What is the evidence that sound travy fugh;hw/ vwdr 53xg)js93+mels as a wave?

What is the evidence that sound is a hr--jsyos) / ppd0 hs1form of energy?

Children sometimes play with a homemade “telephone”gy qtzv-iv/qci:ppf0e9( p x. lm55s5 by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to plsqi-0ice.v5p/gzvxm9 p5yt 5f :q(the other.

When a sound wave passes from air into water, do you edc x0x iv-9h4axpect the frequency or wavelength to chaxvixc9d40h - ange?

What evidence can you give tbc*:x+ cg*o f muz)d,lhat the speed of sound in air does not depend significantly on freqmg+,zu* dc*f)l:cbxouency?

The voice of a person who has inhaled helium sounds very high-pitched. Whouux. a/6y luhoi .3hj:0lo8cy?

How will the air tempi -e26byo7 ba78g gi.1bw7mowe/x qslerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter tff*jlqp5 dlg7n.9 w+n o reduce the amplitude of sounds in various freqg95+wn*ldqj f .p7lf nuency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together a r0da km)7nf.zs you move upd7.0zm)r a nkf the fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but c3;eds l s5elke sd*jo)+o8 9yb e*d8ly53e dsjo)+sl9e obks;annot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spa1-af t;r c60h 16zmxgehmg86isxz/ fmce,” whereas beats can be said to be due to “interference in time.” Eh1- 0mg t8rmfsc zge661fx;/6hi azmxxplain.

In Fig. 12–16, if the frequency of the s5pg( mr/c l-s;6:ueibxy e2oipeakers were lowered, would the points D and C (where destructive and constructive interfeco:6mb r-(lx; s /5 ipu2eyigerence occur) move farther apart or closer together?

Traditional methods of protecting)6or+fee3w ar the hearing of people who work in areas with very high f a )e3wror+6enoise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to 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. 12–3g ;umc74wo*i syc e4w.1. 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 frequencies faywuc7e .4 imo4w ;sgc*rther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directd1 lii vexk)(bek ej:v(l,-+kion, with the same el:(x ivke(- +1jielbv,kk)d velocity? Explain.

If a wind is blowing, will h g+g10wuf oaso7lkxk; ) z,(othis alter the frequency of the sound heard by a person at rest with respect to the source? Is the waveleng(k z+xwgo1fhaog; k u ,l0)7soth or velocity changed?

Figure 12–32 shows various p-/z/gig/fi yj;ztkih .8s)w iositions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through Ez-;gtshf8/)iy k/zgi iw i.j /, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a smt9t g()gg+ klake by listening for the echo of 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 t mt9gg)( +tsgkhe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the+bnww3d.t2 fzf 3aho, side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly belodfn2+. ,tb3f zwa3who w 2.5 s later. How deep is the ocean at this point? Assume 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 inahg-o)e9mmw2 5.j zr y 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 xzq;crk;,4jkovole;2y r1 /u school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before toyu; ,kr z;x21 vroqej/;4lck he backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a qb 58wo7urt jk9b5ok(cliff. The splash it makes when striking the water below is hear8u5otkq7 k (wrbbjo95 d 3.5 s later. How high is the cliff?    m

  A person, with his ear set3ey2 d,+thto 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 they are 1.1 s apart. How far away did the impact ed+ y2,het3stoccur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ov.awpobi*eqsg. ac6l/0nuq 2+er one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temp6qa*saw. lb ui .+q /c2ngp0oeerature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sou/id9l.sef6rxv t 5rmwj7 ,rv-d()4 ilsf.m p knd 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 whos+f+* mn/mosst0yg2 v rnmjy)6ai.xxv. 9bs3fe intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produceca g(xn8-7ja z6x ef9l a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.7e(fx8la6j nzxc 9g-a]    dB

