What is the evidence that sound travels as 6l5rbpdmlx-t/4kq l88 qss9u a wave?

What is the evidence that sounew 58irmlwl86 d is a form of energy?

Children sometimes play with a homemade “telephone” by attac 3jo-.oy/qt0c da+os ching 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 cle3o+qod- oc.ycj ts0/a arly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do youdevflfn*)h)7 ncnzs4 c1q. 1w)c0k z ;z)iba l expect the frequency or wavelength to v znlb1ffcze;ld 7 zcih)0))*qnk ws1n )a4.cchange?

What evidence can you give that the jm(a9d/ljia62 7ig.ta0uuf0y z2n otspeed of sound in air does not depend significantly on fyizo96 nal i(2a .t7fd0/2ju0jt uamg requency?

The voice of a person who has inhaled helium sounds very + e+o0fvywt9z4 ;sfkg high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pi1c.muc zic:v30w5z fhmbs: x*pes?

Explain how a tube might be used as a filteor9 ,f9u1s 4w-ij csxor to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffleroxs4c f sjou-wi 9r9,1.)

Why are the frets on a guitar (Fig. 12–30) spacynmx8sk6 fkn k+e6m/vwm. t jd:h3/ ;eed closer together as you move up the fingerboard / je8mxn3vtw6y6+dm.s ;knk fm:e/ hktoward the bridge?

A noisy truck approaches you fr 0(ykmfycv6v44m z)zk om behind a building. Initially you hear it but cannot see it. Wmy4zk)ymc v(v6 k40fzhen it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatsvdyvq+n0riy kari( vdna 17.+ gh4t+( can be said th+.v7(n iygdy+v+r10ka ia qr dnv(4to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers weref +. (+ h2miwhyx-oc/vgfwh6x lowered, would the points D and C (where destructive and constructive interference occur) move farther .w2( +hff+x/xhygmcv 6-hiow apart or closer together?

Traditional methods of protecting the hearing of peop-y;i xuuc3:vlr n62r-,/bzt 4ned gnk le 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 devic3b,/ z-yl d2cun;x:g 6 ve4-knurnrtie 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 s,k 2or9k r)h-hu+ ckp6 cqtlyt pr ;j8hxur62/hown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. c9kol)p h2 thrq,hx/8uy +k pu;rtj-r62cr k6 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 observer movemaibld 4g66 x3 in the same direction, with the same 63 a4libmx dg6velocity? Explain.

