What is the evidence thady*dyw dp8z x2 8- sspy0 btwte1;*f(zt sound travels as a wave?

What is the evidence that sound is a ft kqwvt1d)1l - 1)b:andprz+i orm of energy?

Children sometimes play with a homemade “telephone” by attaching a string to t s8 u( ux.x w1abol,s*04ebseyhe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from oyea1b8suxbs (, l* eo x.0s4wune cup to the other.

When a sound wave passes froml louktr1 3* e g,*p(huxxwn/) air into water, do you expect the frequency or wavelengwroxl*nkt)(e,p*uhlg / xu 3 1th to change?

What evidence can you give that the speed of sound in air does not depend,x.zgrx*o. mbuim s*t6r*5 nu significanzs 5,i6.xuun xromr***gtm. btly on frequency?

The voice of a person whoje g-s kc5fq548s fi-f xii81,hr-xyo has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a roo w7m/)z4cjyb pm affect the pitch of organ pipes?

Explain how a tube might be used ,p0lz6u m vmu(as a filter to reduce the amplitude of sounds in various frequency zlm,vu0( p6 muranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as: -+zljt7nwvsn(w37hrw6h bn you move up the fingerboard w hz(3w - nvnr7+sjb6wl:7hnttoward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it b c6iyvl(0 8u(ioym p9w+ 0nmvyut cannot see uwcv 8 oy+(pm ny60(iymv90ilit. When 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 to3 i:l;3kn 6puf+ m:wqwym k+ adtg)u8h be due to “interference in space,” whereas beats can be said to be due to “interference in tuhfn3m+ yi6+u :mk8wwlta:)pk d ;3g qime.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would 50 9dnl+.udjyzp4p wb c r*f7v8od3pf the points D and C (where destructive and l p3jd ucd*nb5w.7 zdv oppr4+80ffy9 constructive interference occur) move farther apart or closer together?

Traditional methods of p i9hg,1aar(pm( c4 qqarotecting the 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 amic,4 r (hq apam1(gq9abient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves showm w1xzfy 3l:c.fw ;pgfjxgl* (,f..bcn 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. In which of the waves, (a) or (b), are the two component frequ:llygczbjpf3w.1g(.x c* fw ;x f,f.mencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same d.rxi975ny1ywrgz :7ina adm6qm j/e 8 irection, with the same velocity? 7nqer m6i5x1w/y r7yaji8ad9: nzm .gExplain.

If a wind is blowing, will this alter the frequency of the sound heard by a persh+kgiko +l3h3 on at rest with respect to the source? Is the wavelength or velkog 3ih+3+k hlocity changed?

Figure 12–32 shows various positions of a child in mhop)f 96w+-b ukzy fs;au0ig,r/)f ecotion on a swing. A monitor is blowing a whistle in front of o6-huk0f aew ci uy9fz,;/) fp+gsr)bthe child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo ofmbf 6wm3y:uez;(ywl6w 8u 1br her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of thwrw:m8ym ey; zuub1flw6 3b(6e lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sidegwe;hejo/* * h of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is oh/ *g;ee*jhw1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ()r 2ycy9fu jkkl32c tin air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a scho1 gwt-91mlqdm7 qfw hqo;u6z0ol of tuna on a foggy day. Without warning, an engine backfire ocmlm7 gf9otq hq1uww- 1d6q 0z;curs 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 afg7pxmcah( wd;m7v h*6tf 5k ) cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is thef7(;g mx 5c6 pfdvh7am)th *wk cliff?    m

  A person, with his ear to the ground, sees a hbi q 3q fc;a,kpfsg5,2uge stone strike the concrete pavement. A moment later two sounds are heard fro;ck, bf3i2g sa5fq qp,m 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? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rul1iwam hrc9tew2vxu:qa6 o+ly gr /( ,7e” for estimating the distance from a lightning 2wt v q1xlcw (hg:o+r9ae 6r7maiy,/ustrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity oguc0,1d5af hfzn(rm d 0zz*f +o jt*b(ac u2c(f 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 intensity is:7vor/z0 dh4t3+y moywa 3pvs $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult48hfl/l/i),-l- uj j1b*qa dgshb mqh aneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intebq8b 1u*hgjs4 lf-,dhhj/ mi- /aql)l nsities, not dB’s.]    dB

