What is the evidence t(tsbdz3q z9nex .z*2phat sound travels as a wave?

What is the evidence that sound ap 5fm2v fzy5:h: yan3is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to tpgh;(g jp9r7pum o+y*he bottoms of two paper cups. When the string is stretched and a childmp; p7 (ou9rjh+gp*gy 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 the freqyiid/.v16f-,d j ) uavy ow4rhuency or wavelengt/wo a4 6rj.did y)vhi-vf yu1,h to change?

What evidence can you give that the speed of sound in air does not depend signrufv5 x2kd*c6okxqr3,j8q 8am /c wg:ificantly on k,/3fc8uwk cv:xr5d omax q2jq *r68 gfrequency?

The voice of a person who has inhaled heloziqxr edgptx/ m,032xy.;)h ium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pi27my-jvj0gowg8t z1 p ,a.icr0zffp 1pes?

Explain how a tube might be used as a filter to reduce the amplitukvc jgb9ip7jn o45;lu7i58mx de of sounds in various frequency ranges. (Ai7 p5om7v8n u54;c lgxijbk9j n example is a car muffler.)

Why are the frets on a guitar (Figpdcu1 h ct,o ).h9s8,xzb+drp. 12–30) spaced closer together as you move up the fingerboard toward the bridge?,oxd r,8t19psh)dp+zbch.u c

A noisy truck approace p*2o bfc3f0jhes you from behind 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 noise. Explain. [Hint: See Se2ef*j b3poc0fction 11–15 on diffraction.]

Standing waves can be said to be duzkb o jk1l2sgy,b69j-e to “interference in space,” whereas beats can be said to be due to “interference in time.” Explaij j,s69zy 2k1-kobg bln.

In Fig. 12–16, if the frequency of the speakers were lowered, wouldb slyr )o *7eoj m*jcov0n(3n: the points D and C (where destructive and constructive interference occur) move farther cl7s :o(nrvn*3)*yboej mo0japart or closer together?

Traditional methods of protecting th7f u6soo 9cl3cft2rrw+ 1i d4te hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to iw d 6s3torfcc4+f1to7 r29luthe 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 thought of as a sup l9i5o9v4dkoa ( y9d+mvd/hp7a tv5d herposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a7 95d(a o9y4 p+9dk/hli5dvhdamvo vt) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mm(qae5 up*xuc* 3o0fm ove in the same direction, wiq m0* fc5mxae o3(puu*th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of thefn )fjxs-z /an9 aj)a: sound heard by a person at rest with respect to the source? Is the wavelen :axfsj n9nfa/-)a)zjgth or velocity changed?

Figure 12–32 shows various positions of a chiy ,4kdvv agv/zr,o/( ald in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sou,ykd/,4(a ovr zv/ga vnd of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for tyyo00wa x;;)kbr0 hmxhe echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoum0 ay0b;;hyow xk)rx 0ting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He h1: o-nwrd,ban8ie+b*a0b cnv ears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speedad b8-,c wn +oie0:nvab1*bnr of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthqb cv8:(3lrwv aeod,h: 7sbd *s 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- x1qjj ;+lid +wvhx0vwu*hgjd 5k6:p drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much timejh*xw5pd; +l+1-qd0vvw ju hji g:k6x 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 splash it make (vrg(,zsiw -s2 *aibk-nrt0o s when striking the water below is heard 3.5 s later. How high i s--0z tk,nbravowi2ig (r*s( s the cliff?    m

  A person, with his ear to the ground, serudi:l0v k 2h w8au mg)2iy3zc1q;a g8es 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, and they are 1.1 s apart. How far away did the impact occur? Seezy g8dg v32 uh)alm18u:0 kw2 iqci;ar Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distancoz4 q*h;kbwl 2 z( 3mrls*vi4ke by the “5-second rule” for estimating the distance from a lightning strike if the h bkolvi 4(wk* *;qzz4mr32s ltemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level o32+ 91s xziqro z*p9far-4zp h xejj*cf 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 ov 7bor +gz*s7 kb,-nckf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simud1 +3zlkq/t p:*k umm ,ncgh6eltaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensit1z+ l n/:,u3cek th gkm6dpm*qies, not dB’s.]    dB

  A person standing a certain distancex8.)w znj aiy3 from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would tjya w)z83in x.his 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 siuqnf7oitc 17t -(h n2lgnal-to-noise ratio of 58 dB, whereas for a-oqchu2if1 7 t(nt7nl CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of 7ifkpcaq+r,*nqg3qj 0k n2p-sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rouni-ck2qqgfanj*p 3 q p7+r0,kghly 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 anbt0p c.*nvk3 g eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifierf6+ sm*h1nksmnaw.9g B is rated at 40 W. (a) Estimate the sound level in decibels you would masws9g*nm 6nh + .fk1expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of a u0hjn3jmchm( 9-qb w)loudspeaker on the stagbhu39 (0q mh-)wjcn jme.
(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 ajuhs:/v 2pnpglw )2twt87k i, difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:pj w: hg7k2,u 2i)8 vlnstt/pw See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is 7zs,gg7ip vlo 0ksojgei( f(s.)x36+dgpam/ tripled, (a) by what factor will the intensity incrf7)3pp,k m(gse 0g7do /+gizvig(l osxas6 .jease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemn76nj fsbf05pd n3a;ment amplitudes, but one has twice the frequency of the other. What is the ratio of their intenfj5nb703;mf6 pnn asdsities?   

