What is the evidence c ci4r//uts4p5k,av dthat sound travels as a wave?

What is the evidence that sound is a form of enem+a( wbfzee 9:rgy?

Children sometimes play with a homemade “tee3iqm x9t7h-8bko rf8lephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks f-ire 837motk9qhx 8binto 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 thh8 j y6fl4bwo.e frequency or wavelength w 4j6.8yobfl hto change?

What evidence can you give that the speed of sound in air does n0 +ur0 rt4 2atj,hfua udpi:+kot depend significantly onp ita4r2 f,thudjk+:ua0r0+u frequency?

The voice of a persojh qua10:b7rr dke*m,n who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the l)cjmm p-vf2z( 1v0nrpitch of organ pipes?

Explain how a tube might be used as a filter to reduce the am j 84bkwu y1lzdzm j7 wk91np5)9ajb rux;o(u4plitude of sounds in various frequency ranges. (An example is a oj w1xl j 4pkrb(1 4m589u9zwuny;k7dau) bzjcar muffler.)

Why are the frets on a gup;b hquc;:;kritar (Fig. 12–30) spaced closer together as you move up the fingerb: ;;hcukpq br;oard toward the bridge?

A noisy truck approaches yox :a4njg j,sjj)o 3fz4u 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 sj, fa)gjon4z:xj 4j3 more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference ing/ oi6w7)rui h)-p)g gdbi3ff space,” whereas beats can be said to be due to “interference in time.” Explain.u) w )fg idr7h/igfi63g-pb )o

In Fig. 12–16, if the frequency of the speakedyu7v2 1y w-cl, yhr4crs were lowered, would the points D and C (where destructive and construc4ydc1lw2ru yc y7v -h,tive interference occur) move farther apart or closer together?

Traditional methods of protecting 9c 4o0hxk(j yathe 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 0ahoj c(4xy9kdetects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be t -;slvaro 68g cf)ybkre.(pe 1jp,y*y hought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequenciesvcfar*,yp ) 68l;y1-sp eo.gberj(k y farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sa-j y,mmsr.2*t8h a6h nhaz .kqme direction, with the s qtnm.h*.a-h,ha2s8rz 6ym jkame velocity? Explain.

If a wind is blowing, will this alter the frequency of the shx7;kc o 5xc t oyp)k8j704hcnq-h qj6ound heard by a person at resn6xcxc48ohhckj- 7;y )0t q5jkhpq7 ot with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on fevv,zyl/ 4054i5 yz s4bghqn a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, w5 eb 4zyi,/qnh 4gs50vly zv4fill the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a l p6jzh /6bbp0bake by listening for the echo of her shout reflectez bbhpb/j6 06pd by a cliff at 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 hd6 i/,mt u*yu pol3 )ki:7o eqftc,vr1ears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? A rui*:1 ,olc dtev7o/t3 6puyfk) m,iqssume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2k: q7 nkaau1r00 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a umwv, j 9dz 1z*v9dzz*foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapse,zjm dvzzv1w u9 *z9*ds 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 splapsqdyy8wx 5ee c;5u45sh it makes when striking the water below 4 pqce5dsyx5 e w;y58uis heard 3.5 s later. How high is the cliff?    m

