What is the evidence that sound travels as a 1d 6j uaadws3ib:bq3 2wave?

What is the evidence that soum5cl 5 ud9dxqqf8- o-xnd is a form of energy?

Children sometimes play with a homemade “telephone” (pqokqx 0r:y8: mayd- 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 clearlydoxk m8a:- (0p qq:yyr how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, lusx m66 27x.ysd5yuo;drcd6 do you expect the frequency or waveleng6.x 66 u2d;7x5d ussmdryocy lth to change?

What evidence can you gia,c gx5z:e;x ive that the speed of sound in air does not depend significantlxa,5z:eg i cx;y on frequency?

The voice of a person who has inhaled helium sounds very hig1,,q rbbbu tny x+ku)9h-pitched. Why?

How will the air temperature in a room awzhidf/r: pa3zb j;-3ffect the pitch of organ pipes?

Explain how a tube might be use m),(kjds;-wg r*p;:v sy 8)rdfo glrjkaz.k- d as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler;kry-,.gdsp w8kr gjz-* );)lmds(ojv fr:ak.)

Why are the frets on a g( pef l9k:64uy 3 gmb,.jnapmruitar (Fig. 12–30) spaced closer together as you move up the fingerboaepmfg(rk9n.lay,6uj4p3b:m rd toward the bridge?

A noisy truck approaches you from bg4by(k,v tdv, h-vc :lehind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Expla: (,y-dtvhlc4, vkgb vin. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatz0*u2a+ n2c sqtph2xbs can be said to be due to “interference in time.” Exp 2pa0c qszt+ n2x2*uhblain.

In Fig. 12–16, if the frequency of the speakers were lower1 *n* )vrugsczobuvshm) :/ouar79e8i,- h s hed, would the points D and C (where destructive and constructive interfer)1*n h*s/ s ova, ubvesh:8mirhug)9- 7ozcurence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in area z hi27mz4amo,:(zh zos with very high noise lezz4o:7o hahi(m2 zm,zvels 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. 1vku 4om8ohy 6d.-sp 6v2–31. Each wave can be thought of as a superposition of two soun- 6.vkd oyum4o8h6sv pd waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same diog- 3c(qp 6mdtrection, with the same d -gpqt3co(6m velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a perv0 2ptmb9b+ioson at rest with respect tobtiv b 2+p9o0m the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positiofje).5dri2 ; 7ik6 wz els(fpxns 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 e7)rp (di5s izj6fwk. e;2xlf 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 vk d,xsvfpaf +8k*)ie3x .4gcby 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 kex gc.p kiv*xa)+ vff34 8sd,length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship j,muwkqrb1 6l.:1;iryggonwy c 5s ag bd)q(3; ust 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 1560 m/s (Table 12–1)6wky )wqng3g bsar:y qb;drgm c1(u io .15;l, and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wa )b.hxp.ezhz/4q kooeu(mq( )velengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting justzj na+ovrc56xn9e( *f above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much tim6rnanx9 fc(+ez o*5jv e elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Th)du8nm9+rrbm y; uocu+qk5 u*e splash it makes when striking the water below is heard 3.5 s+9cu unuqrk;5 b mom*u ryd)+8 later. How high is the cliff?    m

  A person, with his ear to the ground, seeshl*/f// 1 bedjag jl+h; hni4o a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one tiehlf hgad/*b+ljj/1/ on h;4 ravels 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-seconl/g*m .wof;wi4k:ug7qom:j bix 0 .rpd rule” for estimating the distance from a lightning strike if the temperature is (/: 7igr:p 4g quifmbxo.w *.0omjkl;wa) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of bbg -47r :mg-b5mrae h120 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 o+x ;hs+sg n+pis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producu (.plb*hj 5 anz2xlg/e a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hixl/ l (pa.hbgj5zu*n 2nt: Add intensities, not dB’s.]    dB

  A person standing a certain distance from;eqku( 94ka 4asw .wrc an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the csa ec;kw44r uq9(k .awaptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sign5x w3mf78f5rw u3smlk +roq j0al-to-noise ratio of 58 dB, whereas for a CD player 7 w om5qk+ 3x3s rufjwlr8f0m5it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in(p)dw( n fmgb(/xvr0t normal conversation. Use Table 12–2. Assume the sound bw mvx )f((gp/rn0d(t 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 whose aaj ka fb3:..ulrea 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 An4g7w(nf r-:p z das(r is rated at 250 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 loudspeaker connegzr-7 ((n 4:ra snwpfdcted 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 registerxf6 6psh:heawq, i93j ed 130 dB when placed 2.8 m in front of a loudeh3 fjxp,aq6si:h 96 wspeaker 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 typically detect a difference in sound level of 2.0 dB. Wha5ae c)8vftz ,jt is the ratio of the amplitudes of two sounds whose levels differ by this amojcvf 85) ezat,unt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripqw gx20g/ cdu0l(p9zc+j cuv +led, (a) by what factor will the intensity increase? Increase by a factor of9 (0puxd+ujgz/0g cvwq+2cc l    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one un5+l)bdzd+fn*c0n f,yw k -vhas twice the frequency of the other. What is the ra+k*vd+bd cf 0)yn n lzu,n-fw5tio of their intensities?   

