What is the evidence that sound travels as a cg 1(p77pawqn wave?

What is the evidence ttdx f0 hzy* kb;i;s4w,mb. 3rt5 ejw.rhat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching aj wat2 jn;lz26 string to the bottoms of two paper cup2lzj w6n2;t ajs. 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 the other.

When a sound wave passes from :hc/i.z+s4.j w:y;b utkzayg air into water, do you expect the frequency or wavukt g: .izhw:/sa;4y.yzcjb+ elength to change?

What evidence can you give that the speed of soyxct1 9(. niuyund in air does not depend significantly y.(1xni 9ytuc on frequency?

The voice of a person who has inhaled helium sounds very k7w;:s2ri;f / cuqpjk high-pitched. Why?

How will the air temperature i(/tecp3rel z gp/l7,fly)l (gn a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter h)qwipc5 un 7q 9wf/dnc4y,9fbm 48ib to reduce the amplitude of sounds in various frequency ranges. (An ex 98fp)mc9wfw/d5iin hnuq ,cb y44qb7ample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov ffsx)ulp57 m-6nh( r1wm mtz5h5mr3me up the fingerboard towhm-wrt 61mh5nz5p ) mmlf5r7xu(f s3mard the bridge?

A noisy truck approache):e q(pl11 ejr74 1k eibiyljws you from behind a building. Initially you hear it but cannot see it. When it eme1pbrel7yel j:j4 (iw11i k)qerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,”7u rn,gv4b r)u0pkqa/ whereas beats can be said to be due t rnv)a qbu,up0r74/gko “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wou8,xmcmq.:6s0gbhvia j4zlw 7ld the points D and C (where destructive and constructive interference occur) move farther apart or closer toget0 b wc mzls.a:hj, g847ivqxm6her?

Traditional methods of prottn2m y1: 3(fsfkw( 8ce: jzvejecting 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 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 msjm38(n2zjvf:(yt:kef we 1 core noise reduce the sound levels reaching the ears?

Consider the two waves shown in Figd.vvc9kza8j ;5 ;ceee . 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 frequencies farther e 58jc;; e c9vvak.ezdapart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sh+ gu)b9o ixx4ource and observer move in the same direction, wih4bugi +9) xxoth the same velocity? Explain.

If a wind is blowing, will thp9.w0 kbgve2d is alter the frequency of the sound heard by a persk 9p2 g0vdbwe.on at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito1u-pq l :1npsseo*: mor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain yopoonse1s*q: m u p-:l1ur reasoning.

  A hiker determines the length of a lakex y3c2sdbu)iw0 ug+(y 0vqaq+ 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 )+aub d3vqg ( q+0i02wsxycyuthe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side/z z (+3lpzaxaxyz*+q of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directpxy z3a(xl* zz a+z+/qly 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) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wav wzh;:35.mzpssxag1h s.bz(p elengths 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 just above a school of tuna on90spg( np ;b p0frlipa0w n64g a foggy day. Without warning, an engine pfw0bsp40i0nr(l 6p a;gg9npbackfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striki3b foo9vjk jnvo1) h+9ng the watervobhn)o1v 9 kf 9oj+j3 below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huaav,csdk- rv5t+2)mz)mk/*k acz 2f hge 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 occur? See Tab )vm+/dkzaczsh) 2 k-,c5a2 vf tkmr*ale 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent /tddfv4y 5f0hz8n8:o a/fmnx error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 3d d 8yv/on4f:8f0/fzanxhtm 50 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB?- xx8aef9m 3 r( :huma;lf2gcmagkw1(    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levifw:*, ov thx1wp dy5s3)8mo rel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultanupu f/sa4cf1- eously at a certain place, what will be the sound level if only one is exploded? [fp 4uu s/c1fa-Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fouog(6 8gclp p:;oyozx 2r equally noisy jet engines is experiencing a sound levecz6go2(y;o :xp p 8glol bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whh lqdy97 kl75e x-,lgq9 6e tldugmacl4(*mf1ereas for a CD player 7l-eheg 9ayu6lk75x1ll4l*qtfdqm9 c(,gdm it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powerwmeo6f,ln 6q4 9or d2h output of sound from a person speaking in normal conversation. Use Table 12–2. Assume theo9h 24eo 6ld,wqfm rn6 sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strik4g1 zs24f + lxp;vmxpdse 7g;pes 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 r: 8.mytszeb8 eated 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 conee8mz s:ybt .8nected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed x:-ylue 5 9thv)ph u6/s* mounl5;nqx2.8 m in front of a loudspeaker on the stagenmx s5t- lnpu;9u:q6ye5x*vo/)hh u l.
(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 lehs*d 5 ode,t.g,x(wv tvel of 2.0 dB. What is the ratio of the amplitudes ofv*g,dx5 ot shw .d,et( two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what f75v /uvkyrm3e,)pwfc actor will the intensity increase? Increase by a vp /5e ,r3kwcvy)m7uffactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tz5a,fn-c 0o wmhe frequency of the other. What is the ratio of theioa nc-w 5fz0,mr intensities?   

