What is the evidence that sound travels as a wsf-p q:lep2q6sz k5q 8ave?

What is the evidence that sound is a form of enwz( 0wp)z i(pkergy?

Children sometimes play with a homemade “telephone”itg id fbc.n8 18cv,8t by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to thec,fn dt1tivg8i .88cb other.

When a sound wave passes from air into water, do you z/klf0w 6 q*z cl2fl7eexpect the frequency or wavelength to c6cfwlz/7q 2ezfl l0k*hange?

What evidence can you give that the speed of sound in air does n6 iwkaj8rzle35v i)0not depend significantly58ai rk ewvlz30i6n)j on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whyuzr)*f. akk;1z axd,t?

How will the air temperature in a rc*q uw7nss4)zoom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reducewg0 k1/qjf 3qljo s+i+ the amplitude of sounds in various frequency ranges. (An exam+s1+logjjkfiq/3qw 0ple is a car muffler.)

Why are the frets on a guitar (Fig.2)6 ,oq sr ecemj.5yxg dx.;mai*z5dt 12–30) spaced closer together as you move up the fingerboard toward tdtzrm; *)q6 x syig,.oc2ea55mxe .jdhe bridge?

A noisy truck approaches you from behindd ;r-vsp;c r55zmsx 6n a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noisz r56 v5snrxs-;mcd;pe. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be dodc8;z,etw8d)ull2 :ga b5xsaid to be due to “interference in space,” whereas beats can be said to be due to “intw: ;beta8cdd zlo 8,gl u52)xderference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulwrypztws l.oo0 68i1)lk(z t/d the points D and C (where destrl8z s1wwkio)6l r o/z y(tt.0puctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with(l)ygb o1x nt, 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 usedo,(ntgx1) lyb 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 syiingo4jy;,2 o pwe1,r; y(ychown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 1y;i2o,c4ijyy, ngw ;reo py( 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 shi( .tzg2g *a6sz.3afqj omafawfm1 b-2 sns2r.ft if the source and observer move in the same direction, with the same velocity? Explm sra..1swg*anq-fg2 6 .f af3z oat s(2bmz2jain.

If a wind is blowing, will this alter the frequency of the sound h u1zi6rm; v 7c+ul2ikdeard by a person at rem vcl1ui6+ r dik2u;7zst with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chil u8oy6tljm 6:gphh pa7.xa.o(d in motion on a swing. A monitor is blowing a xp :ajuyoolg6p 7a h8.mh.t6(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 zw,9jc43 gaefp, 1blp a lake by listening for the echo of her shout reflected by a cliff a4pzjcb 1 ,apl9,wg3eft the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thecaet3126; vvbf7m dgoyse-o; echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume t2 dg7co e;;1 3masvoevy-t6b fhe 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 wavelengths in wd3e ea3igaoq7t/y3- 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 abo4kvm 3m mk0wwz7wm x .l+*()hu vdzpx4ve a school of tuna on a foggy day. Without warning, an engine backfire occurs on 0 vk+wd . (mvuz4lm*3)pwhzkxm7w4mx 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.a l7c+o5 dfo4ahw2yysh it makes when striking the water below is heard 3.5 s later. How high is the cliffa.7cyl h4 yof5a d2w+o?    m

  A person, with his ear to the grz5smtb64 vwcilor (/ 1/ lixc-ound, sees a huge stone 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, andrilsx4otmc l1 zi5/-v /(wbc6 they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent uzvlt)c4ij4 *-rd8uo-:g 7k ckujqf (error made over one mile of distance by the “5-second rule” for e(q k78fz-vj goi-4j :lrk4 t*)cdcuu ustimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the p0j 7y19nv ojrcr3ffnhc(0a2xain 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 ah*v rs bj (edoz7f7tm9l,i2o 3. :prbb sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simul aiez9g :f.9tv6y:rv 9r3vxvk+qg 9bqtaneously at a certain place, what wila qv96 q3 be9t:v:vxig f9 9rv+zk.ygrl be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an ahu:b9hb1 hnb4irplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut d1hn9u 4bb:hbh own all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ra 4)s +lwj.p iv9brcif gwa;/k+tio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities o9s j4r/wv .+lf) +gi;kpciwbaf the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in no .w/r6qvjkk 2+rm gc4qrmal conversation. Use Table 12–2. Assume +wrcr gkq4.q 6mk2v/jthe 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 istou s*e7+jm*b $5 \times10^{ -5} m^2$ (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, whi ie9*edu1bi3 tle 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 loudspeaker connected 9eu 3*idbei1t 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 regist ppxresrk;-gs/*4x c p*3ihs9 ered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. pipkr9g 3- *;hc4xspssre/ * x
(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 67elpbl4bmw2 4 irmh5 9 dusdvyd,)9dof 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:2b6dp47e d9ir4y b m,ul)5whl 9vs dmd See Section 11–9.]$\approx$   

  If the amplitude of a sound/hi 97omwti k16as.m n wave is tripled, (a) by what factor will the intensitythim 6 snm.7 awo/i19k increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freque.w f2w xtmdl)3ncy of the other. What.wl m32ftx)dw is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound w9y a.wxy17oe 5oh t (outvh4g9ave in air that corresponds to a d71 9gto45 .xuoothywv a(ehy9isplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone cnot0h4u))f6yqqb:gn j * n9qthat has a 50-dB soun oj:)bc0 t n*9q46uhgq)ynnqfd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies t 9hj+ig;gkjy/ hat an ear can detect when the sound levkg yijg+9j /h;el is 30 dB? (See Fig. 12–6.)