  A person, with his ear ,nq zoq z8-uyy*4o9 -jid7e zoto the 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 yd-u oq8y7 9ojzn4iq -* ze,ozthey are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made o oa am)g*qmx j.wm6r/-ver one mile of distance by the “5-second rule” for estimating the distanc-rga )ja qmwxo 6m.m/*e 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 pain level of 120 dB8vxu(4 +x1-wfgbo5u mfnlwnu3x0 v5 f?    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 )a:8mtr7ffd+2d vo rgsound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atkz 3+)sffqd 97 mkus6w a certain place, what will be the sound level if onqk wm)+6u9d7k zfs 3sfly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with foxugib2v u (p98ur equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person expu(gb u2x 8i9vperience 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-noise ratio of 58 dr)( 4-tp2tmmi8fz 1o f9wly(du upwd1B, whereas for a CD player it is 95 dB. What is the ratio of intensities of thz81dl (2 4tmd)w-ip9wtf our(pyfum 1e signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conv gs*276 p3lb l7ewemktersation. Use Table 12–2. Assume th* e blgkmp2 67sl7et3we 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 whoe d./69ol mahose 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 t9lebjh e oxh:)y,;d2h* oky326ny q nhhe 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 lol 6,nxnhyd 9hoq:2h*yobyk;)3eh e2j udspeaker 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 fu5eee(n8dat lex 7zd;:gp*)g , sc;pc ront of a loun85ue*sap( eeczg,x7ec)p:ddl g; ;tdspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typic+ .smnkhnz0 6+v -vtfpally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes tfz+m0nsk. v v6h-+npof two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)rg f8l63rpzz ;l9a.rw s z-+j uhpzf4: by what factor will the intensity increas wz hz;8lurs rf azppzg6 r+-l3j94:.fe? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equa7mb q567x 1lk vhr;zsiaz)ah8l displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intens7 )8a xl5;iazh 7vbz sqr16kmhities?   

  What would be the sou:cy-73tcvv :c, u rcplnd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm atcltv uy7cvp c:3 :cr,- 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that gty xg*1n94w 2yrw/ byhas a 50-dB sound leve/4 2bywy grwtyg*9xn1 l? (See Fig. 12–6.)    dB

What are the lowest and highest7mqbhwgw2(o 6p -sm qa5(cd:b frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)pq m-cw:b( s62g(a5mb d7ohqw

  Your auditory system can accommodate a huge range of sound levez, rbea2 v r;tfq:a )n:5ubm+lls. What is the ratio of highest to lowest intensityf mt5:)rq bln:a2r b+;uze,v a 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 fuo rniej:3zf5o /wo8 0jndamental frequency of 440 Hz. The length of the vibratii:3 fzj r5ow/oj0 8eonng 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.m gm+ )gaokkivh8( n;qx( xp.1 What are the fundamental and first three audible overtones if theq. kp ; gg hoa8xk)i+(m1xnv(m 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 expec3wj;9q nb i1x+;facrdt from blowing across the top of an empd9qfna;+;rw x 31 jbicty soda 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 spannin/x :4nsiibnb5 g the range of human hearing (20 Hz to 20 kHz), what would be the range of the bniibsn54/ :x lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmrwb)7 hlzv,v1onic. What will be its fundamental frequency if it is fin1,v7 hw)br lzvgered at a length of only 60% of its original length?   Hz

  An unfingered guitark:s(nd(l0fo f string is 0.73 m long and is tuned to play E above middle C (33(sf:n( f0lo dk0 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 midd9er(vjv*1qo rmhu c3n rz 9gmw:q:z))le C (262 Hz) when the temperatuq*1q9g rvujmh3r)o9 mwvr)cn:: ze(z re 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 lq6 ig.2 zhrcr6.*pt dcp l ;x3m3n-gupjj: k2$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hol)jgm)d* db4j*/x khmk- d (dxky-n5tle be that must be uncoveredh md kdky * -)5x )/n4jgmkdbjl*(-tdx 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 pipe7bovd 0(lv j 9vj*7 4tvc, )umnbbkua* can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other freq( v)d*b7,juba 79 vc 0v*noulvbj 4ktmuencies 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 lon*cv o)gaxi:* 8vi 1dvdg is open at both ends. It resonates at two successive harmonics of freqa)c*vdid*8 xi o 1v:gvuencies 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 puqu obx2 7:g y-l8u/s2upex,$^{\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 presenms-c)c:c gi/1h4anay6 i(aemt within the audible range for a 2.14-m-long organ y1e)a gcm-a6m:ci4(hc i/ sanpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longj0hozu5e+4+peec7dngq p c6 ). It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relau4h+zpqg50e +e 6cecjodp) 7ntionship 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 strjh)ou)x k.a) u2pgz -vings, one of which is sounding 440 Hz. How far off in frequency is tukzu-o )g.a)pvh x2j )he other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and /x q, l ,75n(s0irzd(wd vypvp$C^＃$ (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, whi u9des*d(s h-/,p6db;e ez5vbu1hu q ele another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shr puzh*eeb 9e1ub6usvh,/s 5 q(-d; ddeill 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/p 5b/8:plu5n6t+cyoyi mw1cc-xtdm7 s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stricc+p1 myttyxbc n 5-/iopl65w8m: d7ung? Explain your reasoning.    Hz

