What is the evidence that sound travels as 5xno4f0bii2b 91emcp a wave?

What is the evidence that sound is a form of enejke(xac 1c4tbw:gl300dw6e/ k 4eore rgy?

Children sometimes play with a homemade “ta waw ixgf;15 hml0/0aelephone” 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 awa 1fil x0h;mw0ga5/the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o:7do/sq8r jr jr wavelenj7jrq ord /:8sgth to change?

What evidence can you give that thez 2w qonm0qu3c9u5gl .7xjt(g speed of sound in air does not depend significantly on freq53tz 0.j cgqwx7 oug(u2n9mqluency?

The voice of a person who has inhaled helium sounds very high-pit6z wjkl;ppn:dex, 0gn 4kqn4:ched. Why?

How will the air temperature in a room af,l567s- jrvc,epbt7 na :yms yfect the pitch of organ pipes?

Explain how a tube might b 7bq yig,mww*,e used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a c,iw b w,g7y*mqar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closa .7qacnzw3 ;ser together as you move up the aa .qs zc;37nwfingerboard toward the bridge?

A noisy truck approaches you from behh 8yykf1w )d1sind 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-frew18hf1ks)yd yquency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bea6 fnt/rg gt23m7 uj-lcts can be said to be due to “interference in time.” Explaingu l-tct 7n6 fg/r3j2m.

In Fig. 12–16, if the frequency of the speakers were lowered, would the ohh2((l.bgdp zvo* +esbjo i;n ,ix3. points D and Cb2 p3sh (+*(djb vl .igoz.i,eonoxh; (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in area7f 3r5l 2xdgxcq(c3kas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. fca ql 3(7xg3k25xc drWith 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. 12–31. Each wave can bm8y c9amn yt kmpd/0(abs hwe:5 jw*6,4oddz/e thought of as a superposition of two 8nke6yd5at/ *j 4 ,/0hm9yd(awsopcz:md wmbsound 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 dir :0yps qqnchs-q,we x.fq54+gection, with the sahq0 pqgy-5+ cqsns, x:qwf .4eme velocity? Explain.

If a wind is blowing, will this alter the frequency of the sounat a : 5w22.hi:.kz) fuyvkzgkd heard by a person at rest with respecay:.kw a2z2:fviuh k5g.t k) zt to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on ai(j rlz*g7p-f3 i y 2c6ivpdp: swing. A monitor is blowing a whistle in front of the child on tvzl:yp(rp2* -7 iifdp3j i 6gche ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for i(ku, knt ,ncf/1d.r;*nud) onch0otthe echo of her shout reflected by a cliff at the far end of o c n( t.nn/u,;dk,uo c0*nfr 1tikdh)the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just my,8ulr+c v)ti4k 8qacx xc7 n(9ml2e 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 sou )l e xc987v(layi4mmcx 2qr+8,tkc nund in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ai8 ba/zncd)n6 jyf69 fgr 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 on ;yn (/vft .de0ptb7a1b icx/ka foggy day. Without warning, an engine backfire occurs cy.1ekb/dtti xnv 0f;pb 7(a/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 tov84my ca2w5m n 0/uhaop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How highn /845muo h aywv2mca0 is the cliff?    m

