What is the evidence that sound tradhpk jg*(*1lf vels as a wave?

What is the evidence that sound is a form ox1o: jacwl9hm*,k gz0f energy?

Children sometimes play with a homemade “telephone” by r bg,0 1vj1etxy3b)e7n zcie- 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 (Fij-berbee3ytxci z,g10 v n17)g. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wavsmilhh11 w 6wxwgt/6zy :7iu9elength to c :xw1t6iiw1u7m/gyz69h lh swhange?

What evidence can you give that the speed of sountz5vec;1m9 q* 2doiz5ias wr* d1:kzhd in air does not depend significantly on frequ2 vd:1izsih9 z oc;t1 dz kqa*e*5wr5mency?

The voice of a person who has iewf- (e/cqv*p 2 4xikp 6by1ztnhaled helium sounds very high-pitched. Why?

How will the air tempe 22pxaor- p /;:ocjtvlv25psmrature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to r:4ff**qu9.oof)a rm dj 3lvb jeduce the amplitude of sounds in various frequency ranges. (Ao dr: * f93u f4jm.loq*ajb)fvn example is a car muffler.)

Why are the frets on a guit- uwb nlew2q6qg)axnq/:d9: dx sw2*ik4u8ni ar (Fig. 12–30) spaced closer together as you move up the fiw 2bl/k 9e*:)nnag2-isqiwdd un:x84 qwu6qx ngerboard toward the bridge?

A noisy truck approaches you from behind a buildzdm,exkv8w4ckt ,05y ecz+u)ing. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” —mvdez ,ku 8c+zy kew,xt 0)54c 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,” whereas b( q dp)wav2:uble 56qvyys /crg:ae*1eats can be said to be dsb1ac v) :apry6 (5g yvl:w/qeu2*d eque to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would t7ppv5j:-oz qehe points D and C (where destructive and constrpvp jz7-e :5oquctive interference occur) move farther apart or closer together?

Traditional methods of protecting the heariwhzpr q;saax 0c3lt3 :3zzt;/ng 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 technol q;axl h3 swzc/r;pta3z3:0tzogy, 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.9(eulxmxi4i0 12–31. Each wave can be thought of as a superposition of two sound waves with slightly difxueixm( i40 l9ferent 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 oaxr 4 3pj8:8rzkfz t-k/nsj5 the same direction, with the same velocity? Explai tar3oxnkrzzj k fj5p:/8s -84n.

If a wind is blowing, will this alter the frequency of the sound heatcm2z,4 /uuge rd by a person at rest with respec meg2 t4/z,uuct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monits-6lgw8x( .t /f(g 2bh /rxlprate2ji or 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 whistx/tbf/rp-hlejwx i g(g.ta(2 8 l6sr 2le? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her c9 o w+mir(owtp7ar *4shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of ther(+9 w 7oma4 tocpi*rw lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belo8rcb 9 q2hw1zgw 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) and does notc9 wbr21gqz8h vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airbmdeil 81dq y7oy xs7 56e l8455rbdir 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 schwp9+(*kh kp w/ zdii7jool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard *wp9dp/ hi+7jkzk w(i (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frg-8jug1f dal ;h,qzk0om the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the c;0kju l1d,-qa fh8z ggliff?    m