  What would be the sound level (in dB) of a sound wave in airf;h,yf22.tx+rw l hso x;28zxwdlp- la1c8op that corresponds to a cx xw+8psf ldloahw.1przxt ;2,8-hf22 ;oy ldisplacement 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 ,y xu1izh 3*pja 100-Hz tone that has a 50-dB sound level? (See Fig.3u*1, hyjiz px 12–6.)    dB

What are the lowest and hig.jf j+2 qbxc:r6s+f mdhest frequencies that an ear can detect when the sound level is 30 dB? (See Fig.6+2jxfb .+scmqj df :r 12–6.)

  Your auditory system cy:nqpg 6sg:x 9an accommodate a huge range of sound levels. What is the ratio of n6yx::p q gsg9highest 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 frequency of 440 Hz. Tca;n*8 4whawbhe length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tens b4 ca;w*hawn8ion must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threw6ktq,j5cpk28hikzh( nkr) 3 2i 7inpe audible overtones if th7hiknk)2kt,nrip( 53 qk26iz jw c8phe 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 th; +ixem6-efhl(t9or2el .lj l y9 by;oe top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube? 9 li.y6jrlbemoe2- x9oell;t+ h;fy (   Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the rang:0-auyaft rb fcm igz8il3 pa n)*:2m+e of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes rm8faaatm- +0zu2lb r :ci :pfg )3yn*iequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonik7 ic3afb q+3vc. What will be its fundamenf7+ kc3b3qv iatal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0. 9qxs1gg cl(m;73 m long and is tuned to play E above middle C (33mx1sg ; 9gq(lc0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle (c 0hvl vm.1ehC (262 Hz) when the temperature is 21 v (h.e hcml1v0$^{\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 2mz/n/ addmzoi 4ocau/l. 0+7s 0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exs* gxkvd+;sr: wqm r)1ample 12–10 should the hole be that must be +1dx;sgms kq:w)r*rv 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 at 264 Hz, 440 Hz, and 616 Hzxql18m rv/e acjm2 1cg 2rd;j.ufl ,r-, but not at any other frequencies in between. (a) Show why this is an open or /d ruvmccr f, rgl je2.j8la-2x ;qm11a 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 botk (tab w79 z avp(px+94jyfv8yh ends. It resonates at two successive harmon4ypb+av( 7xft9y 9pvj (8azkwics 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 2e6 -vyyouw8k$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long org)r( as(7nls5mf dy:df an pif( sd7adl rsy5f)n:(mpe 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 ope suye,t*w(cn;zk 2)lpn to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the w(pzu*cs l);n ky,et2 standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying tj 6mg+ *dt 32h-byywiso adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the 23+6 t-*ibmgyjs y wdhother string? ±    Hz

  What is the beat frequency if middle C x bfbg1b);x 5y(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 23.5 kHz, whil1p s25hl) vt-tjxbca p( ll7k7e another (brand X) operates at an unknownx(lcavp7 21 5t7blp - kshlt)j 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, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a y2uq zbu6 bq4u l):0md350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frez bq2u)m0 lyuqd46u:bquency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Thelvp;x km tk39l hm5:yp3z50is tension in one string is then decreased by 2.0%. What wmpik5lv 9ph:t3 ;xml yz 3k0s5ill 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 m8fikn,d r i 4n5h6zbp9m30sv identical flutes each try to play middle C (262 Hz), but one is mni9mbfs0rnz8k dih346 5v,pat 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fre5fw7 ovhr /;qf my.em8quency 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 fvw o;f5e87 m./qrhmy 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 g/ 53x7dvc d; 7qbwbtjone speaker and 3.50 m from the oth3wvbgx 7 dcbt7;5 d/jqer.
(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 vibratin ln ;lq+cw:k1ag at 132 Hz, but a piano tuner hears three beatcnl: l+wk1;aq s every 2.0 s when they are 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 i7b 6e1w;wxy k2.76 m in air. How many beats per second wilwe x;bki7 1wy6l be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 155itdisqxm6 7 9b os.v(*0 Hz when at rest. What frequq b xdi*ss67(im.vt 9oency do you detect 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 0ergdn c ,g(5pdo you detect if a fire engine whose siren emits at 1550 Hz moves at a speed o pd5eg (gnc,0rf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequ / zmw;*xkob;cency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sa *k;bzw;/oxmcme? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is ath e9g.ac)qfu 8 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 te .)hagfqcu98 he horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soundi;dar7o6 2m q89 ctdwo 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 fo2cm8dwo9;a67dr qt irequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As ih/bp k 6dk(wz)t flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat 6 bp(whk d/)kzhear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pl8 8a 9oxs,qkrdayed 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 dqk 8,r 8soa9xfrequency was heard 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-flow sp14swnkze: 17k0cu 3kotkozw:a vf1j-eeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s dzk01 eunozk awtf -s :j71vo c3:1wkk4irectly away from the sound source?   Hz