  Your auditory system can acco9l3uditxno w/r50r* pq;avn , mmodate a huge range of sound levels. What is the ratio of highesn* rt0,wnvpqdai5/o lru3x;9t 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 has a fundamental frequencqaz4 fi+*blk y60 6-xn,bfhbgy of 440 Hz. The length of thq*bba4,6n-f6blx+g i hzk0 f ye vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the f/ i0 g9;l s:z/z1.0fk f k4xuukvv)ao vq:juofundamental and first three audible overt;jkxguuv9z ) 1l0oki f/zu: f0 v/vsa4 k:qo.fones 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 twwrw 5g0 g4-uwhe top of an empty soda wwwgu405grw -bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanni.zt3n 3k(fbg*z4 kt1up, m gtqng the range of human hearing (20 Hz to 20 kHz), what would be the raktng*1z(zktq3 gtb, 4p.m3 uf nge 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 al13obi sk jy11cv89ks s its third harmonic. What will be its fundamental frequency if it is fingered at a length o3cliv y ss1bk 19k81ojf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middl .cbh dm-5/aezum5 2z +-spinle C (330 + 2.znm-ium e5b-pa5/hdscl zHz).
(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 j ke;k +zj- 5i9clz0t(:hgvuv organ pipe that emits middle C (262 Hz) when the temperature is 21jh;zk gk eu0cvzi:9+jl -v5( t $^{\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 2 lh-:ijpzz wn+tn ),u90 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute 3ve as0b(h/r ck89ph:jhc3q yg5q nc6 in Example 12–10 should the hole be that must be uncovered to play D above n5h rc0/3eayq(sh963cp jv:gk c8h qbmiddle 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, ylwe 3 hxf:7y/440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is 7he 3:/wyl fxyan open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at bnwsfp)/.bdc(rdcr3lu a7( d/ oth ends. It resonates at two successive harmonics of fc dcpdr)l(3fr d/b(u ws /an7.requencies 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 vd+oqthl av,3w 4z6k* -w x3h0n(aa dv$^{\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 uxx2u.xi f8+ ifor a 2.14-m-long organ p.u8+2 uxixxfiipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cmjzk9h emk+k /7 long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequenckmh/9e+zk j7kies (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 s53x43kxwuxvvhsip,g(fd + n/ when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± wfxhg vuxd 335pn(s/ +vk,xi4   Hz

  What is the beat frequency if middle mxu(lek a.5;yC (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 at 74op1lnagn 1a23.5 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 are4l pano1ag71n played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when k/qwy81 hv.aft.xma8 sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork q1aha8 x mtv.8w.k/yf. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hx5w1yh k bp/o92rol d6z. The tension in one string is then decreased by 2.0%. What will be the be2x/h wy6ook dp l9r51bat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middl2jjdl4h6 b q/fe C (262 Hz), but one is at 5.0°C and the othe4qh/ j bl6dj2fr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; iw*, u j,wsgx5when A and B are sounded together, a is 5wu xj,w*,gbeat 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 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 speake;u 1 p+e tnkwquv3l98mr and 3.50 m from the other.+ulmq;pw13e nu98vk t
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pi0j i 6y*ov-mqk 4s+n zca+;ubnano tuner hears three beats every 2.0 s when they are played togethe-qucj 06 n+b;svy*i4 a mko+nzr. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beab:v 3-pwvf+qq8) brq,dqhz(o ts per second will be heard? (Assume T = bpq:d+bh qqqf3 -)8 rowvz,(v20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engijraa:sz7c w)j3.h ru)ne’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speedjh.:w uc)sara7) rj3z of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you derb0 g1rd2 copg,31frdh.j g58)0m9n cxoxxa ttect if a fire engine whose siren emits at 15.d b,xa13r00jn8 r hpf9gc2c )mrog 51tgoxd x50 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 movw i3f: :yhpg.ging toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly t::g 3yihpgw. fhe 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 j64 l)lg ;6:y+ cmwiup owl,qhequipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 ml)o;iy: w6 gmpu lqh4lcw6+ j,/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 yrz/mg*5 e9vwnd-b b4ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequege vn5d* b-rwby/m 9z4ncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an uobadupx6b.)*m q h5+lltrasonic sound wave with fpoh*56l. bmbdxq+u a)requency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mo+c;jn4mo rid / 8ciu:mving 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.c: cdj+;uir4onmm / 8i What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves tdldpi2w.k*ua7 4w8uwj l,4at o 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 expecta.wdpud8j, 4*a uw ilk 472lwted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasoniwxob( k 1 ;r;t 9ssqx,k2rv,ync 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 Hzz8hjx )/kl51v9 j1bbpmf xk -n,ww kl:. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loca-9k1 wk:xjz bn,1l/p5wbv )lf8mkh jxted, 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 uf6mm/395l)v vspb za 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 2.3d eu)1o1*a zdm em4;kr where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the air md1o1;d r4ezu amk)*eplane’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 enterspu5s-eb myj /6 the thin atmosphere of a planet where the speed of sound is on5mpb 6-sey j/uly about 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 m/s st2nnv)(:cg zynw5gyx4 xv 99b oll912n: qglxtrikes the ocean. Determine the shock wave angle it produces )ogzct4nq( :x 9nlv2vyn9x n2:9wgl bl51xyg
(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 ox,ka 6+rb/uo$/theta$ 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 thtl7 c)rljnx.z rqm67 7e ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 rzcm 6 nrllj).77qxt7 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 1;tt81op pt wtthat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the min ttt1tp w1o8;pimum time between pulses (in fresh water)?    s