  A person, with his ear to the ground, sees a huge stone std3h.dg5rp93tup6r bec; i c q7rike 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 q dtdcr purg.p c3e i5b;37h69the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mitbhs 3 oq,0/i 4fxr ay/w oylft61r7z-le of distance by the “5-second rule” for estimating the distance from a lightning striki6 rqlx,thw-bfoaz7/yr3 f0y4 t1/o se if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a :g 0aqvxgk -7j(m ; a9ov )9rs7nkicuvsound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound lev/d pthdp:qve+cfj:4 ,fo f3fk3:wht 9el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prodn6xfngtudyjx bkm h7-x z2*m1;0ht:/uce a sound level of 95 dB when fired simultaneously at a certain place, what will be the x nk;hgntx md0f/x hb:t 6*m712ujyz-sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance froaqzq h2s3l96 km an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Wqq9 326ka lszhhat 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-n67pnx vmw*ffr9pj6 *koise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intenm*9p 6 kfrwp6vf7 nj*xsities 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 .pn.amvb .*yqbbiw)v umj-q- 3h2, s hnormal conversation. Use Table 12–2. Assub hby s.2-3viw ,b.*.nqqmjp-a hvmu) me the 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 strikes an eardruvj 5er)7khn,-* ywaq fm 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 9 x cm 1a.in6+n*hltsjq51iin xg0cy, rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would e5gqlsn 1icnihjyaxcm06+ i,t9 n x *1.xpect 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 dB meter registered 130 dB when placed 2.8 m in front of adf n75/3zozk53qp21 g . 0un epgvoicm loudspeaker on the stage. ci3n5fe qp523u7 1gzo.0/mond pvk gz
(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 typiiry5:zzw;k 7j mla 2sd399vdmcally detect a difference in sound level of 2.0 dB. What is the ratio ofamz d59dlr29k; jw:mi73zsvy the amplitudes of 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 factor will the/zh:q 4w;yzgbqc+v-w intensity increase? Increase by a factor ofc+ /gqz-vwwz:yb4q;h    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal nej2.f 7 b-4g+ t 4io+c)8s ualt0eoitffoex* displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their nalxue f2+et gf +ico)fbot-j.*e470 to4i8s intensities?   

  What would be the sound level (in dB) of a sound wab 2a8zue40zp. sd u1g:p*di5whwe+ tjve in air that corresponds to a displacement amplitude si8pe hwbd+2 :u4je wgp1*0.d5ut zaz of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see:wwoim ( .wjhwqya/9 1f)x:c 3(sog pym as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12– p:mqjw:afcwyyi(o/3w) s x(1 howg.96.)    dB

What are the lowest and highest frequencies that an vbn*4/qpa9xu h- tw8h ear can detect when the sound level is 30 dB? (See Fig.ta/u4 h* bhwpx9-q vn8 12–6.)

  Your auditory system can9p4;:mn w yd mf(b+thoni9xt5 accommodate a huge range of sound levels. What is the ratio of highest to lowest intensi w4niom5t+b;t( 9xyp9:mdnh fty at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a vigef. * z . *4njohzo;b0ufx4vpolin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32unfp4;* 40j z zov.hfbx* e.go cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm log5,tw)b0mn ;/ crdzikv g)fx.4e )5zfurw*xz ng. What are the fundamental and first three audible ove0 zrtg k5ve5x u,ifwx.z/cbz) m )rfd)n;*w4grtones 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 youj2 jm)c se 1owh+f ,qqp/ kfs34f7/dxk expect from blowing across the top of an empty soda bottle that ieqp f3 js+ 7,jqh2ks1oc4fxdk )wf//ms 18 cm deep, if you assumed 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 th 29k 4cqbrtwlui93mn3 e range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes r9ci rlk3nq49m2bw 3utequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar stringlf h0shtj(df ;-: rt:k2g0r7zk+,s cfmsw h4v has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lenf zs,h;f mtjd+hcs0:gsh tf4wk2-l7(r vr 0 :kgth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above midd if0jwh0wx dcj)1-fs : 5nya6nle C (3fnx0 wacs016h5n j:jy i-d)wf30 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 C30z v0r)vzzmfee 68h f (262 Hz) when the temperature is 21 3z6fezz0 vhrve)0 f8m$^{\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:fjgy (7w yp) f )7rp:gpb/fdn $^{\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 b4ag6m: msb*q de that must be uncovered to play D above middle C ad :a4g6sm*mbqt 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 nopoyi.e6 3q( qh((tluyt at any other frequencies ine3 yq piho6q(lu(t (.y between. (a) Show why 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 at both ends. It resona2zlvstmx0b89 2 w9mtx nt )/n8sdek;q tes at two successive harmonicmqsd tte2892wt x9bsn;)/lvnkxmz 80 s of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 l,88 hgga- 6qrwwepb t2j0u .d$^{\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 presen(jk7 bw8k yj,nk3;ka wt within the audible range for a 2.14-m-long organ pipe at 2kn 8ybj3k;ww, (k 7ajk0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appr( bkxeo ,j76eroximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What iob6r jk7(xe e,s 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 on0dafvs68/+u 4winbl ywx/m 3rxt4jc; e beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in f4tw48v cb fj lyxd uarx+/6wm/03s ;nirequency is the other string? ±    Hz