If a wind is blowing, will this alter the frequen ,;nyy k3i niik1lzn4 i,s3wc)cy of the sound heard by a person at rest with respect to the s;i,4l3z,nin)kkc iw y ni3y1source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swi f 82ojo3o67n8pd1dosfk+rr t ng. A monitor is blowing a whis1p26of38t jo+nor k 8df7sdortle 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 leng( acmmdrlu tt/+bepn 52kod+* s784fv+vd hn+th of a lake by listening for the echo of her shout reflected by a cliff edk +b/s 4nmt+ u2ot+vm d 5v8pafd7l+*(chr nat 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 waterl+oks(dlftj 99 r5x-xwine. 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 point? Assume the speed o x j-owsx9f5d9(lr+tk f 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 air ts8whgt2-k5t t0fz 9 aat 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 a4* ibo 7or r./+twymlhv84yp a school of tuna on a foggy day. Without warning, an engine backfire occurs vra oh+y* tlmpy4br7oiw84./ on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when st48slij.dbl4,-p /khd l bynh:riking the wbl4ll, hsi4 hy/.npdd8-:b jkater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to d (4o,0f/hfwf-7i.ag vn j ukhthe ground, 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, and they are 1. 47 kf/(jfiughanf.w- ohv,0d1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percentox l4: jtukcda 97, 1dgy7h4j+jysi e- error made over one mile of distance by the “5-second rule” for estimating the distanojt+y7 7 4j14sdk gy 9xjhuaecdl: i-,ce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensit4o: v7 vvmrchz /i.lg41 ic2eby of a sound 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 in76tet 2 j0flmwtensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fqp 3;6fv ka*yi qgo:y.ired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensi;pao*yq k3.6i q:vfgy ties, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nh(aq j-;-j0kcxyw .stzp t/m3ons5c*oisy jet engines is experiencing a sound level bordering on pain, 120 dw(;0x okzchat-pq3s sc/jm5 n*.y-jt B. 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-nois**( 0o*if1y4if3r dpv bsk pmxe ratio of 58 dB, whereas for a CD playe0v *xp*soy4r(kifp mb df*13ir 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 sound from a person speaking x/n;+8u+ dsp. b15 dddlus:xm7y kk q(sgu,xi in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformlyd +:5 uux.k7g;(ddbxq8 u,s /xss pi1myn +kld 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 earu:fxde m6-bj ndsz.9 ,drum 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 amplifier B*aiz v/ cu5e5el aj(nk;/qw) m is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 mn;aca w*v(uz 5em /l kqe5i)/j 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 bv 23/8cyioh: ie5jbt6dilm 3of a loudspeaker on the stage. /bbo3 26hi3 mvidt8:l cey5ji
(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 olra2urj 96,bz 7mb*slevel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels difs bmoz*7j6r ul a2b,r9fer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripledz)rj/uu qu*q +, (a) by what factor will the intensity increase? * zu/qj)u+uqrIncrease 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 thk0osvwhpom-5n +lbhxo45 3 2 fe frequenchbv2 o4o5sxn0fl5pwo-k h 3+my of the other. What is the ratio of their intensities?   

  What would be the sound le.l23ggsv0 tog vel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.so 0ggv3t2gl.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see quu a1)-ak)0eq *gzzbm as loud as a 100-Hz tone that has a 50-dB sound level? (Seeb *)0-1q)qazuzau gke Fig. 12–6.)    dB

What are the lowest and high1sf w(( u5 xp2irpf /ud78xjjiest frequencies that an ear can detect when the sound level x(rji 2 5 x(ifpusf18d/jp7w uis 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of xz.97nr4n r ynsound levels. What is the ray9nr7xr n.n4 ztio of highest 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. The length of th9-maa i*-f 2oxbcalv3 e vibratingmal2 *a fcvb3ao9ix -- 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 8s qqhwo6w 8s0the fundamental and first three audible ovwq6hsw o80s q8ertones 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 blowin4;0l 1fcql :yzgd/qlyg across the top of an empty soda bottle that isl zq:c/yl1q 0ylg;4fd 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 spanning the range52p.v0p dwnm + qnisz/ of human hearing (20 Hz to 20 kHz), what would be the range of the lengtpnsdn+/205. wqvizpm hs of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5 f vhi:ea3r(.e40 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% rv :ehai(.e3fof its original length?   Hz

  An unfingered guitar string is 0.73 m lonu9or(iug. k 9fg and is tuned to play E above middle C (3 9(kug u9.fori30 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 organbyyu0jl1 , 7 y:swph3z pipe that emits middle C (262 Hz) when the tehy:y7l3 1j,ypzuwb0s mperature 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 20 wdd20gbz nde jiv pn.7r)l.bx.i 2 u:2$^{\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 shou;ke8lrf-r:a f ld the hole be that must be uncovered tor:f l;8ak -erf 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, 440yyd 93gw*w2p7leku.j Hz, and 616 Hz, but not at any w l2u93jk*.wdg7yp ye other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both 2*4m wep eui es/86l1vulae4w ends. It resonates at two successive harmonics of frequencies ew*v1wam8ils4up/46 ee ue2l 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 uex axia c hoj+07 9qx1fc*c6*$^{\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 tq:7blc ls,vojmwy eg+2 +c- 32.14-m-long organ pipe at 20 cyj+ bes, tlw3ogl72 qcv-+m:$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxu tk 3 z 0rlxykj,ncs0-rc4t7;imately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the scl,4kutryntck 7;z03x -r0jfrequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, bghy 2 +pxeezb1 z:8r-one of which is sounding 440 Hz. How far off in frequency is thr:81gy-2b+z xp beze he other string? ±    Hz