  What would be the sound level (in dB) of a sound zojpy*4v7a/ :wal im( wave in air that corresponds to a displacemel7yz a p 4:m/jv*owa(int amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wy9t8x9 +h:xky7 xhd4zm, . mndf)sqr jhat sound level to seem as loud as a 100-Hz tone that has a 50-dx9t djxn9yh,k7 4m.zr )dyq:m h8sx +fB sound level? (See Fig. 12–6.)    dB

What are the lowest afra4 5;1x hdg5deemy (nd highest frequencies that an ear can detect when the sound ledgx ;r 1ma5fy5dh e4(evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range lm z;i3/ur*ptkaay)5of sound levels. What is the rrm za;3ip5)*u t kyal/atio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length us . hyy p8g4;n(jdj8(2bdx qfof the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed? j8yj.2 ( 48usn f;dbydxq (ghp   N

  An organ pipe is 112 cm long. What are the fundamental and first thld*xy fc96/a6; t itklree audible overtones if the pipe iia x tc/kf6t 9*yld;6ls
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowinja y sj ;xhlenh ii6lun;/5h.;:*nvb1 g across the top of an empty soda bottle that is 18 cm deep, if you assumejhhnu. ; li;/;yvin 6hnsjla:e*5x 1 bd it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of how .;*g3 w wne/xozxbr4or( -buman hearing (20 Hz tox g3b nr4/oo(rwzx.eww*-o; b 20 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 a frequency of 5cp-d2uxxv ))l 40 Hz as its third harmonic. What will be its fundamental frequen )dlxvcpx)2u -cy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ac(d f ji)et92f,yvyp7w+be)y n4cp 6 jbove middle C (3302pb t()c9yc4wdp+je, iye)7f y6jnvf 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 Hz 6 v2)u wpazx*wu9d7la) when the tempera *v d)9lwuza27upw6x 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 at 20 le),d q wik3y9iyq,s8$^{\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 hole tf;w6fb:21g68 ocndsaz, 0nu cqv+n bbe that must be uncovered :ca8,2ztdv bnqbsf fn61cg06 u+wno;to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and yhg-r,ca, 8*/ivk; 5r hyypi0mtm/le616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a ey,/atrv85 hiy/mlrc *h p ;0myigk,-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 suctdiw-/e:k +c mcessive harmonics of frequencies 275 tik-/ ewc:md+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 r eon uyhjli.q; )3r/5$^{\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 audible1 /jhyzpwx mnw2mr weu/5:m4 4 range for a 2.14-m-long organ pipe ajrypnu x / w :hw4wm2/mm5ez41t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is ati1knuz:df ;8 :kwa.upproximately 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) :f kiz na uku1;8.tw:dof the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryintsb1,lyai k6, lu 8;wog to adjust two strings, one of which is sounding 440 Hz. How far off in freq s6w,akl;,yb8lt1iouuency is the other string? ±    Hz

  What is the beat frequena (c8qj.l/ vp /j6auyacy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHzbympfm fd;; ;5, while another (brand X) operates at an unkyb5 fpf;;d; mmnown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces g +:pyau0x4zcy5ug:v 4 beats/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 ygugzv0ua4 +c:x: yp5frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2;*9*( qfr* wakbuceij zg i0/q94 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency 0(jr;ikbawz9f*e*qcu i /*qgheard 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 plakuxh)6uuvrm/2 gu1b9 y middle C (262 Hz), but one 69gur hv xuu1)/k2um bis at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency ocl(5 /daj8eowt115gkpkbc i ( f 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 (cb( g5/ 8ic5kwal1tedoj k1pof A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one spe4;bp fu x)mi8daker and 3.50 f ;iubpx)m84dm from 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 vibratingrfu qu-(n.kk06z.j ff at 132 Hz, but a piano tuner hears three beats .rfufkuq kz0j.6 -nf( every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengthsozlfku1z:h)7emw:v1+eba6 df:yi) z yc ab,, 2.64 m and 2.76 m in air. How many beats per second will beayz1 :yhffc za ,mdob)v1w 76:kee:)l i,b+zu 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 5. hzywh1-npwat rest. What frequency do you detect if you 1h.pwy-5nwzhmove 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 fire en/92pysnvh/ w kgine whose siren emits at 1550 Hz moves a v2pywn9/hsk/ t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shiftuo- pb1lpd9 e8 in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it ude-1po 9 p8lbat 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 samee-ilc :,/mwzqn*/trq single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the drivem- ,/clenrqzq*:i/ wtr 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 ultrasonic sound waves at 50fv+-q, cvkerl e 8y2jtbc4* *v.0 kHz and receives them returned from an obje *f y vcrtvjq,c2+-lk*e8 bev4ct moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at h.muwf6tl)s 2 a speed of 5 m/s As it flies, the bat emits an ultrasos)h6 uf2wtm.lnic 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, a tuba wt: v,v. 9zq6s xe lvek2oy,y,pas 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 approached the station at a speed 6 yet2 :,epz qs,,vk.y9vov lxof 10 m/s ?   Hz

