What is the evidence that sf.s+ixqa.d m-iygb*-,j9s xj0x)r yaound travels as a wave?

What is the evidence thbrn7iu 7)vq9tat sound is a form of energy?

Children sometimes play w9zz91t8ccs ar:hbae86 6qw hsith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sounda c69ch6 8:wrq1e h sbz98ztsa wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency ojzf)uu*3 w*n 2 d7tmgdr wavelength to chand37*mg2 tuz j)* fuwndge?

What evidence can you give that the speed of sound in air does not d1 d2dy4d -kd.4j1tmo by zskbrp6d c3;epend significan 4yt 11d m26.c;dbyok3dpd-rj dz4sbk tly on frequency?

The voice of a person who has inhaled helium sounds very highoss 79i5 1fo)eogs:in -pitched. Why?

How will the air temperature in a room affect the pitch of org z+nkd,i c h:zo,i3o.can pipes?

Explain how a tube might be used as a fiufk+gu0 s6p8qlter to reduce the amplitude of sounds in various frequency ranges. (An example is0gfq kups6u+ 8 a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together 6ze-;k qvsd nesdp8q,r;p9,kas you move up the f kzn;s; , 8 dqpq6-derp9,evskingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially j *j2hikh9yjc2n5, mjza0 5 1dqmtcj:you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more t2*jc: i9 q25az5nchyh dkmj 1jjjm0,of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “intem 7j0:i)ajsx+1rb b u/mwhiggd,3h2jrference in space,” whereas beats can be said to be due to “interferen,i rixh/ aj2gb7h3b 0:dmjg1 jsu+ mw)ce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points Dc ,7ocv pp7;q7xmrok- and C (where destructive and constructive interference occur) move farther apart or closer together? q7cok;pc-7m7o x,rv p

Traditional methods of protecting the hearing of people who work iiyf7x - h,zkfs; 8ig jbz:1wrh(l4s 7fn areas with very high noisewfilsx - gyh 8bzk,7:f jhs1 izf(;4r7 levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig2rm,1t vc r,2bwwuo+b. 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, (tw2+b1,b u2wr m cr,ova) 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 moian k.*:h/csame direction, with the sa a/*onm: .chikme velocity? Explain.

If a wind is blowing, will this alter the freque)ifw pg(+h9p u1+; fnifbu2 ibncy of the sound heard by a person at fpi;wb9f iuui(f1 bp2++)nhgrest 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 monitg ah .j2c5utv,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 fret. gu5vcj a,2hquency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of ac2nj,lu2s:smw 4cu4w lake 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. Estimatel42s2:c wjus wu,4n cm the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the rzsr5e9pjh9 m , 0pwty tl662wecho of the sound reflected from the ocean floor directplrwsrpztt 62 ,m6ej5yw9h90ly 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 wavelengthte;fmy 4, 7vp )lmxqm3s 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 drifti. qp2p)kb7h4x zy obs-ng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How7.ps4h-)oxkzb2 ybp q 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 66 8sg,1m* q(tjgym ot)j /sj- zw ose*1pipglsplash it makes when striking the wa zlmjqmopswtp186/,jj-*ysgsg*16)t i g(eo ter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cj mgp32uj,ijeo77iy5n i 9/hp0bw4 jroncrete 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 4ijrj0e9ijpb2,75o /g3iwnm u yp jh7 Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made oa/q.. lz* jk9 esy7b(k3ermy uver one mile of distance by the “5-second rule” for estima m kr*y.e(sj3a7y9e/zqu kl.b ting the 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 thw7 a u6l8eughc (ku:g.f /r(ese pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a so d7 rb;t;7 s1za ph1jw:b.n fwzl9q,kfund whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers przc evj46c*n gy*th+.w5dkq fuze 8,5r oduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,g rh .+vzzdc*,jcw8e5k uy n*45qf et6 not dB’s.]    dB

  A person standing a certain4o4 jpa.e 12fzdxs:lk distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 l1 kxj.zps4e4oad: 2fdB. 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 b aof t5i,mk9058 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 m,k9of 05 aitbdB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outp9 ;pd kcjqke1a;hl:b/ ut of sound from a person speaking in normal conversation. Use Table 191ekhpcj ad: l/q;;bk 2–2. Assume 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 q.2yccver)2nmo -pd1 el8 e.7bx0bu i 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 2)u qc6*( 5zypz pphdym;uj c *6kh6un350 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 fropqu pyzzyc6u* jh3h u )6c d*5;6(kmnpm 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 regi(hcce3qbn1c: stered 130 dB when placed 2.8 m in front of a l: en1hb3cccq (oudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically kkq 0i0 *tdig*2uxz d*detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds wqx iz*tdug i2 0k*0*dkhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor w:lcbiai /y(xo6 /axp3 ill the intensity increase? Increase by a factor of i:pl3 cb i(oa6a/xy x/   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hasr-xe9k,.dfnjc mm60(u 3lxuy twice the frequency of the other.jkx n- fer(,0l uxmc9m36d.u y What is the ratio of their intensities?   