  What is the beat freque.-nwa,l s(t p k8rnzj3ncy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, jyz0 h*wd4 (hvwhile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, bu(jvh 4 *hyd0wzt 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 350-Hz tuning fork ank t5,ey** rssdx to;p8d 9 beats/s when sount xk5,**y8;o dpsrt seded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequ7bg0nt5gnrd 7c683vj la rt5vency, 294 Hz. The tension in one string i l376dtvn587 ggv0n5 jc tbrars then decreased by 2.0%. 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 identical flute5(sqgc(lmqc h 8 g2kd)s each try to play middle C (262 Hz),(kcgq dh2 cg8 5(q)lms but one is at 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 frequency i g.l6/s2onegihr 6a;5avs k+ :ni y;eof 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B ;g no:s; iseh2a.6e a+k gir6v/nyil5and 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. f993g wmldg7o00 m from one speaker and 3.50 m from the other. 3wdg9mo l f7g9
(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 v j/,s,lv +u s+z0bw+*wfqhrn xibrating at 132 Hz, but a piano tuner hears three beat*fx+wv qbs+wnu,/r z0 j lh+s,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 wavelenfa ;l .lnowe5:gths 2.64 m and 2.76 m in air. How many beats per second will be h5.wfan e;l: oleard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqx1q6yiq ajgpg.1h(.zmm h-f- uency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s mixh (j1zyg6f1 h q-m..-aqpg
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yjzy33rg:jawn 2 ucud:*qo4a)*.yk e nou detect if a fire engine whose siren emit*)ao.43w:djayeun*qy gznkj u 32r:c s 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 st n2rkkyd( / 3z+i2t ilv*uwd2j(.e esource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenci.ivku( 2dkeridw(j32zy+2n* tste l /es 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 wloznk 4x 3c**yith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a o*z3*ln4yc xk beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and++4h9(q8ea.wd6 ,rlz eqqrhzxtb4 iw receives them returned from an object 4hqb6w8erq 4q(,9ahz+ rw te+d.lzxi moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a 9mqvodrb7k8 c7 ,8nt 5,sw peuwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat he ,5 nucp9mqs bo, e7tw8rvd8k7ar in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler en g( kx.uky-6r -kxgz6xperiments, 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 wasnxuk-xk6( g .6kzy rg- heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to me-f*y xp. +9uh ghoyrk;asure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 15ky+ph-f. xu; g*9yhro 40 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 using ultrasonic wn+d(-c k m9n)kqzf b/48qjeqvaves 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. Wh lgpw5o9vv,(y en the wind velocity is 12 m/s from the north, wha9(owvpg5v l, yt 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 its speed at 20 lpv) ,-ofq 79l6ms,wtkvl.u k$^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is )m6 wy0vykm3db4rkw6310 m/s (a) What is the angle the sho y0vyd664km)rmkw3 bw ck wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wpe,a/,vy0e h al *yow q6w. g6lr3(andhere the speed of sound is ogay/e3,vdae6pl a 0 yw.( hwoqrn,*6lnly 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 bg jcgz/kv/ *vkb -2/f8500 m/s strikes the ocean. Determine the shock wave angle it produckvz* 2///c fgbgbkj- ves
(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 -7z5ou nv,d 4,lo c.qekx9hys$/theta$ 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 1.5c2zgjsp+ +b3 jre,vmqcj3/ ue845e fj km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontau8e3q+mfce+jv ,3 j/25gprsjejzcb4 l distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sot 9l77ikyz qb*k v xdpfw;c3t6x1ks 17und pulses downward from the bottom of the boat, and then detects echoes.6pqx1kk liw719yzsv 3x bf7 c*td 7k;t If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there ifo,4ohrart*3 :-iktg w*1smz n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a diil0k/tfw-uvg(m 0s5- r8neec,x b6 onsplay called a sewer pipe symphony. It consists of many plastic pipes of var,t/gnveceo k snr6 m0(fu0l8-- x5w ibious 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 5.01 i6h7ry6dere3 o)ah byl yat1n72xgr0 yx./j m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquiaae71l h.y/er3r6b0j xy ydg7 6htyno2 1i)rxtoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are m 3( f6nq**+ m rv )xey71p2 *ss)pdnekknyxeoheard simultaneously? )ynyos 2k*xn1 (eq)*nsevpkerxm 3m7pf*+d6   dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1f/.ab+;ax +hfc khpn78b,mlj 05 dB. What is the acoustic power output (W) of thf7/pxm;8h+,bknh la+ j. bafce speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops baq f5weros2 g: ;2lm.7-pjj bvy 10 dB at 15 kHz. What is the power output in walq52p; ej gofvb7.-sw:jm a2rtts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.* gbok5,3k rlh wv 2itlks-b34xxg.;i 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 intercepted by an unprotectk ii,g234b*x g;rsxowt- 3kvklbl5h . ed ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gaif/x*sswz5 rx5n, $\beta$ 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 tun5sff a5 e oe0e(;9oglued 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 vih5u5s;z :.bk tg6zxun olin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass pe5:hu 6g.kb txzzsun5;r 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 vibration8p xhvc;.g ir00kjt5 c 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 f0jig5x0;r hvcpt8.k cork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open-46jm w5cj a of(sp)hw at one end and also -(6 5hjo mjswcf )4apw75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observesb7kj 9)z;ziid 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 500mblq ;-gn+bz, h17,aly at i1l–1000-Hz range coming from two sources. The sound inb,+1lmya ,hb;aqtg7 iz1l -ls loudest 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-Hvmeeb7gy:/cj d em ,4b6bf 7k1z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appro6,gec1kbb7v bed/7 mmy 4fje:aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as z*b m 3di0h*bq.gxg6xw2at(kit approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (a*3 gmtx .hkxz(*b0iagdq6 b2wssume constant velocity)?    m/s