  A Doppler flow metercpwurkw-vs f1/6,g 4 y uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the spgkru,-swwpyfc4v6/ 1 eed 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 away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fre4 gf7-b p3vkh;vvzek7 quency $2.25 \times10^{ 6}$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 wind velocity is 12 wy6goy k,s9b-r jx; -cm/s from-jgywkr x- ,ys;6 ocb9 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 land ai;o c6m22 ek7j rn6ar3ewiw1if 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 twc3n -k:f q)ovaj w-+f4(jgsdhe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of th:)d4jwsf+go-aj3k q c v w-nf(e 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 off74xec; bdjwz/i mr/d xf218 z sound is only;z/d x wezjcmff8 4bd7/2rix1 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 oc, ef4fn*wfp7sean. Determine the shock wave angle it prodef 4w7*p ffs,nuces
(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 tshy-5p:jno 9;ou 5ok$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and swx7b dw07eh, qee a plane exactly 1.5 km above the ground flying faster than the speed of sound 0hd7 bwq,xe7w. 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 n 5+,-j+f.stbevmjdux apk2c0ei s:1sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh w1kcvbj. -02pxs :efj,5ie dnum+ +sta ater)?    s

  Approximately how many octaves are there in the human audible rz9g3w+ 6m(0 cu mst nao2 +keqn8)cmapange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer :uko -qt rn4/zpipe symphony. It consists of many plastic pipes of various leng-u:t4 o/zkrqnths, 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 th*l3 bjs.la0s erj5v4we threshold of human hearing (0 dB). We4la v .0rj3ls 5swbj*hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whencq. ;+bk2h: m3kavfye1a yk o( an 82-dB sound and an 87-dB sound are heard simultaneousahky3;2 y fk1(:b +qmvok.a cely?    dB

  The sound level 12.0 m from a:qs7u1 b4:;i:kmfsudvf qhmg 1e s9 z d+i6k8l loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equa:b;:usgd+ ii usq7q l 1v6h81mk s9e:dkzff4mlly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output d6 zyx6u 3ls3bzps-fw-(bgf11 bzinh 1rops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? (n pszi- w1l zb6 -fby13ug3b 1hfzxs6   dB

  Workers around jet aircraft typically wear protective devices over their e,z-t+8ryvw0 a+mw mqrkst z*vvn-0- ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and thmky0as-w we+tr-r,*8mz0-vt zv qn+ vat 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 communicati. f-hvc: 2l 0nn;gspa1xr/jqjons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned tl44yol2, iqdx o 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 betweenb5j7d;b *n:x*2yb1t k6zf0lrtw k otn fixed points with a fundamental frequency of 440 Hz and a mass per 0znokj5twfb;nt * 1y 7brb 6d *:2kltxunit 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 fillyw.uzx / wdu8)ed 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 y)/x8u.wuzw dopening 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 gkmaa5 thp) 9emuq +u2 y(2kfs2 is near a tube that is open at one end and also 75 cm long. How much ey(m2sfkpa9a 2humu5+)qk t2 tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to uk:;6gi, qe siresonate 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. p hlx00t;mfj f *o 2(: si:x2j4luyhpeThe sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds t2lp2x:4x0 emt 0;j y(f u*is: lhhofpjhat the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Htl9 c:m th.): (onk 7ydxspxx3z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed otp3n s:mo : ( t)7xc.kxdxl9yhf the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hd ogo nscwh*3 ele)m7qe4zr( 74*:gnlz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving ( mdo7g l44e( nnwe:zog*h 7s3)c*qelrassume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars justia/ 8kmqv. n*z by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain mv* / qzik8an.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,e idiaqq-yjn- n7d 0il63azo80s g+;r produce a beat frequency of 11 Hz. The shorter one is 2.40 m lo7yd6 qa n- 0zln8oqi+dae;3gr s-i0ijng. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad ca k x)z:rqq0p7xr as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical70)z :qqpx xrk 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 2q9a;dd wmhe 6about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reah w9edq;6d m2flected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth ntf wg, -+)bpstq:yh /at speed 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 frequency of the wave detected by the bat after that wave reflects whnsb /:g,qy-ttf)+ p off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approac/mm*(u8d68 m2hmqrwsg skk/fhes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returh68m(/wm ksg8 *2dkqsmr fmu/ ns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signwq ,g.mf 6;eqcals from one Alpine village t;.mfg,qewq6c o another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m 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 compromised by the presence of sta-sw41p,or lnohe4wqp n 7g e-9nding waves, which can cause acoustic “dead spots” at the locations of the pressure nodepq,epwgn n4o r794l o-w1eh -ss. 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 demonstrationa-jk ;v dya(1tkx3;b d, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod ca; jaakv13t b d-x;k(dyn 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 ajmg +po0yd 6s-t a frequency of about 1000 Hmgsp d6o-yj+0z 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 o8+du8aw*/ax*wq9vilnw l)u o n the ground hears the sonic boom 1.5 min after the plane pasd x+i lw8w/uulv oq)98a aw*n*ses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatry 2/t ck-mnosf:nry-4g 5g5i 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