  The Doppler effect usin csd,)y gxw.l, uaz+x/g 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 t 1bu df1dpiw+(he wind velocity is 12 m/s from the1ui dfb1(+p wd north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land sfz,x; owd2*dlss 89d 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 w8nw7.ez-br b of sound is 310 m/s (a) What is the angle the shock wave makes with the de.zb-ww87 r bnirection 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 atmospher0n--p/ etn)q6 oa ofmoe of a planet where the speed of sound is only about 35 m/s6 0)ao /qofn n--tmoep
(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. Deter 0sjdg(2( wmzomine the shock wave angle it gmoz( 2d0wj( sproduces
(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 k145dr qw(b rt$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheaa(i ;+xuze0be0f hx run 8oh:7d and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By th0x euf xohainz:er h0+7;b( u8e time you hear the sonic boom, the plane has traveled 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 sonar9+bvh6elz (a ,d s6bo/odi9hb0t y6pd device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it 9 yd le09bahzd,o+d v6sp6i6htb(b/ois designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are xsxehodu *: 27cge-t ;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 cono9g/ebd t5cv*sists of many plastic pipes of various lengths, whi9tbd c/5g*o vech 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 froms3/4kk v h;v sux9q;us a person makes a sound close to the threshold of human hearing (0 dB). What will h/k 9v 4k;su;vsx3qusbe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level wnl0s+ 1 eimmw h.;xrwsp;4fn+hen an 82-dB sound and an 87-dB sound are heard simultane4s+0x.1lfi +s nwrw;; hnmmpeously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the 808 aw 8nvtx ed1sux6aopen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directionsuv 0a1at xd8w 88esx6n?    W

  A stereo amplifier is rated at 150 W outp; edciny)*t3 ush k6v5tql- b7ut at 1000 Hz. The power output drops by7 i)l s36qu*te vt-5bdky ;cnh 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices oveg(9e2f.hl(zvylm k ;tr their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the averz;vey mfkh( 2t.9lg( lage 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 communicatioa+pus nhfs-66b k hrgzd:0;b3ns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned . u ge-gc30,bd e5iggsto 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 violinm)nw;f6v 1 j0dxr) tk syn23do is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a maskvxr6j3o 2yn)1n ;)d0dmf wtss 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 verticalz(h (i( i;ldrfn49g.j fsud. x open tube filled with water ((h r9iild 4gz( fx.jd(s;ufn .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 and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of zojhjke6 tg6y 19k/b8mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) t6hg jjk81eyk ob/9z6 with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was v4 irvu)t w0-wobserved 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 tlj,x6hn t-gk (he 500–1000-Hz range coming from two sources. The sound is loud tk,nj-l(gx6hest at 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. The conductor on the s b dr;-no8).,gbial,oue- vs otationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movinoov;o anl8gub)i.,e-br- ds,g train?   m/s

  The frequency of a steam tr,nygade v :a;:r0ue1t ain whistle as it approaches you is 538 Hz. After it dvg1ua: t:e;n ary0 e,passes you, 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 o2+:a*4yk5 gsggb)cfzj n- ik speed of cars just by listening to the difference in pitch of the engine noise between approaching and recedno 5sajg2gbf+ky )4gk*: z i-cing 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, prmjpzy4ofn bn 2zvr mj9-)8fpk6sk)4* oduce a beat frequency of 11 Hz. The n 2kj m894)yf-sn )omzkrp4f6v*b zpjshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sta- fma+oa; fu,bl8j9odogw3a 0tionary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies offa 9fo,l-o wg08+a;modbau3j 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 abou/hml9 4eixcd, v:p/mct 0.32 m/s what beat frequency would you expect if 5.50-MHz ul/:p 4xel/ c9mmich,d vtrasound 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/lbjdip*ulc:9x: i q 80s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave oqu ip9 jx::il*0l8 bdcf 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 frequencyjedh+-qzgr bj04/ ji8 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 d0 jbd-/h4r+j ejgqi8z etected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one A nz6 n3qlr8x5 ex(yz- 4qx9+ a;fvxikclpine 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 blown5+l(cx 84zr3ynv;9 a-xeizxk 6x fnqq 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 ip;r0,j. ry/n6;vwtrnhx 6kq compromised by the presence of 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, .rv6j pyxwn, 6ihrnk r/;tq;0and 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, slender (uki8q 8lvw0o aluminum rod held in the hand near the rod’s midpoint 8 l(u0viok8qw. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. 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 of a)42d rn)8 pnoa-y4z wy xhu/webout 100hpy4n/uzr)a - w8n wo4y2xe )d0 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 obsewmv,j 3gzo-cjxs:zt+kuthj76 0)8xurver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitv-tuj0ktz6c3zxw:h ,j j +7oumx s)8gude?    $ \times10^{4 }$ m

  The wake of a speedboat is 154a 9w1b 6:cm(nbsii nj $^{\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