  A person standing a certain distance from an airplaneo,fc iy0c4r ly)-a cge50(k bs with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB.(oc,ykl- 0ie)0fcbsrc a 5y4g 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 tsgw7b7c)hh7 +7 lgjwj k:kt.ehmt9c /o have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the /m th )7h 7c.kj97c7wb+setjglh :kw gsignal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ou y0a o;r )nn*r/f(gjfotput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sounn() r;/o njr goffya*0d 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 strikeskay:q , ws1gl1 an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 gzp.,4iqsc1p*:r qea.bjkf25n:dzc2z 4wu t W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeake c12 szt4qpd2iz4,jw*5r u feb qan.zgp.:k:cr 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+n e*:y 8 mz-u4cuewvg meter registered 130 dB when placed 2.8 m in front of a loudspeaker *wvueg 4unc:e-yz+ 8mon 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 typically detect a difference in sound level of 2.0 dB. What ;a-; r8f exvp/zgl y3nis the ratio of the amplitudes of two sounds whose levels differ by this amlf yg;3z-;e p/ rvan8xount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the ipkn)/s:my 4xjxl * 0mll/7 kxyntensity increase? Increase by a factor ofy*mxjs k ynpllx/ k:0 4)/xlm7    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice t4mwzdlfxw ei;lwa/a;*3 l78i;o v /gxhe frequency ofi;w7lvx*w8e;3fl g xa/ld/ zo mwa;i4 the other. What is the ratio of their intensities?   

  What would be the sound level (in dv4b4;llgko nrk 6q*,y B) of a sound wave in air that corresponds to a displacement amplitude of vibrating abokv6qky;l *4lrn4, g ir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thtj,w g2/3p xgfe6kzx0at has a 50-dB sound level? (S2g6px/t,3zg j 0f ewxkee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cc(u/j /u 4(l oq dtaaht752uhxan detect when the sound level is 30 dB? (See F a2t ou(q4 (x//hl7 ahcutj5duig. 12–6.)

  Your auditory system can ac 5ov4 xeoaukdx 5l9(y1commodate a huge range of sound levels. What is the ratio of highest to lowest ov5x4kel1(xdya 95o uintensity 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 4.lukrw-vjbb - z* aj )tv7rndg39 g4cb 7edi.640 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wha 7-c.).6jd3b tiald wuberg vgbkrn7 vz4*j 9-t tension must the string be placed?    N

  An organ pipe is 112 cm l6+veqi q i y45o+re-ixong. What are the fundamental and first three audible overv+i q4o+x5i ieq-6 yertones 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 wouw a8agt)mwd7 dllo6:px+ ry 96ld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a cl97rw 6)d6l xglmtpa8 dwoy:+a osed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe orgo).rit)bm/tq ;j m aa)an with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), wh/)a boi .)mtra) tj;qmat would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freq j)p1bsr. 06q4vmwvp auency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 6p1)awj . bv4 mrvsp0q60% of its original length?   Hz

  An unfingered guitar string is 0.73 myiwka 05u2g),thm ww1.nacv - long and is tuned to play E above middle C ac 1 vaku tww)20w.mi-,n5 gyh(330 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 (262(m bltc/gykmb y5 0ip9(vhq0 + Hz) when the p 5lkv(0mythb/9mbcg+yi 0(q temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune avt.m:w 2ub 5qs4ivluvl3x n 3.t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpi77jn p+/tfw4d gxjh*:gnd o 8hece of the flute in Example 12–10 should the hole be that must be uncovered to play D above midd+gg7wtdf hxpd8nnjj4:7 o/*hle 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, ands nmlw0r)ak,mc( 4vg0g4ihc8 616 Hz, but not at any other frequencies in between. (a) Show why this is h4a 0gg(k) svm c4l 8incr0,wman 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 ends. It resonates at two succtrjmo 1e8rp8 h)uu ;ijjy35 d9essive harmonics of freqhy9rujt3p o1ijmr u j5de 8)8;uencies 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 ed2a 2 67ygeeh7dx/.bamw idcjl (a(* $^{\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 rans+ll7k96+yo vq dkp4hvl8 l l/ge for a 2.14-m-long organ pk dvkll6l+4/+l hv l9o ps7qy8ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long.hlo95b rn37:l h5ve2v4fof tx It is open to the outside and is close2b3efvvof x4rhl h59lt75 no:d 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 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 bs nph00w-v).ecztz c;c b2wot5 6 (kvone beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequenc(6c0vtz;2 - t w0kb h)s5copezn.bvwc y is the other string? ±    Hz