  A person standing a certain distance from an airplkvy p-tf. gfgx 7e4;9*1cq(xko tvqm 9ane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would th(tvt1 x7q9poy *xff-ve.km;gg4cqk9is 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-noise ratio of 58 6bhz 7cy7q)dg dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB = b )67z7dqchy g   $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persone cg.jr jyo1j r528w74pkmv 2b speaking in normal conversation. Use Table 12–2. Assume the sounm8rj2ck7g 5poj4 rj b.ev1y2w d 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 strikekriyj(mzgf6+f3-kupa hs, (k3v ir. 2s 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 W, while the more modest a iusod *bt6gk9 h:,7djmplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a l,ti7duh9k b:js* odg6 oudspeaker 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 meterp1r wtlg2h 7.b registered 130 dB when placed 2.8 m in front of a loudspeaker on7hb1g .2w rtpl 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. ueslg2j- ztc)4ez l 1ry;;8vy What is the ratio of the amplitudes of two sounds ;1ygzect4evy; ulsjl z-2 r)8 whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will t*,spn ilcugmb q-o 3);he intensity ic-m qgbpol), su*ni ;3ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenz4-c:,kj ;qzo5yl+h xw: ic5 pf 2gsdzt amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities? 52oh-swzip 5c j;cdg:+xl4f zqy ,kz:  

  What would be the sound level (in dB) of a sound wave in air that corrf 5d 7oi ev(vtcqnbfd a65w:(nst+ 0,sesponds to a displacement amplitude of vibrating air molecules of 0.13 mm ati+fd 60 :td 5n (bv,nse5qcavsfw7o( t 300 Hz?    dB

