the evidence that sou9st uaau/sa+k isu1/,nd travels as a wave?

What is the evidence that sound is a form of eo7 tj8d2x nx5energy?

Children sometimes play with a homemade “telephone” by attac*na :ldi+kfk9tw:o0bhing a string to the bottoms of two paper cups. i: *a kowf0bk:+9 ntdlWhen the 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 into water, do you expect thet7ah;iav(.cwby,eg nl:m : /c frequency or wavelenbc;h na/aw:vc:it, gmle7( .y gth to change?

What evidence can you gbjt.l(no/;-ff f-hc-e n bc*e ive that the speed of sound in air does not depend significantly on frequency?-hbftfecno.elcb -j*( f-n/;

The voice of a person who has inhaled helium sounds very high-pi 1+zq* s lf5pa.,(tba;l jjxtwtched. Why?

How will the air temperature in a room affect the pitch of orgad jqx-z)j0 o9dn pipes?

Explain how a tube might be used as a filter to reduce the amplitude olj1vlrn01cm8+w5 bv p0fbb6in n ;s3 sf sounds in various frequency ranges. (An example is a car muffler.) i;p+ lbn f1306n5vsn1wbm 0vcbl8jrs

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yolh8w 4 f(dq:pxs;h0 ze,azmu0(xr; agu move up the fingerboard towaw;rd( 40axmszh8qexzh f u;ga 0:p, l(rd the bridge?

A noisy truck approaches you from behind a building16o28m2zw+iehrb7nk8 vg muf. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — yfg82+me6o7 rbv kn1 uwi8mz2h ou 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 beats 8y+zrafh rbhn )7(hz3can be said to be due to “interference in timfyzhr a8hnzbr 7+ )(3he.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points D(gt *goeaj, 8t bmve*) and C (where destructive and constructive interference occur) move farther apart or closer tg* vmt,b(e*j8ae)g to ogether?

Traditional methods of protecting the hearing of people who work in areas witai.z +)f-0 ci yv +eemx5:nn2 b:gavoeh very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatiaizveaee mx+f 0bo2-:)i.+5vc n yg:nvely new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tho p96zolzfn0*pich(gti x9:*m ught of as a superposition of two sound waves with slightly diz9h0(*9 ix p*fz6g cnltpi:mofferent 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 source and obsef1 nrzm,zu.3uyt6ex -))ek(lkd-fj rrver move in the same direction, with the13 ,kl .x)urer-z-unz( dtmf)eyjf6k same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound ,womn9l bip nu3v/5 2d15ojcwheard by a person aw3uoj5 vpoc2ml1n , 9w 5bdin/t rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor gpj,.gdxd+;b o*r ;us 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 f;x; us g,r*godd b.pj+or the sound of the whistle? Explain your reasoning.

  A hiker determines the length ry4 acpb btgnt9b,rin /s8 bf37;/vk;of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoub;pntk,c i7r3 ag8b;b/v t 9nrfsy/4b ting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side odo/1fr;8dz rx f his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this pointrrzo;fx1 8dd/? 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 wavelenh,3mdne7z *nk gths 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 fog b3n6b doqvw:;oc)yb9gy day. Without warning, an engine backfire occurs on another boat 1 6vdb9)oyon;bwbc: 3q.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 cliffm9y 9 xonv6,3t eb,aal. The splash it makes when striking the water below is heard 3.5 s later.bm,vx3 t,eo 9nyl6aa9 How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrer8530cxxp26r uvnf hu te pavement. A moment later two sounds are heard from the rx0 8f3xpv5h urc2nu 6impact: 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 erkn(4+j: 2 uwbfnucwwpo,/ e:rror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if jw (:feocnnb2/:+r wuu4 ,pwkthe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soky-4h 7jto)jr6h+o )) ko zxvnund at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensitytg-6nh ckb9/9c frn 4v is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sim+f+bw-w rv h.p5ae:,udj cg h6ultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not gvce5 j,ba+pwu +-h.6dfhr w:dB’s.]    dB

  A person standing a certain distance from an airplane with foj)6k qp1 1kckso *m1wmur equally noisy jet engines ms pk) km ocj*qk111w6is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noiu3 p;ymh +otj:se ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and th3yuptm :oj+; he background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe) uxi-dfn 3k0fx sr yhj110*zer output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on y 3-f01k0uz nj*fixxe)r 1dhsthe 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 sc:pw2 dnms4q(trikes 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, 3scd xf;8 lsl+k i6vk0while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a l8f30xl6+v ;klkc isd soudspeaker 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 register2q8dw5r q be9qok;3 580/p mqpnahwbued 130 dB when placed 2.8 m in front of a loudspeaker on9e pp qrw8q/a2bwhqq5 ; n k03udo85bm 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 typsj4dqxi kcyb187rw9.ically detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ bj8.rd q x94kc1iwsyb 7y this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor y94ygvog v j442loge24e. v ax1iqu(awill the intensity increase? Increay2vg .g guvljo4x4 a49iy2v4 eoa(eq1 se by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal c4 mv*k1f7 9id bmo;odz: -atrdisplacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitier 14im cofdkdzt 7a b9:m;v*o-s?   