  Approximately how many octaves qdfyob5,k+d d0 vk/ k0are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists l p3 p/;ljn7afof many plastic pipes of vpl;pf3l/nja 7arious lengths, 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 gfa -jyux5 *l2no )ry(k2x7ks threshold of human hearing (0 dB). What will be the2y x g5foay7n2r*j-slk )x(k u sound level of 1000 such mosquitoes?    dB

  What is the resultan xc3pp.)jpd -zi2 n/vmsa8h *at sound level when an 82-dB sound and an 87-dB sound are heard simultaneously?8*h-z) 23n.jam/ppx idsavcp    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, istr)m( *pb:k ,ziwkqbi4xau.. 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directiomb. tkkia,z4 (pq b.w*)i rx:uns?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power out - h;cx -j6bklbr/va803tkhloput drops by 10 dB at 15 kHz. What is the p;cb l a0kkoj/ hx-b6-tr83lvhower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears(-ny pnaat 2;k. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intenanka; 2(- yptrcepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, t )+tfevw-j nawajk*3;he 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 viol2n,gv+ eytuxxt+c f*5 jua.y9qg p3 2min is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixe s.fza;x21dl vd points with a fundamental frequency of 2.1fld;avsxz 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 viv t dyultd 4fm06xdn;d65.wb 7bration above a vertical 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 level is heard to resonate with the tuning fork when the distance from ndd u6b6fl 5wv47.;tt 0x dymdthe 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 *7 qx; kroo-jwh69jk fnear a tube that is open at one end and also 75 cm long. How much tension should be in the string if itrxk7 o;6 qjwf-*j9 kho is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tu nb15oa,c vx 18cba;po 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 purh(u,ii (uyy r.e tone in the 500–1000-Hz range coming from two sources. The sound is loudest y,y.( h u(riuiat points equidistant from the two sources. To determine exactly 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 stationary. Theqdj2+j1j s, wx conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speej+wsx qdj2 1j,d of the moving train?   m/s

  The frequency of a steam train whistle jff/ .;jbbz, ap.lh,ten (d q9as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. zd/ af;jftj9b,pb..qh en(l, How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spe bg 7.vi xkghw-mq60j*ed of cars just by listening to the difference in pitch of the engine noise between approaching and reck jg.bm 06wvqx7i*h-geding 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 be fmj4: 0 t/:mgmrzav+iat frequency of 11 Hz. The shorter one is 2.4jmm:rm0 g/v zi:+t4fa0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad9s;i3wlt:0u p;a:k av ka0bxd car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the w;tv3pkdkl a 0bi 0a 9;usa:x: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 bloo gv +ldrcjd*q4-+x;wwd flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasoun* 4 +cj-lwq+;vxg wddrd waves were directed along the 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 uyh23*d wye 9li3zrpxjd;zojv - 9k-+ is flying toward the bat at9dehux*op9v;dj3+yw rj-2l -kz3 zyi 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 freqfmlevy)gtl k 27 vjn*3rx,.)r uency sound pulses as it approaches a moth. The pulses ar 2)3vlfk jn vr).g*7mrxly,et e 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 emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sendxpn ;1r x 43.v,kiwjgw signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m 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 t; g v3nkj4,1r.iwwxpxo F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence svepwzrd1+)zrf0se49; -up5z 1k u ftof standing waves, which can cause acoustic “dea +rpd1u)kv 9w rs -e0ufztpf1sz5;e4zd spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “spp- ch g w;4,;5+ertf31giyjbhkp:g pzee/*ringing 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 1 y*pw 5rgt-jghep/ ;bhkg 3i;4crzp,pe+ :efto “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 frequency of5rum+3zas i)v about 1000 Hz izai3) 5 ru+mvss $I_0$ = $1 \times10^{12 } W / m^2$ 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 hears the soni7 e9d frl)nl3vc boom 1.5 min after the plane passes directly overheadr39)fel7dn v l. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 y:gi ywci u**;ei 7n/m$^{\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