  What would be the sound level (in dB) of a sound wave iuh,/ t2zb myu7.x oow1tpd :t9n air that corresponds to a displacttz7ux: hdw/2ob9m p1y u,t.oement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as yxh2djxs4f xk9tm:rnk:ay3 sn f, ) 78loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)s,asy fjnxy x k78f :2)4tdh9xmnrk3:    dB

What are the lowest and highest frequj4jmx) 2gk 7+ jwlh4xyarzw 0 -2svi,uencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) a472x -i jm kg)4+r0 xwwjjs,uzvly2h

  Your auditory system can accommodate / 7r hbbj/j;6lkfrd9ea huge range of sound levels. What is the ratio of highest to lowest intensity at 6b f jrb//l7;er djkh9
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamen-);ku rq 7+ei 21emdo m7*rbh gmdesr-tal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the s1rhmeeodu2* er-i-mgk+7mb)d7 qrs; tring be placed?    N

  An organ pipe is 112 cm long. What are the fundamenth q4rw5 6-himn5d9d. vpi2lrlal and first three audible ov2 m i5h.iplnr v4h-5q9d6lrwdertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would yp+k1d1aa pdb t:r44xloeo s 96w(rr;vou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closp41rw e6 v:14p t9srkl do(rdabxoa ;+ed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a9jrcn(y 5,vy7 yn gj-q pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what ny-9y 7 jj v(yrn,5cgqwould 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 540 Hz as its third harmonic. Whar*ar lnd+e( k0 jev1xq.mcs9rg- ;b2i t will be its fundamental frequency if it is fingered at a length of only 60% of its origin-eb; 02 ci*(e+krrv.9jgnrsdma l1qx al length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E au wilp .p (.j7ehq20jibove middle C (337jh j.lw0uqe2.(piip 0 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 oy y a3*wn647gd;hx*m daq7edlrgan pipe that emits middle C (262 Hz) when the temperature i;y lqxan dd d y7mhw6eg7*a34*s 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 a 55h-l.u,uy+gwlhi y mt 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 Example 1a4uw4 a, f m3m:rwo+ wg0i1scz2–10 should the hole be that must be uncovered to pri0 mzwmc3,sfu:4 +gaa4ww1o lay 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 616 Hz, but not at k1bgg*wfr) 1;w-gy;uyr vx0z any other frequencies in between. (a) Show why this is an open or a clos;g0fz ky)b1 rrywg;vu g*x-1wed 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 ww8dk:bg/ v 6qends. It resonates at two successive harmonics of 6vwb/k:dq8 gw 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 lh8+jspt:, fg$^{\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 prun2 )i(ombg * wic.1dczae q6;h9t 5bmesent within the audible range for a 2.14-m-long organ pipe.i) hi m*bb 9ucm2ae5tdqo( cgw6 n1z; at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxidxb3g7a 9095fzzg15bfly4 s2sbyzg fmately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencie4a 912f0 glb5 b d3zs5y 7fgz9xzfysgbs (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to ;fj u lf7 rug;if5. td9v-np :tjy5h1tadjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? glr -i1jtvuf:y;dp7nj 5f59ht.;utf ±    Hz