  A 6000-Hz tone must have what sound ot +q6);pr zpblevel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sp;+q )6orp zbtee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can dapi*puc) on 4dbwm)85etect when the sound ) *n8 ubip5c apmdow4)level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound27wfe-* 8jqaz sb fp9l levels. What is the ratio of highest to lowest intensity ats qaj- lfpz 9bf2e78*w
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundament3fo j lc)v1 zcq8:k*ui/nw ll5al frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass o zfn 8okvw13ul c:jli5*lcq)/f 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible wi6mu yn w7a(who:8 daw. ;ra/ovew :whiumrya. ;7n86a(owdw /a rtones 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 woulde 1b(ar6urt(h you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it w6 (tear(urhb1 as 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 spa(-tk3 ar u*trsnning the range of human hearing (20 Hz to 20*rt3-su(ra tk kHz), what 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 r -hpyql hzaqa) (.h:9 xb:9tta frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only ptq-yxhbzq.ha(l t 9)ra9:h: 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mid58d;it/t2td slwn7gar,ov 2tcoz -;6u g -zeqdle C (330 Hzu 7tltq-tr-;8 ooz/d6cvtzi5 g2,gw;a2de s n).
(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 org 1fc,b62ryk5 m8b8je7z bf lv8sj lu/san pipe that emits middle C (262 Hz) when the temperssu6mz5e bv1y 8lrfc7j/28,lb j f8kb ature 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 vb-otk-n wsk+x m4,) dat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examgq6u ic 4l9cgb ,oc:5qn myx*0ple 12–10 should the hole be that must be uncovered to play D abo5l ,u0: igbcmo964ccqgxy * qnve 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 r;5yazgvgh /kfw(:w ioew73* nesonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open n *gyawohf;:/v7ikgew 53w(z or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 *kmug4vm/u ogv7 : n+mm long is open at both ends. It resonates at two successiv7*ok4n +gu:mm/gmvu ve harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 yy34p j- qr ga.ir+p6c$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14a;;;lokj xm+a-m-long organ pipe xkja;l+o; ; maat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatoq-jdky wlral8o4 2 *pbcc 5r21hq7,yely 2.5 cm long. 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 relationship of your answer qqchyocpw 12lo,52 *8a 4d-rrby7lkj 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 tcd7m a2b5j+ ohwo strings, one of which is sounding 440 Hz. +mh7 jab2c d5oHow far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz);t*pjyw:j y+s 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 (brand X) oakz 8ah .5y+b:nevg) v,r i;vdperates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shril,h k;gy)id8: n.rvav+5vezab l 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 ;3 2stczkepmg, * sb+ewhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded s3*cgmeepz+s2b; k ,twith 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 frequency, 294 Hz. The tensionzl)txaa)ra7-tbs 5 /q in one string is then decreased by 2.-/7xq ataz) 5sbrt)a l0%. 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 bt:dfwonfxu(7 *7ngamr94 i- each try to play middle C (262 Hz), but one is at 5.0°C and the othe7 onrgdn mafxw*tuf -4i7b(9:r at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freq-vlvww 0zfgy w2+ckv*na51y*uency 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 fy5*alw v+ * wygw 1fk0-zcv2nvrequencies 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 m0yh3fv; l 2hxl apart. A person stands 3.00 m from one speaker and 3.50 m fromfx l0y3 2lvhh; 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 hfj to: x+zd4660eo9w(dq8wobb6p e4x *m daxvibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibb oze4*xf8px96 :dwq 0ewx ob (+4odt6j6dmharating 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)2v5nf0qwy4n 7jhp ak m and 2.76 m in air. How many beats per second will) vnj5an4p qh70 2kfwy be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencv fg3y anj64u-w a ;(1tk:qajoy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if yk:-goa1ja43;uqnav 6ftwy j ( ou move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing sti)n:,wcm8lpd y0wo f9jll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves amyo f0wj ,cl)w dp9:n8t 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 yo-3g2 /wnkcft 1qji4clg5;e jsu at 15 m/s verss12fijct klqc3 g54-eng;w j/us you moving 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 withfyy8, *wy+mplu 8hb m, the same single frequency horn. When one is at rest and the other ism,byfy p8mh +w,8y*ul 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 emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrfok)/lj p/m l3asonic sound waves at 50.0 kHz and receives them returned from an object moving diref/)/l mplk3 joctly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it,9zr+jerywq ma v8npxb(., 0q flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fr wbaznq 9pmej (r 0+r8q,x.,yvequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played onlaaa dedwf l h+d o,(0bv17.x- a moving flat train car at a fv , d(d7l l +haae0wodxa.1-bfrequency 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 approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measuree0b6hbhrghk5, 2n q mh2 v2oz, blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound i2g,5q2hzhhnb6hb0 mve 2 ok,rn 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 away from the sound source?   Hz

  The Doppler effect usinl u 0.x ()f/ 9ridyqrexm,ocf .ujl/d+g ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the w y 0 m02iey0:g)h+yegzay-ojcind velocity is 12 m/s from the nor0gjoge0ye z2yi) m:ay- hyc0+th, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2cc, *hk8ic/cu u4wsq f(t;vmy1gv; bnd6i w 060 $^{\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 8c r0tcbqr , v(p ,,bmfuck.hu0g5j*fspeed of sound is 310 m/s (a) What is the a0,c*kbfbgpqtrvc 5, 8 cjf h(0rm uu.,ngle the shock 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 o/ s uu;zl9cmm.qo(; sxf sound is onlys;msxolcm 9.u q/zu;( about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the 7qhiw1ld6 b(o g3uyc (ocean. Determine the shock wave angle iu 3hgyco7qw1 i6db( l(t 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 qgd+smzk5bv9osv/ ,p0)*y .ypzf4jj t t 9cq *$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly over; +l2 tv,5vdsmqle 1vcbqm.-ghead and see a plane exactly 1.5 km above the ground flying faster th, vqtsevl;1v 2- qml5+db.mcgan the 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-Hz soc:oj 5 zerg ;541ljcw/fh) wbnund 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, 4w 5g :jn/o)c ;cwrlebj1 fz5hwhat is the minimum time between pulses (in fresh water)?    s