  What is the beat frequency if middle C ckvfmnyixs f7pyo k+r+26;;/(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, while another (br7w/a( 4hi lyytand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when thyyh(l/4 wtia7 ey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz p+ e8,fyix :l0p jf/ c c524tz.cvczvgtuning fork and 9 beats/s when sounded with al/,:jxi 4cvec8fgv+ .pt5f 0 zyc2 czp 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequel(wa;w*:bmzcqltclp;z3 / t, ncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat; (3 cqza *mwt; /ptlllw:cb,z frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will kq l )spto(4,nbe heard if two identical flutes each try to play middle C (262 Hz), but one is at 5)o pknst4l(q ,.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Form2 ujay6 xe9q+k B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possiby mequj92a6 +xle when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from ;jpr. r3ccpt0sgpk61 one speaker and 3.50 m from0g pstpc cjkp6.3;1r r the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pkgwxan. 5l(wqj;r64tiano tuner hears three beats every 2.0 s when they are played together. (a) Ijklw;5 gxrqaw 4t(n6 .f 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 airsc.qq(vf. 0yh. How many beats per second willh0 c(v.s.yq fq 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 1550 Hz when at r2vbtvt 4hn8( jest. What frequency do you detect if you move with a stn2vhjv 4b t(8peed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Ws*vh x e ;qlz0v555ekvhat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at5vse* v q50xekv;h5z l a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencyl xvr4wd d)i3, 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 same? Are th3rw) ldxd,i4 vey 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 si 0hzlhu j-*wn)ngle 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 beat frequ-*luj) 0h whznency 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 receives th/d34 vt3; xgst2gjmgwy jxx12em retg3g 234v/2jwmx sjxxtygd 1;turned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wal/ :fzf0drn)lpfjh+6qfj:s 4gfn6ds. l at a speed of 5 m/s As it flies, the bat emits an ultrasoni)l zd :4gjssq:dfp/r.jn+ ff f06hn f6c sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, 8zi 9jd wiw1irw,l (g-sh61 oma tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approw i l-1w(6sg wzd8hri,i1moj9ached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo zxu*c/rl4ba3yrw fmhv2 6 *6dd-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 frequ ** v6 wbumd364c/lrafzryhx2ency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of ftpdo.s)hd68v/ ys , vxx.js 4qrequency $2.25 \times10^{ 6}$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 sofaso7*og*x+u7h-x5cae q m *d und of frequency 570 Hz. When the wind velocity is 12 m/s gshe* m-5uxq *fa cadoo*+x77from the 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 land2qwmrdmau-7f34 o n7i 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 of sound is 310 m/s (a :w3a,e nxk* 3pzzrdir11 inc() What is the angle the shock wave makes with the direction of the a( rxa *kz,3c e1nri3i:z wpd1nirplane’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 oywzsmx6 d: (8qu qzz3dx-/.c xf sound is only about 35 8.xczyz(:z md/-uq qs6wx3xd 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 vqo*3rpuxmkg,6 a+q*/- la yjbns6 8z 6frx2 pstrikes the ocean. Determine the shock wave angle it pbaf/3 puo**l rrzp 6msya,xv8k6qn2 jq6g+x-roduces
(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 8/xcprc)4gs 6 2c sq;wrtlzfd-i*uc6$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly over -u7e b,*ufioqhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the ueqo-,bi f7*u 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 senc6r 9 :eub,pkj;0xzlj(5xsg a6 o*z rkds 20,000-Hz sound pulses downward from the botp:o;g6ezlu9 k(jxxz b,r 6c0j aks5r *tom of the boat, and then detects echoes. 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 in the human audiblez2guqp7 - lt/s v(noj1e- y(sf range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syi 2,f-8yi7iv: v s1nx5j ;ybalozoq0 dmphony. It consists of many plastic pipes of various lengths, which ana1i:8o bzlv f;ij ix05v 2oyd-,7yqsre 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 sou8t1iatm m* js1nd close to the threshold of human mm tj1t1 8is*ahearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultanlzc e 1pl4 nle) xkag0dp6z,ia05z4 k2t sound level when an 82-dB sound and an 87-dB sound are heard sil6pdzz5cga40pxa1ei, lek02 ln )4 kzmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in9uf f wh*x 63,f4arzro the open, is 105 dB. What is the acouwurar64 h 3*o xf,zff9stic power output (W) of the 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 d+2q x *n0aug*ytih 1efk-r5lby 10 dB at 15 kHz. What is the power output in watts at 15 k5 tx1n y uh*+dl2rki0egfaq- *Hz?    dB

