What is the evidence that skv2 c ,ju u8swq8p0lg7ound travels as a wave?

What is the evidence that sound is a form of energy?2o0fnv7 id/9vuzne+k 4o/ j:ilje g+g

Children sometimes play with a homemozdz* 9)qup( ,xzwr+-p brk q*ade “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 sound wave travels from one cup(q*pwox)q*z+- ,zz ru9rbkd p to the other.

When a sound wave passes from air into water, do n 6h(5tnytx8a ohrbnu(rp;77 you expect the frequency or wavelength to cxnn; 876nt ah(b7t 5 urh(pryohange?

What evidence can you give that the speed 9ggwa6r dp0s)of sound in air does not depend significantsa9d)wgp 06 grly on frequency?

The voice of a person who has inh3 i2dh1bn xb (9gkt w:(vra3bjwd 3m5zaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect theubk:1)dg8v i wby. cs, pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude oztmr08.nj g 0of sounds in various 0no08mg z.tjrfrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togey uf :7n6ucb3ht/hnh9 ther as you move up th tn3h h9uych6: n7ubf/e fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but cp s))l u82lw dhj 4vshojxg7o)*t)zj 5annot see it. When it emerg))sldg*2ox) opl) v5jt7u4zw hhjj8ses and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfe4mgwjo; 4sl)n( d8 forrence in space,” whereas beats can be said to be due to “interference in)wld;8 f(jn rgs 44oom time.” Explain.

In Fig. 12–16, if the frequency of the speakers were q2im zc;1ql654 /od-qqgk 1z+mibtw h lowered, would the points D and C (where destructive and construct4/5qz +i; mqtgc1hbkwq16lom2 idz- qive interference occur) move farther apart or closer together?

Traditional methods of protecting the q82ccq.boc8*huoy 2q hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambienu q.ccoc2b8q* y8ho2 qt 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. 12–3hjeatz-hi3xw t:6h *;1. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) iett*h:zh ;hja6- x3 wor (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 direction,.y88ld; rrv0em6 wjg y with the same red6l 0.j g8 mvyy;8wrvelocity? Explain.

If a wind is blowing, will this alterx x)kk;v vp3t, the frequency of the sound heard by a person at rest with respect to the source? Is the k3v;, x)kxvptwavelength or velocity changed?

Figure 12–32 shows various posit/ m/t+ evrgxo-ions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the /re+t-/x mogvwhistle? Explain your reasoning.

  A hiker determines the f(,hlwtj dhgpch.6 2 1b.1bmtlength of a 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. Esti 1.tgtdh1w,b6lj2 c. hpm(fbhmate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlijolr6v udd72oh7-9x)ju d ns6 ne. He hears the echo of the sound reflected from the ocean floor duljv h) -oddu6n7srx9djo267irectly 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 wavelengths in;6rzz 4/cp +v k*ejiobgpa6c4 air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on ang-vr1zrwl( d(6 k qb0 w1;bfp 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 ikb1wq rn1-z;g( 6 0f plwdrvb(s heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when 8x 36w4qzfdb qstriking the water below is heard 3.5 s later. How high i fx683q d4bqwzs the cliff?    m

  A person, with his ear to the grr -7e1:dd)nggi a/pzf0 h9z juound, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impacie1 u9d:gn7 h0dg )jazfrz/-pt: 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 Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent e (n;ud-3 8oj v-blg3,n, wfrqbe.utlnrror made over one mile of distance by the “5-second rule” for estimating the distance fro. r ln,,tjl;83 bn( b-nugqd-fwev3o um a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sour k10lq:5lrpq , + 7rd*molhdznd 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 leve)3/q: veze exrl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneo bjpnl)++v1 f7km1:i1 (l lahd nv6-eaicx3hxusly at a certain place, what will be the soum1xhc 1 na7jpl+b:d 6-le3+a(h)kil1ix vf nvnd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equaah4jw *bs9:2 mgx1(h g8o+n nv ucti7vlly 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 intensities, not dug2s+1 hj*bat4 7: wxcmighnvvon(98 B’s.]    dB

  A cassette player is said to have a signal-to-noise skbf1b dr1,bwh l+ys+1fk5;jak. ip *ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio k a bsrjk+1*,if;+fk bsh1w1p5 dyl.b 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 normal co:d v-,1oij2(pcx ec 1.emtja,l tw0 qrnversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouthwev1etmj iox0 c1, 2qarpj,dl-. t:(c . $\approx$    $ \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 eardri ckn9g 3ahxo8j22+ slum 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 t- 9 - lxv.tevg,bv*pqis rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conne, pvblqt9v vteg.- -*xcted 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 fzwjxii: 8dc518r m3vstered 130 dB when placed 2.8 m in front of a loudspeaker on tm1 5 fc83:drwx8viiz jhe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whixy/yry hx7 /2at is the //yxyy2xih7r ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of aj/v r3(iai bn o(xv,+z sound wave is tripled, (a) by what factor will the intensity incri rvj xv3a(oniz,(+b /ease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tc,e3fwsf- 5mh c1 dn*rhe frequency of tf-dnw*fr c5 ech3m1,she other. What is the ratio of their intensities?   