  A person, with his ear to the grivig9 u/*1ck-t )r 0f.ccr5hg( ,klyfsk -vz lound, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one t 9)kh1v*u f.rvziyi,gr5 g(c k0-f/-ksctlc l 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 err2yb;qsj8/y+ k i aq5m4qkx-q yor made over one mile of distance by the “5-second rule” for estimating th8qb-js/ m xy4yq k 2i;5aqqyk+e distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levewlh+e fsl (:-7af4bsw1zs5xr l 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 s atbt k1zqzco-),;(k 6hdzaz4 ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simv2 t76hx;lx7diixb (sultaneously at a certain place, what will be the sound level if only 7l sht6 x 7(x;vdxbii2one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from a i9p-mfkarw /u a 5r(;dcu.e2on 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 captain shut down all but one engine? [Hint: Add intensita;w / rikf5 pc29(-uar.m oeduies, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for t ibd4l+o:* jofytd2j, 3vwm/a CD player it is 95 dB. What is the ratio*,+4tm2vl j w/di3 jybodtof: 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 norp,phe6wqwnmka- *n-s w s;/3vmal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o6nwq 3 n;epwhav-psmw /-sk*, n 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 strikejie 7/78. wgaszhkw/r s 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 mq a a9f/zr5z v(jmns)p6+xan -odest amplifier B is rated at v6az5j ap/n-+qax(z m )r9snf 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker 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 /dcny. tdr8)wtpha h-u4 * d(tdB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the sthncdtt *ra.d4uh/ t8wd )p-(yage.
(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 2zn kt-1na*lasek;uj- f 9 ke(:.0 dB. What is the ratio of the amplitudes of two sounds whose levels dt:k nj* z (1eln-kka fa-;9esuiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) b;q-bevyng; d ;520 rjtys ga*jy what factor will the intensity increase? Increase bg2*djvsg;ay50 b-; qne;rt jy y a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has f 5v,o6 /gqj2axqcv( ptwice the frequency of the otherv5f/g6ox2cq( a ,jvqp . What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound waven;xs-tk6jmfl7u(+nw; wgh 1g in air that corresponds to a displacement amplitude of vibrating air molec m+ ;uxg 7wn1 lk(thns-;fw6jgules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what dy)b/pux 9t-rsound level to seem as loud as a 100-Hz tone that has a 50-ddyrp9) b/-uxt B sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that ans k19v-)ey tvm ear can detect when the sound level )-km 1tyes 9vvis 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hugytp rsvu4 c,m(yp+ fh-plw00 0e range of sound levels. What is the ratio of highest to lowest intensity at rs0 0f-+,vppyclu4 0hmytp(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 fundamental frequency of 440 Hz. The leng3/p2mnv36n tz7 f vfxbu*- tnvth of the vibrating portion is 32 cm, and it has a mass of 0.35tx7p3v/n fbtz2 unvn-36 fm* v g. Under what tension must the string be placed?    N

  An organ pipe is 112 ko+j)plz x*i r6et0 r6, ecy4scm long. What are the fundamental and first three audible overtones if t cr+6z toyskri4e0lj 6xp,)e*he pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acrossrcp )0lm 94ae7aumol8 the top of an empty soda bottle that is 18 cm deep, if you assumedr 4lola07mm98cp a)eu 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 a1+j5 nawhfkc( c6n 7oi pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? n1jhc6wi+5aockf7( n $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third htmx9 ytxnny5rp;. -z /armonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its or9t/n z5xnp; y. rty-xmiginal length?   Hz

  An unfingered guitar sth -ui, 9olaw;/1edx9 n( d:ylafrt1dcring is 0.73 m long and is tuned to play E above middle C (3th/1w, a ya1uc9 d f; ridd9n(olle:-x30 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 organtw3dk+b24t9 b v*egqnvv q)/q pipe that emits middle C (262 Hz) when the temperature is 21+t tv32bq )gqdn b/ e9vw4*vkq $^{\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 ad-,+h pc 2zvngf4s6e qt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moutjwmgc :,5rmg hm 4 2w0rbg0uc+pd 74yehpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz?0hrmp2 gd,w gym4ce: +br0 4 gmwjuc57    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 6liff (ge gaiq0c:ly1fv(ra,r2m7 3q ; 16 Hz, but not at any other frequencies in between. (a) Show i3ffg1:fle l,7i0 g(2aac(mqqvr r; ywhy this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open if/e pw98z+uxl9 4ntpat both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wh94 p plifn+tu/e8 zw9xat 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 qoewi+ 8x;z2t$^{\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 2.14-m-long lo;+b:pn n. tjorgan pipe .t +polbj:;nnat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.x u2 si8pqsw.l5psga6* w;b *u5 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 sswq ib*u *p8aw2ls5 g;uxp6.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 tgb 1ekgc+iu 9f6eff:n1.qhypi a 9 (n/dl9;w zo adjust two strings, one of which is sounding 440 Hz. How far off in frequency is gwk;dl 99p6qe(n9z hi/ f ac+b1f nfeu g.iy:1the other string? ±    Hz