  What would be the sound level (in dB) of a sound wave in airryf r+7i.+ aif that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?r7 a yif.ifr++    dB

  A 6000-Hz tone must have what sound level to seem as loud as aj- fdb8:gkb05 d7 spn a3;ccem 100-Hz tone that has a 0dkp bd3cngf;5as:bce m 78- j50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the souw4n u 6ptc.hdxs (4(qd,0 atmwnd level is 30 dB? (See Fig. ancp(d64wd ts40tq,.x( muhw 12–6.)

  Your auditory system can accommodate a +i10x tlh+ bhnhuge range of sound levels. What is the ratio of highest t0bh++ x1 lthino 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 h65l/f nn o(yf)p(mmnqas a fundamental 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 ff(n on) (mny5l q6pm/placed?    N

  An organ pipe is 112fccaj+s,o(l, b:xag,q+op; k63 dck a cm long. What are the fundamental and first three audible overtones if thc,ps bx;okgdc :kaqo6, la3,( c +jaf+e 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 4ja fhtw71c4)t m.jb texpect from blowing across the top of an empty soda bottle that is 18 cm deep, 44mttcha) jb.wt1f7j 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 pjbl6 a o,1o*utipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pi*ola bt,o16j upes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third har+t8i*3majp41i uwukj monic. What will be its fundamental frequency if it is finpt+1ii3j4 u ajm*uw8 kgered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned tov n8noq8pyz94.9se g m play E above middle C (330 qz.g nsyo 8v 94mep89nHz).
(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 C (c8gs ;jj()rkzm7o sv*boc. e5262 Hz) when the *bsmekcc 8v g5(;orsj7)ozj .temperature 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 2iroph *, 9ic 7uehx*c10 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hk0s 44sk;v efhole be that must be uncovered to plas4v;se k4kfh 0y D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 8tn c8hxgz8r1o;7 :l giln,k sHz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a g7nx zctk, l8:h; ri18g8ln soclosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It ro(:ler 7qve( zv0u1tresonates at two successive harmozuov(e:r qverl( 7 t01nics 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 ma+gqnsn/my n*g tb )ru8 ;.ha5n6tb0$^{\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 p5z;q4l /vs1 +c6ldg7s z+na6assgyso resent within the audible range for a 2.14-m-long organ pipe at 20 ss ca1on64ssz+y/;g+gsq7 z6 vla5ld $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal iv.07 s/ esqftex p)a(js approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible ranga( /q0 ejsfvte. s7)xpe) 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.btn4 aob t 5(z:)sfj 7qz8kay 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other ft5tj7b8 ).oask n(a4: z yqbzstring? ±    Hz

  What is the beat frequency if middle C (20tekr2td94: ahn -elklzg; ykum * :)m62 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 at 23.5 kHz, while anoet0 172 vrc1njqtq0f ather (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 theyjea10qqnc2v 1f 07 rtt are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork a38hplb3/j f 5 rn nc;-7tu;7bejmv wlcnd 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequenc7u;vfbp5jhwm3c-r nct ej8l3;l bn/7y of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz.,q 9(pnkq 2loc The tension in one string is then decreased by 2.(9oql,n ck pq20%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two (zvrjoq z1wm) d3;jy*7 v an:e29tg luidentical flutes each try to play middle C (262 Hz), but one is at 5.0ylm a z9*vne3jdgzj 7rq1u(t;)v :2wo °C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, an ei;,jdql+vz, d C. Fork B has a 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 +de ij, ,zqv;lfrequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one spe-opn;g* 8-kmoyuu 8 s :da5igtaker and 3.50 mky-;n5u-tg8:8*aom gs uido p from 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 vibrating at jax.2p3gp b7vx m7r2l132 Hz, but a piano tuner hears three beats every 2.0 s when they are played tog7ja mp2x b. lvxp7gr32ether. (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 i/4ap rmaeo8ygbf 00+ dn air. How many beats per second will be pfoy0bd/4 08+eg ra amheard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirebejiqj.3 8w0 6px:inn8 qx43v, ciiuvoa )jc9n is 1550 Hz when at rest. What frequency do you detect if you move with a speuxjq )n8, 9bepqjo 4j.8vi6c3 cia3 ixw:v0nied 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 whooxj; nrbpbu75 6sq0q5se siren e65p jbx70;oruq5nsqb mits at 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-Hz source is moving toward youkn2oha :gny1 dhs 9n.6 at 15 m/s versus you movigns n ah2.1y6o9:kh dnng 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 f:19- rvuuj+6xicggflrequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 2 6cu9g:gliv -fjr+1x u0 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receiveo 0s3lueaa-h mj5hu+ .s them returned from an object moving directl+u3h0 jam5as.hu -e oly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ; w 9wzf:*/kvoql9sse lej0m.ultrasonic sound wave with frequency 30.0 kHz. What *m .fqov9se9/j wkl ; e:wlzs0frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopd2l 8(u4 -re(:w x5u5ot czxralv4g0-wsyf sg pler 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 heard if the train car approac yxv 0tg-u xd5f8ll24gsuawro4ce(zws(r5:-hed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound (kj fl 0gvt+aul5qi*5 waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the (j iv5 fqk5tg+* a0ullspeed 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 usi5 leb:+b gct2rng 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. When the wind velocity is 125tri kt5a loo-+st y,)5zp)g tq+z8 ez m/s from the north,p+8 io kz55t)eztzo t 5+ qatr)l-,gys what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if xbqi qo(0i e:ovxw17 3its 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 spec)idkk u07oo0 ed of sound is 310 m/s (a) What is the angle the shock wave makes with the do)7k0io k u0cdirection 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 thxk.qb 4nu)8 gve speed of sound is only agu4n.kb)x 8vq bout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500).1b gig p) (n hjcp8y6j5xcxh m/s strikes the ocean. Determine the shock wave angle it8jhn5 c.16gg p(pxihbj ycx)) produces
(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 * y bn p*v,4cxwwf ixo-9:unm-$/theta$ 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 gc,e0w e1s a kxp*06/acmr-+,hw ibzm tround flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dis1pc,r tw0zb ,ca+ mh* 0ewxam/ei6s-k tance 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 soi gs 1u/jn*x1eww/z3-xtyed/ und pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed j3nw e-e* x1x//gs 1i/wut yzdto work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huk;zpf1 iq+( yn20xeu uman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manyga-me403.x vtwfnd d5l m g1i- plastic pipes of various lengths, .g 3 aidw0d14fl-vnge t5mxm-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 threscu4e 7oqz ;:0qf)rsgf0oa7tmhold of human hearing (0 dB). What will be the sound level ofergoft 7z7) f4aqq oc:u0s0 m; 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB suf;)wd pks-9a ijfay, *kr3 1gound and an 87-dB sound are heard siu,*a-gaj 3kkwsdi fyrp1 9 ;f)multaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, w tc0 fouqrt. hmra1a3p5(j(;is 105 dB. What is the acoustic power output ((t.p1fqoa ; r5t (hrc0wu j3maW) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rb;hp; 2us/h*w s ub hh nmy83:bsv-yv.ated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in hybp;svyv/;23shmwb 8:.b hns* uuh- watts at 15 kHz?    dB