  What would be the sound lr 2ftarmwj6:ei 19mn9evel (in dB) of a sound wave in air that corresponds to a displamn1a t :fm jew9rir692cement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have s+r6m:rze6t *ws *uvl what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6 srs em+ lzt*vw:r6u*6.)    dB

What are the lowest and highest fkv-b-3y9m i -kgi3pgvhkh x-*(aq :u8z fp)d lrequencies that an ear can detect when the sound level is 30 dB?v-vg-apkhd ) 9kxh-y83fl( * q -uikim3zbgp : (See Fig. 12–6.)

  Your auditory system v1y u,h iup4+tu).ekqcan accommodate a huge range of sound levels. What is the ratio of highest p+h4 u) .euqk,yivtu 1to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The len7 m7)pkhx8/.pxr k gdxgth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string b)p8px77k xmk.xhdgr / e placed?    N

  An organ pipe is 112 cm1 x:uo+mwrv10 q grln: long. What are the fundamental and first three audible overtones if the vwngq r0 our:xm:l+11 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 expec/4x 7aadv ycdvx/)nb 8k9 o/htt from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubeaxd/acbv v4y/ t89n/ hxk)7od ?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range wf8i,s cvxry6;l9:kxwv il1 , of human hearing (20 Hz to 20 kHz), what would be the range of the length,ixyv89,1ls; :flkr wic v6wxs 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. What willfg)s j+.qgfum -g*f;oe,vn/o di+j 9x be its fundamental frequency if it is fingered at a jg+/9e*d gof is,ujfvfm ngq)x-+o ;.length of only 60% of its original length?   Hz

  An unfingered guitar string +rx6hw2 yj0mb6xs5xe zw/k 6b is 0.73 m long and is tuned to play E above middle C (3j 6xbr26+x0wwkx 5 6emsbh/yz 30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C 0q d*pebe6uw8 (262 Hz) when the 608euebp qwd*temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 202jzoyxp8 igj.7rl5 873 pnvsf $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of r(ihg1 wd,z/uw,n :mcdewj1:the flute in Example 12–10 should the hole be that must be uncov:(jwhe z/ug n1 ,dwc,1i dwrm:ered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at au*me (dkx ujo4qe )x(7ny other frequencies in between. (a) Show why this is an open odu( mu)4x* j xk7ee(qor a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tubtpe) w+0c,3o8.pjt a l4ssxn ge 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 ,+xj)e3w 0 lp.tc8an t4osg spHz. 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 1r.oe4lb ut(n $^{\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 withs61hv8d a91h.y vl ayp,vbrl8 in the audible range for a 2.14-m-long organ pipe at lyb9h.r hl 8, yvav6 18v1adps20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximat pmqrl j)en3d8*j ,rb5ely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationrj58m,*dpj l) 3ebrnqship 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 eveb)*oys c* s8hu-1rbqxry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequenc1b* syqxu-8r s*) hbcoy is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) r31+h vivedv g0.1dtvand $C^＃$ (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)xco:a7cnfa . operates at 23.5 kHz, while 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, en a:7.fxoc)castimate the operating frequency of brand X.    kHz

  A guitar string produces 4 berwf3iqkp+nj:l lh3usrak9* 1 /hxs3 3 ats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hzrkl/r1iuk*xj9 3l h3 a3hs+ wn:q3 pfs tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hpdji1cl, 9nx *z. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the d9npj,*1 x icltwo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard t lyhnehq g.92g.us z68)w3q lamb/g9if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C a9g/hqh8 ysl3getgq6 .m ln2b.z a)wu9nd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencydzvii;6 p nlq m+e+3bbx9rd(5 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 frequencies of A and C? What beat frequencies are possible when A and nb pi6dbe + d+qv rl5(i;39xzmC are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m4 t,7s. svtuub2c izy+ from one speaker and 3.50 m from the ou4y sbt. vz2 sui7+,ctther.
(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 arew+-1hu l4sld q supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one+wllu dq 1s4-h is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in ai;ocn*-*uf ppp emr3zt m 5+pe.r. How many beats per second wi. npzepcp *umrfm-p;eto*5+3ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firem z /.j97pvied; ylrl: engine’s siren is 1550 Hz when at rest. What frequency do you detect if yl vd:;eijl9r7 / .zmpyou 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 h rn*d u+-twtv(:;b iwdo you detect if a fire engine whose siren emits at 1550 Hz moves b (+n:hv tw wuidr-*;tat a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freq(.fa-p a ob4ww3co-ux b /z+gvuency if a 2000-Hz source is moving toward you at 15 m/s versus you moving towardpu(fgov.aa+-bo4zw / cx 3- bw it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. hfimr ;/8zjb8ah9ye3When 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? As;hra8/em hb8 f9 iy3zjsume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ulot mmr0:8j ig*trasonic sound waves at 50.0 kHz and receives them returned from an object moving dire* m 0g:m8rojtictly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speedqt t *+cf-cpk/3j 5fgn of 5 m/s As it flies, the bat emits an ultrasonic sound wave with fre/ng3fp5+ tt-fq cjk *cquency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving*e,)i :kmy(v tg9b iuqkzd9;a-9 sqe* hpwc6w flat train car at a frequencys,p(kezc;w 9wua *ki-*m9t9 qgvb)ie q :hdy6 of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spwk+ a yq.-wd*keeds. Suppose the device emits sound at 3.5 MHz, and the speed +-aqwyw* dk k.of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr3 t5y(p c(v,6e* xpbuiyo/5 xt6gvtxmequency $2.25 \times10^{ 6}$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 fre0+il xb;0g rhqzq3f0bquency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, atr+0lqb30 0gi b xf;zqh rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spe 18weka;8 8bq6 nnwvjeed 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) What4 d c0:h0,gm outrf;rc is the angle the shock wave makes with the direction of the airplanec4r0f,huo0r;:dm gtc ’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of szwuc;6ijbh14c1 e1si y1 ds. ejkny),ound is only .by;ywcjhziun1k) 1e6di, c1 4 1ssjeabout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500es g n qvlf(leiw50+-/8hxj*b m/s strikes the ocean. Determine the shock wave anglel i5en /8vh+f -(sx0jqlgw*be it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle )f-rpgwg3(+pqrm 0d i $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead an x(uo,rr6u uj,+qd z 8j.ukyku :ql2b2d 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 traveled a horizontall zk:odu u82,r (uq2 byx,qu+j.r 6kuj 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 thaut:gip.ea ype 066a p*t sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in:p6 ya0 ieg*a.ptep6 u fresh water)?    s