  Two violin strings are tuned to i97d:uvny- zf the same frequency, 294 Hz. The tension in one string iy 7i-v9nd fz:us 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 flutes each try to ply/omiet u9e;: ay middle C (262 Hz), but one is at 5.0°C and the other at :e/mo9t;uy ie 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44w, : ovptlvj. tg)8ei(+n9ppv 1 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 whenpn8 oivg9j +tv)l:et,p.p(v w 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 1vbht4k3 js;e,uk/t u-wwhi4n+ t+2px.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the xj4h - tkwtk ;hvunt4ep/swi3+,b +2u other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibra-4vc* vh dyfv.c+ qec 6o7ot6lowk7i4ting at 132 Hz, but a piano tuner hears three beats everv6t dleq* -c vy+4 hc o7owk7vf.4io6cy 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 2.76 m in air. How1rq12 hewkwef7*u u-7i :s zxk many beats per second7 ekw hui11 q k2:f7eux-wsr*z will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequeb;pr8g h:vf /7i4qsbe ncy of a certain fire engine’s siren is 1550 Hz when at rest. What b bv;q :/7e8sipg f4hrfrequency 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 do you detect if a 9obk2os- ue0v8 5v ftffire engine whose siren ems2u 5 k9ovb08-teoffvits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at yl 5v/0g 5xwlrf2px, r15 m/s versus you m /r5gwx0 lv y25,pflxroving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn.kg2;5y0 sf 85bg d93ru j22nexy fjf+g 3xoepf When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emieo82 uxyjf f gj2eb frs 93fg32;k5 nydx5g+p0t? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ruwim+2b 7d co8eturned from an object moving directly away from it at 25 m/s What is the received sound freque7 wo8uc+ib m2dncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5es/ :slhkygmo v0 hy./6 sg)9v m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear ink /os. )e6 v9gl0hhsmvsyyg/: the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler y7 0:pq0pkwpcw x5*srexperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba p:pxyp r7w0c0qk*s5 wplayed the same tone while at rest in the railway station. 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 to measuretsjzb,1:yngo4 o1n/s 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 expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly tby1o:j g1s,z4on n/saway from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencybknd8jx*m48n $2.25 \times10^{ 6}$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 rjj iukfxkoi6*q757.the wind velocity is 12 m/s from the north, what frequency will ooik j6irk 5 7u7f.q*xjbservers 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 i + 6cnb/p1v dqbtu5b4 syj/.evts speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s m3 pmr* f-+yshzbyyy66(y / wh(a) What is the angle the /+yybmyypmw sz*fh y - (r36h6shock 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 where the speed of scid uygnymbdf;y /73a9g653 cound is only about y3a/u7m gd yg n;c6iyd3bc95f35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oceal 9thluo/*r(r n1 lqvfp)s( .gn. Determine the shock wave angle fl( .qlrptsn uo* 9gl()/v1 hrit produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle zwy11-8v o 5wet0bp vb$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead an1iib*fomkd9q8pt1 kxl;(b 2 sd see a plane exactly 1.5 km above the ground flying faster than t df1*2ix mq1;(ktb s9li8pkbohe speed of sound. By the 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 sonar device that sends 20,000-Hzs)q7tavld5 su:-am 1c 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 ia:da71v5sqcs)t- mlu s the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human a )z.xen dt0k8i e).gqvudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum hasi-cz*q2ctifva; kx6qoax/ * , a display called a sewer pipe symphony. It consists of many ptqoxx- cfaq k,izv2 ci/*a; 6*lastic pipes of various 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 threshold qa md uv*7vgrsddt32 (qs101g of human hearing (0 dB). What vv71 3 tqsrus1g0g2dq*(damdwill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB ),o5 9g dv+ghuf wzxis8zl71usound are heard simulu9v 5izs 8)1hw,gg udx+fo7z ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 qeu1 zhtg3ts)y* nd28x v1z.cdB. What is the acoustic power output (W) of the speaker, assuming it radiuny12.)szch 38 1x ezt*gqdtvates equally in all directions?    W