  Workers around jet air/ ,wq5rvu +.q sirfzmvgs9w08 craft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and i5u,wrwfrsq8m/vz gsq +9v .0that the average 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 communications systems, the gain,em d9 q62rmcgp( 4qdhgatp30) $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1r1-w d efawyk::hye0ed:9clq3r 8; co$\frac{1}{2}$ 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 points with a fundamec,kioxjskt 85 tvaa3:+8b; )2jvhxwbntal frequency of 440 Hz and)tb88:jvkx biax a3vk2cotw+ ,js5;h 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 .s7y+ezmo e3k vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tu +ys.zk3m7eoe ning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at ow*zc)c mf0la2x9rcln.ao5, , : gttdmne end and also 75 cm long. How much tension should be in the string if iz,*9)rloftmwn.mxcg l:0a 25ctdca ,t is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r:y:cai;ax -q knd hdh3hz;yg .0u1 5pxq6yos (esonate 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 )g)nq/ 5/ dwmzin.q4wmd hf lc6qbx:-coming from two sources. The 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 sound level is minimczimd/bq)fqn. 4hl5m)d /wnq 6w-xg :al 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 cond 8(gtckjhqic 55/a6da uctor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving trchd 8ac55 /qgiajt(6 kain?   m/s

  The frequency of a steam train whistle as it approaches you isb:ywjot/ o8e1.n(/ej3 h0suzwgo dm0 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was t 3m uwdz(w /s1e0. 0h/toyjben :8goojhe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeniq(*r7wkm+ aahng 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 straightawa qwr m(7a+k*hay. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a fj del,jhm8*iu lfl4*m unxt-sh4:1 / beat frequency of 11 Hz. The shorter one is 2.40 m long. How f8nf*,xl ml4utmd j hhs-l1i*u4 /je:long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s.4glci o ;a-v4i: bjfntationary 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, (b) he is between the speakers, at B, and (c ca 4iin:lf;o. bjg4-v) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta oywv*c t2v (c)zy;h8rp+lp + uis 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 the waves travel with a )+tr 8uo *zcyvpc;y (w2hvlp+ speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at s:j.k mpex9; h6gq.n8+jaw kkypeed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the fhmnak kg6 e k+xjp.:;.yw8qj9requency 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 avjf.+hwgs* -h(paj3 a,-mdmj s it approaches a moth. The pulses are approxim ,-ga -+.jjhpjv a3hm*d(w mfsately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once u) gp k(a1,pe7:heapbhsed 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. 1ae be7p ph:kagph),(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 ci-h:m96a6jk0t* ej fu o .pnhjhjv2r 3an be compromised by the presence of standing waves, which can cau6v *h3-n.mjtuhfe9aipj: r2ho kj 0j6se 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,” involv:16hrs a6.pvdtmvp7m es a long, slender aluminum rod held in the hand na7dvp spmt 1rv6 m:.h6ear 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 human ear a,nd1 9a krx5xlt a frequency of about5dxxn1 ar9l,k 1000 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 onc7sm ns0bqa- 3 the ground hears the sonic boom 1.5 min after the plane pa7-3nsm0cqsa b sses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 fa9miw8a ec7z2. s ,lf$^{\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