  What is the beat frequency da :;rxgt f2-ogclt 0izcl 58ypms: ;-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 kHz, while another (brand X) opera3(-jdoffs5*k gqkvx0 m p/pj 3tes at an kf0-q(j/xgv 5osmd kp3pf*j3unknown 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 4 beats/s when sounded with a 350-Hz tuning fork 23)jnhp w7or gand 9 beats/s when sounded with a 355-Hz tuning fork. What inr2jg)h7 o pw3s the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequev1 drl/ lif,m7ncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the / rfli7l1m ,vdbeat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will ) 0y:abyq t4rwbe heard if two identical flutes each try to play middle C (262 Hz), buw0 brqy 4y:t)at one is 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 foa8we/ v5f75dcx1k ycz. k9 yurequency of 441 Hz; when A and B are sounded together, a beat freqfv wko5k eaxzy.1/9y58u7dccuency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible 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 a 1;9v+ ore(hxk q8iszkpart. A person stands 3.00 m from one speaker and 3.50 m from the othk9o8xh 1sk+e iq z;(vrer.
(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 /l-l: ty wu9sp4xf)zvat 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one i l) pwv4tul9:y/z sx-fs 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 waveleng(p tmx.4leuzqbw jz.v:79j4f ths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 t4jwx.fl4u(qz.jvp 7m9 zbe:$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 sn/a2 jjs i)): v8drgbg7) ,se/oardyHz when at rest. What frequency do you detect if you move with a vbe as y n gr/ad8ri ogsdjj:,)s)2/7)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 firex)(dbxwkn t z/(r- ca* )y4csm+jf(ou engine whose siren emitby k) x(zf+*)us(njrcc(oaw4/t xd m-s at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movingwxu39mofi s 0)o)q6gg toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they wguf)g6 0somi9 x oq)3close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequenc p29y u tljvgb-3muua8c;,fs). elb:fy 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 frequency the horns emit? Assume T = 20 a9:-tc g, s b) 2ueu ufmb3.8yflvj;lp$^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recsqf25:4 nzxjgq.hzy1* wqlb ( eives them returned from axzjw q. 4hn 15fl2qq:bgsz(* yn object 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 a speed of 5 m/s As it flies, the bat 27zagsw -xucj)(ynjp(*+h p z;x :gfgemits an ultrasonic sound wa:z -g(gps(x)j*f;uhjwz2+ cn7p x aygve with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originalh81r1fr*ym xgn0, v9z.f sd6smi f ey( Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached th(8 r01yfeig xr,y6df*h z1fvnsm9m.s e station at a speed of 10 m/s ?   Hz

  A Doppler flow meter79 zhgsq0+h ww uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat freqz0q7+wsh w gh9uency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonicoamisnf yy.-be/t46 / 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:ongcrr .-hk( of frequency 570 Hz. When the wind velocity is 12 m/s from the north,go- ch :(nrrk. 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 f/28pobeka rya)te md cp, h:578bz-wits speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What isno lx.n z;5 h pw;0td,3ugw/ec the angle the shock wave makes with the direction of the airplane’s thg .uz0w5p;ld,/ ;3 xwnneoc 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 thbr7 i)vwath)qtu u, i1o27a5 ye thin atmosphere of a planet where the speed of sound is only about ot1avi2u5 wy tqru)7ha,i7) b35 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 ocean. Determi*42 f0ecaribf;y+yl qne the shock wave angle it produc 4yb0;yirf+*a ec ql2fes
(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 veeuu )2;. vmq$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead an* kuatjg 8go8oti0+ plj;4ro,d see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveledolj r joau*o;,g4t +tgk8p8 i0 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..( mi x6pwsgu q0clz* 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If wqxm.c sz u0(i.p*lg6 the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human ax2an kaw+*rf1 udible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sym +eemr2al:b; mphony. It consists of many plastic pipes of various lengths, which are open om r+:lab2;eme n 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 toe,p e+xfe.,n e the threshold of human hearing (0 dB). What will be the sound level exe,epefn, .+ of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 7mv)l ;kn ;uddwa i4nji4+0fo87-dB sound are heard simultaneousd 0nu;mw);v4 naj kod4ii+f7lly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB;t5z/k/ .r+ldp)ukja lheht 2. What is the acoustic power outpk/ahr 2j/dl t)5 te.u;khz+plut (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drop t k,cs(0r; .tv* 6jpko8fpjpps by 10cvt* frto6 jpkpp0pjk8( s; ,. dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typiu8aghq,w: o wj 1ae2/acally wear protective devices over their ears. Assume that the sounqaew2 hao a8/u1:wg,j d 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 engine?    W