  What is the beat frequenc; lijrfvl xy m l/))pt.y3(t(uv;a:acy 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) o)ifwlmb z- ,kd- g squxum(05.perates at an unknown frequency. d5- uklwg)u.-(mf ms0xq, bziIf 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 souns+le v7 )0u.fckxo2eg ded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency o.0elu7)csv ex fk+og2f the string? Explain your reasoning.    Hz

  Two violin strings are tun 6jy)0jq;gin jed to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when tjin ;)6gq 0jyjhe two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard i8 4yopaugiw7m olz+ ; u4;jsp+f two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C a;p+sg l wpz4oioj 8a7;u+ 4uymnd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,cdjin dcu480 qc(ws ;7 A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible n7cudc8jw40qs ( ; icdfrequencies 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 perso zxso4 )awnr+i0s 6k7sn stands 3.00 m from one speaker and 3.50 m from thr6a)wkn7o4s s + x0izse 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 pianopfe 4x5g/ xbhbe/ (5 fs y49v+hzttc.a tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132/hg+. 59 pfxhf( bcvya/4es54xb tz et Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How m/c r7dof 8)a2l qxu .xadod45gany beats per second will be heard? (Assume T = 27)do5qr.du8 o4a /xl f2gdxac 0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren i hdr,rc;o s)cm/q6yx+ s 1550 Hz when at rest. What frequenc/);qd shc+m,x c6yrro y do 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 frequency do you detect if a w4 ylhlvfu--c ;n73je fire engine whose sirenf -3n4 ;e7ly j-vwhulc emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifmg +a 6x w)yfmn)od1xyd8 kr-)t in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Area1d x8))xr -dfo kg+)yn6mmy w 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 same single frequency hor8(tkd0ha cq e2n. 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 tk0d8 (2ec tqhahe frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends q1ki +5yyi b95fq /qgsout ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly awa5q/y 15+kbqy9 f giqsiy 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 ba-hqhcu4 ( c7 e1.baqqdt emits an ultrasonic sound wave with frequency 30.0 kHz. What fe aquq d.h c4hc(b1q7-requency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playewhlq 1n .kl:6zd 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 6l.l: wnzhq1k 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 speeds. Sux3ww(xm/p*tf k x*.xg ppose the device emits sound at 3.5 MHz, and the speed of sound in human xg3x .twxfwx(*/kpm *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 fp7 k xkb5htj/g qkg,;h91ztd9requency $2.25 \times10^{ 6}$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 (l7:+i6a xwi s nku9vtwind velocity is 12 m/s from the north, what frequency will observers hear +l7ax(iswk9ituv n6: 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 1)6*y6zre l kait:zwd 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 o**d zv*6dhj pif sound is 310 m/s (a) What is the angle the shock wave makes with the direction ofd *pidvj6**zh the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wh0z,zik,6 gl;ulno / zdere the speed of sound is onz ;6/ n0kzogduzl i,,lly 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 travelingnjrp : 4)yexp:.xhl v-)if jw7 8500 m/s strikes the ocean. Determine the shock wave angle it produ-w7)ij :exjp):n.4p f xvl yrhces
(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 ,.evkwx syi)9$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a qm8q5argc4 gl ,6-97acbnn* g )nfaklplane 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 traveled a horizontal distance of 2.0 km. See Fig. 12–34.m98 qnrn64alka7g ,g*c- lf)n5 abcgq Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz soufg)i2:r l(nrm5iyuv 2nd pulses downward from the bottom of the boat, and 2 ril( 52mi)fgruv :nythen detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible gf,zz/vkyd +7q*b ac/range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal-ecrqnep. xu3* :5qwuled a sewer pipe symphony. It consists of manywxq 5 .un*r3ee-pcqu: plastic pipes of various lengths, 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 makessgg d(hggczq( 7;1 bsl/zb4y / a sound close to the threshold of human hes (q7;( ggldcbgyz h/s4/zgb1aring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant pvdiu5p6tb2l f c3vk8q6yg. :sound level when an 82-dB sound and an 87-dB sound are heard simul py q8:5gd6pf6u32vk lvt.bictaneously?    dB