  What is the beat frequency if mihkm7*o jsi0- f mr5cy*ddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whil-k8vswt3mmu4f v1s: x e another (brand 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 they are played simultaneously, estimate the operatmw1 xf8s 4kvv3-um:sting frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9bo-cad 8j.(bm6u2m84ft-edyfo y v7a beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fre6ftyd j2m.fae vb c8-ombu8a7 oy4d(-quency of the string? Explain your reasoning.    Hz

  Two violin strings are t(ksxa.y9 zf:*k -tzau uned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard wtz:(xs9a.k-ay z ku*f hen 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 pifv 147p5xdaf owdwa)3(ton2lay middle C (262 Hz), but one is at 5.0°C and the other tv1 pna d2d3 woff4a5 w)i7(xoat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bm1 b :o;4skcpxva a:7n 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 v :p;bx71m: akno s4acbeat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person sta5m;z /tk vpi-vr6r/c ands 3.00 m from one speaker and 3.50 m fro; krvc5a-/6z/pt mvri m 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 piano tuner hear7.du igrhjt- vo26dp s2+rj 0wsvwy)1 s three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must2guv)j ww vyj0psr7 r+dhtis6-od 12 . 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 2.64d ygv28 12jwa v8d eh0tqrxbd8u 751co m and 2.76 m in air. How many beats per secog 87utvjy82h2cr5oq1v b da xdew8d 01nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’aj.8; y 7xyyrps siren is 1550 Hz when at rest. What frequency doy.yyrjpax7 8; you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequencykn6p* (xoqxw*ukxt 86 do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m6wxp *t8x6q x(*ko kun/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source tw7 g+ihwxu7. is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenu7t x+.hwwgi7cies 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 equippe63oam e9jd w*t hphf3 l+02cdgs5cg 8kd with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the fr93g 638* cjpe t gdsohla +hmf5c2dkw0equency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and re/zea x9c;z qocj3w41fceives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency? fe wzz jqcoa/;4 31cx9   $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As1uc d/2 ku/u c 6r:ujcr/g2sae it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hea6ue 1c2dkuu ar2c/u grjc:s//r in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played c zlwa1y0f0 q8on a moving flat train car at a frequency of 75 Hz, and a second identical tuba pwa80c yl01fzq layed 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 measure blood-flow * b9 yxak/ah g2nr6u/ 0l .sq/g+edzobspeeds. Suppose the device emits sound at 3.5 MHz, and the s/bo xg uza/*sr2h+.qe09ygdk 6/ab lnpeed 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+umo 6) jnxz,rg8zi;w 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 wind )v*y xcraehj,t)msjh 3 f8hl+jth+79velocity is 12 m/s from the north, what frequency will observers hear who are located,yl8*vh mfjtah+,93c)rjxtsj)7 +heh 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 lan6fe+ kza3gtt 4d 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 ux);j ezes8 ;fm/s (a) What is the angle the shock wave makes with the direction of the airplane’s motiozxf esj8u);e ;n?    $^{\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 plans9 cl 5nfdqef:ia*:/ pet where the speed of sound is only about 35 m/s * s: q9d/fialepn:5cf
(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 ocean. Determ3*z dyvvxn 4;6oivik/ine the shock wave angle it pro k ;*nz4y/6v3doixivvduces
(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 rhdiw; , l 0zlkypkx rr496b7-$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1egjm a.dq ou(z+/ 5wv nny8+wq1x./ lr.5 km above the ground flying faster than the speed of sound (axgju +5mnd1q+/zvlrqwoy8ne/.w .. 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 sona0:k)ua u.g-4yjibkq oke19 rzr device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. Iueajiy- 1b:u. 0k koz)k 9g4qrf 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 i uja v 5coq,n/hvit (3.ju1zh+n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.qmpwu 9g/:ht 8rb 29ig It consists of many plastic pipes of various lengths, which are open on both ends. t hg29rg8w : /pqumi9b
(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 fx:6ppc/ll+ c-0fw pwpm :g5 3:pqh.v nowrtg+rom a person makes a sound close to the threshold of human hearing (0 dB pctpn:+p+f 5oc3l 0.6r::ppwmg q vxhwg/-wl). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soun+c -darpm xng j0la8/;d are heard simxald+cm- /0rjn8;g p aultaneously?    dB