  Approximately how many octaves aar+6.h47xl zu,:y1qa qc prkt re there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cals gv3 dr2d,)doled a sewer pipe symphony. It consists of many plastic pipes of var3drg2v s) d,odious 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 fpp+cf )b)hu x9r:t l:srom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of bppfcu9:)hx+:s) rtl 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are m; v94a31xwqqoz5fvhq 6 b j uz0rj2:cheard simultaneo6hj4 ;:uafrcvoz jvq0q 9w b5m1zqx3 2usly?    dB

  The sound level 12.0 m from a loudspeaker,dnq;mi g2m17 t tro+(a placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assumin(1nm;tm7ga o ir+td2 qg it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hi i:am3 kl*+col2a-ch z. The power output drops by 10 dB at 15 kHc+hk 3ia*2ol l:c m-aiz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typ1 ape16lhj fn,ically wear protective devices over their ears. Assume that thl1j1p ,e6hn fae sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,mrub*k(l*uh * 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 frequenclyk,e oics sjs4 4( d/1ih)d:uy 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 le sy1x1*qae j7t1, guqwt )g3e jiy6n+ong between fixed points with a fundamental frequency of 4 uqjx1w,yn7yqat *13i)g s g+6jet1ee40 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 in(zse;e wmuu-2-pr11 e-vye p wto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to p epwy;e(z ver-1um2eu w-s-1 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 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 teszg/5 up)u 1a tube that is open at one end and also 75 cm long. How much te5su g)zte/u1p nsion should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop:- d9ixj:gj,hhiup-br*w n(l ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming fro qfpkoe94hx0h6o s1a 2dv4h h-m 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 thh okfx61eh 44h0o p s9d2q-have other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condb97te2ne n 9wmuctor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. wm e7ebnnt992 What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it a;b8 zjneewt h3/)vu ;re1 .cbspproaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was 8be)s; j.trw/ ;1nv3uczebhe the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenin; 5zmtkht,pkqtrj3) 0l/y.big to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain/ kz)tit;3 p.,bht0k5lrqym j car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency u),0/pvosfmlvrs 3:mof 11 Hz. The shorter one is 2.40 m long. How long is thepsf :vmls3,/vomr ) u0 other?    m

Two loudspeakers are at opposite ends of a railroad car as it hf .n dfga2y4( 4e:kuxyr*nxuwe).0c moves past a stationary observer at 10 m/s as 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,r4e:.fy *kanxxuc4(u nfyw .2e d)gh0 and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in thm*y vt),6kzqyk3zyf7k-3 d1- u( kop vah 1mqwe 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 1pzazyq3v *kw m)do17 yk,v- qh3 ukf-kmty (6reflected 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 aw*t/fxj9uw h-t speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. jhw9 wu* ft-/xWhat 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 frequency sbiss09nl)k 9 tound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one s9bisntk9) l0chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1/dno- w 8fhtum:i)r d32–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are oh : fdmd38ir/-w)u ntless 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 ebq,03dcmq u 2-q0of yby the presence of standing waves, whicuqd q0cy- ,03qb omf2eh can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “sy/ l 8-g awd:n0/hxxiyinging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, l/ ai:l0w8gxdnh/ -yy xoud, 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 thresh3 9ftqdk q mwkfu.v44kg/a+9fold of hearing for the human ear at a frequency of about 1004a 4 3gqkq9w um+fdtk9.fv/ fk0 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the grounddh qbeg) ctcbb j36l* ,pz*x9) hears the sonic boom 1.5 min after the plane passes diredbb h)l6tbe9 ,qc)*3g *cjz xpctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 z o.a gk2 whxqoq rz2o:z-*b4*$^{\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