  A stereo amplifier is rf0r5x v (ewb1h z ;rf+ bb*1aqfq31 autq6i1pvated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the 1q0w f1z+harbb*ffbt;3v(5r p 1x ae6v 1iqu qpower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wm/wi2khwly. sycw82- ear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the powe 8wm-2hsilk c/.2wywyr intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systec9vmn ob 8 rhsntg-* z(9a*bm)ms, 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 ir21g s 0ocmqgfx(3*gts 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 fixed po zfp )nc 1)q/n/x-tm. )5iokynnv+bv iints with a fundamental frequency of 440 Hz anqp)zi .5ntcvni/x)1n/bmk) -fy+ vo nd a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wa elk5:)gklp2u ter (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the aikup25 kgell):r 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 mass 2.10 g is neaecf16it+l+;-hlw zvi f,/ hrmr 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 fzhf l le1iwt/ ifmv ,c+hr;+6-undamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reson( 4sq(a kxdu+nbzq+6nate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. T+88xnot6 +xhnd qda 3rl5 poud r(j8.rhe sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the souhupo38xdaqonr68 x5j8 l.dt (+nrrd+nd 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 stationar4iy zy25e l88mdjiei 9y. The conductor on the stationjmi 84 zy idelei5y289ary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Af-zakl 8fmfnh l:6c. j5ter it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume conf6: .fj5k8-la nhczlmstant velocity)?    m/s

  At a race track, you can estimate the speed q8g t*nw, ew,zof cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fasz8,ngw, *etqw t is it going?    m/s

  Two open organ pipes, soug lzh2z7,f ui n-b7qtzp8:;zrnding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is ng zu zr:2l;fzi tz -7,hpq7b8the other?    m

Two loudspeakers are at opposite ends of a nqqn80r/x y6f b j-td5railroad 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 position A, in front of the car, (bqn r b6q/-j5tdn0yfx8 ) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 mwq:euh,7l-jju: 6dmc/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red b-lu me: dc:qh 7uj6j,wlood 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 sp m4aem. y0o6qceed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound q ymm.e4o6c0 awave 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 it approachbs;02za)ifvu7j wzg* es 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 bgwvz2j)i*ab; u0 7zsfat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–3wi)ccp 7 hmn)g ;bn4mj9kz +hys1c z:28) was once used to send 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 zykn 1bczp:)j+hmhgswcm;4)7n29i c 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 compromfa*th, x)nm 7 *tvxx6qised by the presence of standing waves, which can cauq6x xn, hfv *7tm)a*txse acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. 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, 6l3b p1iaxj:klpw4 :-x i.p ilslender aluminum rod held.a::x3 ji4i ilpw-6lxpb1k lp in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a 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 humah5 q,jkvzvel0 a(0ee / 0pd1ban ear at a frequency of about ea 0leh1 /vkv (be5d 0,qpzj0a1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sodd o3ke0z8ey8x0 (wma9ozkc -nic boom 1.5 min after the plane passes 8e3-ydozca0(0md 9 ekk8 ozw xdirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat /c- syqp ahw24)b16cp6twu lt is 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