  In audio and communications systems, the gai(lls 6lw0;*gyatqy3d f14 mran, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency :kvnc8 +9 ooy+vk ue9a1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed pointidp(0:op:pskz n sg(.s with a fundamental frequenci:nk odgz.sp: s 0(pp(y 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 vibration above a vee5 j:pv vzi wsw dh7:ka146k6wrtical 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 abov 45w:k16ivsezdwjp7k6 h w:va e the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thatlw(7 5kwns dh8(dj/ it is open at one end and also 75 cm long. How much tension should bedkwsl(87i dt n(/hj5w 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 w-iu(qxd*l;fg cvcg9v vj1a52as observed to 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 500–1000-Hz 9* 7yzejs9k v m9 /x(e*urizahrange 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 othzyj7*9s9k9zrem au * / hx(eiver. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stati.pve6e::c1wcjwu 6jbonary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of thecbjewpvj: 6 eu6c:1 .w moving train?   m/s

  The frequency of a steam train whistle as it ap z3 z :s kepu az5tqdr)-xc0b,dr)5ls45myq(z proaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train md c )4(ku- a0x5pq:5tr35rzszdyzb,) mslqz eoving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening t0+q7 zjt cnvt16 iewm2ss9;y to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a ce q7t02svmzi wy;c1 s+9tjte n6rtain 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, sodgbri o;u/)z4 unding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long)gui /d;bozr4 is the other?    m

Two loudspeakers are at opposite ends of a railroad car as iyig)4.20ejc c wk8kpsh 1dnw(t moves past a stationary observer at 10 m/s a42k yk p(hcs 0dic1w8jg.e) nws shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normallyug,:dng )vms24n: cgi about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dirng)cd: ns m 2vgig4u:,ected 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 ata4oxwc (cb7 4i speed 6.5 m/s while the moth is flying toward the bat at scxci47w(o ab4peed 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 off the moth?    kHz

  A bat emits a series of high fr) ybyry .)xm;sequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 myyrs.)b) y; xms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signee2zbq(md0z5 j gdyy eo h+*2.als 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 popuedegzh(5b zmd2qo+ ye0jy*2 . lar 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 byu 5zv;rke fl)aie6274fx7 *etquz5ez the presence of standing waves, 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, andff5veitl)z 6e kz;eue 2*rx5u7az q74 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 ak*k g/p sv+ /ks/9)oy yo(nfohh3j (j,r-frd j 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 can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-ls* fo(j/ny3ksgkh9(r+po o v-/) jyfdrj hk/,ong 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 fo/v5v19gqz w7 6 pljntm-qi o)zr the human ear at a frequency of about 1000 Hz is wj pvz z7qim-l19q6 t g)nov5/$I_0$ = $1 \times10^{12 } W / m^2$ 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 q7w)f v8 hs.zypyjdzpu2t (ur8 oy(31Mach 2.0. An observer on the ground hears the sonic boom .jtyvudyph1(zq8)7pzfsw 8ruo3 ( y 21.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboath y.)(z5eh:j29b a; ltb dququ 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