  The sound level 12.0 m from a loudspeaker, p) r1y33hchio5 k1 jgyylaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equal31y1 5khj3 gr coyy)ihly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The poezsl-xb,n lip:.d7)d8 gvs0 v wer output drops by 10 dB at 15 kHz. What is the power outd 7,nxvs0zlb8p sg)ei : .-vldput in watts at 15 kHz?    dB

  Workers around jet aircraft typ;,:,bpla zu8nmb9v kyx* ix* hically 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 that the average human ear has an effective radius of 2.0 cm. What would be thel; 98 *u*,xakxb mhp b:nvi,yz power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications e4x7uponbgu)2/ s p5b 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 to a fre m1+ 2f(ji96, vnrbnz-a iheqtquency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between f2j-em21twdg j ixed points with a fundamental frequency of 440 Hz and a mass per unit length - 1wmt2egd2jj of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with w kgv*ol yuey9 50el) xoniw6*,ater (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 a9voly 0)o n,gxe*u w*65ie yklt 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is ope 6gmrm l,nri-,n at one end and -rm r 6,ig,lmnalso 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tr6pkaf* iw 3xn7*qno wwn9tq ;(6 j8ndo resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 50ic m y h 7495t3tt+lkm4)medeb0–1000-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 +d9 47b)hteyl e5mt cmmi3k4t 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 conductor on thet k h f2*cfk0l f*7rxrn3d5ma3 stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving trai *ak f nm3r52t30*fk7hd xfrlcn?   m/s

  The frequency of a steam train whistle as it approache k2ky7h5:80jkqfw s: iuolp0 js you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How flk570 kh:j2uij : fwpy08oskqast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to th7pcmm5s(- d npe 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 straighta7 ( ndsp-c5mmpway. How fast is it going?    m/s

  Two open organ pipes, sounding togethe)u 3c hs(m.bvrr, produce a beat frequency of 11 Hz. The short.3bcvm r()hu ser one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car aspz8xqsts p./jf q2t54 it moves past a stationary observer at 10 m/s as zxt 8q5s. s /pj24qfptshown 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) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow inayf1u lv+.0xa-lvlx0 the aorta is normally about 0.32 m/s what beat frequency would youvualx- y x0.1+allfv0 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 speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whgl6bz/sncwp9 kx1u)8 ile 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 fruk/ 986s nw)z1 blxpcgequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high u2 msky ;6.q9awx+43tqyg6 o-mfo1g zbe ;aks 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 thesoaq k;mg3- bu f s+w6yy1 o6;azgexkt92m.4q bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usedr kiltgkeu ,zyf :/1j+ 7a09ft to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular af7el+ ktkz/y, g0 fu9j ai1r:tlpenhorn 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 compyn3*1 a;jzig/i2owt7wkf:n-ab/wu 3xtpd *z romised by the presence of standing waves, which can cause acoustic “dead spots” at the locationwn3 wpx*:oa;idit y zju/nwfk/g71b2a zt3- *s 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 rodsi /(t(rw4tml c,” 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 litt (lrt cm4wt/(ile 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 :/ yps quqj15;qep o,ghuman ear at a frequency of about 1000 H1ojsqpq:/ 5u ;y,gpeqz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground he:e7x s6mn hul;lkrr:h)d6w i+ars the sonic boom 1.5 min after the plane passes directly overhead. What is the pe7 i;l ) h uhnsxdm:krwl6r6+:lane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbl.kepvvc3)x 30 jlp1i oat 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