  Workers around jet airc 58+9ci dufxm4y yb(gpraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius oy+(mud5bf9cypg 4x8i f 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 systems, the gacb2b:)xv. o 6bou5rwdin, $\beta$ 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 ojclt ;b5/k 3xa 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 viol*zz1v xz,f n:.tl7llfd+ ,wq lin is 32 cm long between fixed points with a fundamental freqwntz.ll,dqf*z llf + 1 :v7,xzuency of 440 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 vertical open tube fille6vw hxm b3kh-m.o) 8jbd 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 level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m an3xbbh w )mm-.8o6vj hkd again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thati(twyh4;me- 0 qngca9;v o (gn 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 moon40hm nq(v-wat g ;;i(ceg9yde) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was 9-,7ji (1umbs ,vx ktihrwg8tobserved 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 comingv7w,f bqfnjl79u60p selu r(4 from two sources. The sound is loudest at points equidistant from the two sources. To determine 7(0wjl 4np,r96fu slfu v7bq eexactly 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 station*q j9oc(jhmx9 0v jqs9ary. The conductor on the stationary train hears a 3.0-Hz beat frequency when thjm99c9jqj *q0sxhv (o e other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appz zemo ac kd9r*p7/or3v0n4 x-roaches you is 538 Hz. After it passes yozoa z*moc0d7krx93 nr -v4pe/u, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just b hs ahp8ydn3qwh c584,y listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by cy8 h d8 p4a5nw3sqhh,on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 wl** ylh8v6 yt0 ncei;Hz. The shorter one is 2.40 m long. How long iiy * 6w0ehllvn*;c8tys the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a svl csll*j-iyhu((d8k 9w52f ntationary observec-f*2l5 vyk9hdl l (wsiu (n8jr at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abm1izx ng feh e;sf0b62t4;l:lout 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 thaez b20;l;lgt6e ihxs:4 m1fn ft 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 is flying tu98h8ga d6uv doward the bat atd96 8vuhdag u8 speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as itzq1x9)m .al2 (twia6srbbt1 p approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How2w. sa9rbmtl 6b (at1x1 qzip) 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 f c1hnaq3n/vi-0p f wwa dy*k763s 0yovrom 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 musica c vwwq-vn ypsd/h7o03ayaf*01 in 63kl instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence ofkf0yvf tmlxhzp- r0p 8srtc/- w;*n:7 standing waves, which can cause acoustic “dead spyz0nw -:*h v-8/r0;7srftkxc ppfl t mots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slfuo4)if+tm 8uvyq/yx5z 7 d/zezy9m3ender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, thyfe 84t)mq /3vzzy+u7 59diyzufo m/x e rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a freq i7ui*tbcw: () fd:jpouency of about 107iui::o) *ftwc b(p jd00 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 hea0s/k 5npr quu 67i0pkors the sonic boom 1.5 min after the plane passes diruk0 5prpuk/7n6s0iqoectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 16 h9dbpd)inz(5 $^{\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