  At a race track, you cn ih7r3 nd6z3nan estimate the speed of cars just by listening to the differend6 h3n r7n3zince in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, p5txk 5bfs:z +sounding together, produce a beat frequency of 11 Hz. The shf zpxkbt5:+s5orter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroaddo6z)4wjq6:- mqpoz: zvlk0) z h4 roc 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 fromr pod6mz4hc:zojzw4q6qkz:)) v-ol0 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 bla+l3o1+bc3rf h *mzey vygb);ood flow in the aorta is normally about 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 that theaf3b*ygm ;y1o cb l+ z)vh+re3 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 thqch,qfze0 juqj7+3j u(/t v6ye moth is flying toward the bat at spuqt06ju7q+(j/yq ezvf,3 ch j eed 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 i b*xae,p3cqr 3t approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before thepbcr33eqa ,x* next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send hcs23v1 5.wwko .rts:c3 azqi 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 lo z:32iq ca5rk3wssow.htc .1vng, 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 +c0 j vo,onpj*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 * vj0jo+p,nco 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 lonky(6d ce:a7 yvkm(zf+ g, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing(e+zf(yav m6 y k:k7dc,” 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 ;-ixl3nxrnl1 about 1000 Hz is;1xnlxri3 - nl $I_0$ = $1 \times10^{12 } W / m^2$ 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 grwozloqb 8a4c3+-,r a lt9yqd8ound hears the sonic boom 1.5 min after the plane passes directly ovetb3rcy+alq 8la-d94 oo z,q 8wrhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 7lx 08jzua mi1+,tcxr:q jgf 7is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h