  The sound level 12.0 my,))ub zr7fd n from a loudspeaker, placed in the open, is 105 dB. What is thrf7,) y)nzub de acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power o.d;kn20hf xi9aldd t 9utput drops by 10 dB at 15 kHz. Wh9 ;kd0adi xdh.2ftn9lat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectim4cxl bs 04lotl9w;v4ve devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotect4om b;lc l409wvs lt4xed ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,6j vbxo5v)i i aa6wx:a2i-n0r6 3oaxh 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 qspif6j c)0+ 1aewl) -gwj c(wtuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed poiny*jd i3qkc) +rts with a fundamental frequency of 440 Hkdqi+jc y)*r 3z 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 vibuhmhem ,v;13f ration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the wat,u3mvmh 1fe;h er 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 nea10pwcubkj u6 k9y02 gqr a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (0p kcu9g2yb j06w1uqk in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop l 3:-rxxf3, ujeenh a08jr (jg($\frac{1}{2}\lambda$) 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 tone2dcs ovq(y ;qilk /aatqf(*25 in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is tadi;/cq5t2 qay*( vk 2sl ofq(he frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on tf q abzxmq65n76fc6; nhe stationary train hears a 3.0-Hz beat frequency when the f 76qxnn5fbcq; zm66a other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afted: gvr*n.h6;p-h j 87rsuu jdag id11ur it passes you, its frequency 7p.gh;r:d1-iuu 8h njd6jdg1u savr *is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to 6g-dhxpu iuzb dh4/ j4/9m0l gthe 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 straightaway. How fast is it gmudz6l/dg0 4g/-huxh4 i9bj p oing?    m/s

  Two open organ pipes, sounding g*nhy1;dn lt5x,/zyx:stqk8 yw.ii 7together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Howyi .yyt 7x5t1dk8l;wi*z gh :, qn/xsn long is the other?    m

Two loudspeakers are at opposite ends of a rairfx8s2 rr l( rckigg4 1h*ec.5lroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have ir*glr5gh.k 1c4i(f err c28s xdentical 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 thevr9xp:7e kta ; aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Asa rpvx7; kt9:esume 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/0p4rdwv-exi:2kc +tlsw 1z* us 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 detec ikw1:r+xw0 p u*4sc- zevl2tdted by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencrluo;gp;v:*g *hr lk-ew3d: wy sound pulses as it approaches a moth. The pulses are approximately 70.0 msr; *h *rgl e:wod3k:g -puw;vl apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signh ignjt-t6s3.als from one Alpine villa6j.nitht 3 g-sge 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 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 presenc :f0e1mon nks1tw ()ate 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, and 2.8 m high. Calculate the fundamental frequencies for the standing wavet saen(no fm1w1 0:k)ts in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lon,ft/yqkq vwd:yxop (:enr8/z 5 , owp3g, slender aluminum rofy,qo v53o ,:( k/x pdnww/8 qzpt:yred 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-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequen/l.+0t11fejm vriv tm cy of about 1000 Hz 1.1t/tel v vrm+i mf0jis $I_0$ = $1 \times10^{12 } W / m^2$ 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 hears the sj*qsr8qgj6d ngc/ n6e2o3f- konic boom 1.5 min after the plane passes directly overhead. What is the plane’s alti/3 ek6j* gg8cf2djro-nnsq6 qtude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15v nvrg2 f;oddqq6 ezdyrcp 38+x d79:) $^{\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