  Approximately how many octav*pab+ w,( gubhhrffyt9pw7 749nisg 0es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syup3;eq+q yqu,mphony. It consists of many plastic pipes of various lengths, which are open on both ends,e yquq3qp;u +.
(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 of huufpkxhes nt( : / 63cu*aay7+oman x:caaykeou36n+/psu7(h *t fhearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8wl-3 r8jxn- j/tzd3 ob2-dB sound and an 87-dB sound are heard simultaneotdb 8o/z3 -xjrnjw l-3usly?    dB

  The sound level 12.0 m from a loudspeaker, placed indg 1 ,w:awvvk9 the open, is 105 dB. What is the acoustic power output (W) a9, gd1vw: vkwof the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 15u d6 ei:;,wm;bcl+lkh0 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output ;+;,k clmlw6h:eub id in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear piyd3 v3n74bvarotective 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 power intercepted by an unprotected ear at a distance of 30 m from a jet airplane 3byvnd a473vi engine?    W

  In audio and communications systems, the ga.1e8u ofq/qkxg8p8bmr nnv3426 *2dgx wsbggin, $\beta$ 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 violinde8 cajd:sbz:*e j:y 1 is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm lonuriw44w r md8m ;.b8olg between fixed points with a fundamental frequencyu wl wo8.;48mirm4dbr of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibratioerol tt0fo9wm ; zgi7g563u7sn 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 agaio w96i7teugt 0s5 lr3 omfg7z;n at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g z9rk*oz+n( ci ,2;cim v,-rnmzptg3ris near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce reso9nnzv(-rig piorz3 c*,r +tk2mzm,c; nance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lo6xhzu:w,l 8z b4vjol8op ($\frac{1}{2}\lambda$) 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 purb+.d 2zik j(.9 e prwqo8us5mpmri 60ee tone in the 500–1000-Hz range 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 minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?wd80 u.5mibje.e r26ko 9(pmq+srpzi   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the s)74xnydvhpe5 tationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spene7)54yhv dpx ed of the moving train?   m/s

  The frequency of a sz4h/9ojml .vk r)-mauteam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume ch9 a/m-.4)omj zkv luronstant velocity)?    m/s

  At a race track, you(m:q8huijwwm7x86/ 7fcm j fh can estimate the speed of cars just by listening to the difference in pitq7f m wwu8/m:c8(j i mj7fxh6hch 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, sounding together, produce a beat frequency of 11 Hz. The( :up 5;pni*k-d4ul(osgri; hy qcz )j shorter one is ugk-;5:pihpi s z;d*uynql (4 j(o r)c2.40 m long. How long is the other?    m

Two loudspeakers are at opposity-z2ew 8 p 63lnoebsc-e ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speaepezwlsbn 3 -co86y-2kers 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) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally a pyif+tz)d 1h0bout 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 )iy 1d+zf0thpwaves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the modm3af8rj;ky; tn n1xt k9(b/l n)aef7th is flying toward the bat at speed 5 m/s The bat emits a soundj/ 38akl)bam;7 n 9f(;yrfdttek 1xnn 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 highg 2b-pm)7(xwq 2xh yxi frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirpmq( ipbyw2)7g-xx xh2 returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 9+acxy g2is:l12–38) 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 overtonescy +axi:2 lg9s is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listenie;:j5m pgs2w4;l xkiang can be compromised by the presence of standing waves,lki ag jx;45we;2smp: which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, 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, slen b1+ (rr3 1kxaz)hwxnpder 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 cakwpr r 1nxbzh)(1x+ 3an be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a freq3fi+s8 c0.7pe6mvty k u hy.vsuency of aboutsyk.ti+ 3m0v s8eh y6.f c7uvp 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 on tl (nm xyir-gfby rag e4 hybh0sp));(0n)rw)0he ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the h(4b;m i(-seg 0 w)0arf yrbg)y rnp xh)lyn)0plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is8gmlir mm8mj3w(15ia i 9x.ta 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