  What would be the sound fdkggiw) c 00hnz*d3 ,level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating aiingfd3)dh wck,0* g 0zr molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have)sx1 lgh(bd7 e what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) l7bhs)dx ge1 (   dB

What are the lowest and highest frequencies that at 20r,suaoc7)n;tjw y+. f5 fsskl3zjn ear can detect when the sound level is 30o7j;k2t0z. tl j,s+r nss )3u5fwcfay dB? (See Fig. 12–6.)

  Your auditory system cbw.5- jw8brtgi z8g8han accommodate a huge range of sound levels. What is the ratio of highest to lhtw8iggj8wbb r.z 85 -owest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length -q+ 29lcgkrl mof the vibrating portion is 32 cm, and it has mkll9 q+cr 2-ga mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firsc1 qur 0x-cvwyuq9) (st three audible overtones if the pipe isuqyr-c1)u0c(sq wx v9
(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 freq9i-1dla8k xe67dn b usuency would you expect from blowing across the top of an empty soda bottle d dau69sb 7-n 8ek1xilthat is 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 4+5f/):ntxcisz62jzcsq a3pv gt 8do a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be:z) xo8s i/fzapdq43jvtn6c25sg +t c the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has 4qofpe8,sswfe b407 z a frequency of 540 Hz as its third harmonic. What will be its fundamental ff4 4z80,esesb 7oqwf prequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mid s22h7nbci vl6dle C insl 72c 26bvh(330 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;p *y2*fipck a.xbd +s an open organ pipe that emits middle C (262 Hz) when the t* i afkpdp.s;cb+*2xy emperature 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 20r- o gest/ biw7qnh24;ncm6l2 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouth:*r*o52er s fbm hp5otpiece of the flute in Example 12–10 should the hole be that must be uncovered to pot*p : 5mfresb*2r5holay 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 resonatfzj59a9 lnc+y e at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or 9l9njfc5z+y aa 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 rfe8d,(zf c -gxc7. o, 1dvkt0bivhh-oesonates at two successive harmonhfdtc0vb vi7-, fhkz.doo,cg -e8x( 1 ics 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 xg4y7k d+2p vw$^{\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 witds ;cz vq v-uo1exk4,:hin the audible range for a 2.14-m-long organ pipe 1v,c x-sdzqeko;u4 v: at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It isxhnsd2s s3/a1 open to the outside and is closed at the other end by the eardrum. Estimate thenh /1xs2ds a3s frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tw33gzvo 3b8-bb/wmfoj) rrh )c+ fs8ado strings, one oo/ bf+8)f3r)ga8h cr w zmob3j vsbd3-f which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if.3-/r/rt,o ,exg k iw 6vqzqtl 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 whistlm,6-+epz gorr e operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separ6e- +gr,mpo rzately, 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 tunin51aqzp pdiape4u; *-i g fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your rp51idia eqa4p *p ;u-zeasoning.    Hz

  Two violin strings apojk j:2fo6:e -*ifh5d:gz yu re tuned to the same frequency, 294 Hz. The tension in one string is : 6ou:* f2:fkyoi -jh5gjpezdthen decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identi,xv d(og w1(umcal flutes each try to play middle C (262 Hz), but one is atgw( mxvu,o( d1 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency 9fz8jhg xy2 :zp/a3tu 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 whejf2phz9xtz :a/8 3gy un A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person se7fu sak3dn 8g*jnl(m) usj7+tands 3.00 m from one speaker and 3.50 m from the othekuudf83nel)nm j7g+7sja( s* r.
(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 supp(zm enx-ibg dbt h6 o(89 .m2sw,9efpbosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when thm n-fetd(2mbb i6pzg x o. ws99e8b,h(ey are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many 0)n e 1wl*s8p1elvp bwbeats per second will be heard? (Ass1np le)8wwbl v1p0 e*sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firegm5 h222uv t*f8erbgj engine’s siren is 1550 Hz when at rest. What frequency do y52rb8h2* jt feg2 ugvmou 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 fire engif1 cvp09k ctze4az/2a k r3+cgne whose siren emits at 1550 Hz moves atcav3czc a2/0 4+e9fr1kt zpg k a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-uj8)(bhtr db q50kdz-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencidb)rjhu-ztbk5(d8q 0es 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 equippe:6(6 sbwoerfol7u 0jhv( ,n aqd with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 mbw q a(,j(f evoh6:u0l7ns6o r/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonpe8gf btep(f j5e x/9*ic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is t5p(/f t g9exfj*8b peehe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 mu fk g,pb8m-5wb9vb4 e/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fre,uf 98egv4b - k5wpbmbquency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba waszy ro2:k qn,(s/.hx gw played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at reknw. q :2gyzosrh /x,(st 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 w/l: r 9 ro4k*moq ugaf7/vd7teaves 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 frequency if blood is feq 9*dvk/ rola ug7: f74t/rmolowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequeu8o3(j/fu:lf+ bb ql3f nwl.pncy $2.25 \times10^{ 6}$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)v0m);tmx r0 uyp 9rdi*bw/y a wind velocity is 12 m/s from the north, what frequency will observers hear who wvt;mu)yy 0ami/p*r)9 0xdbr 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 its speedta4a 6 4 ;wfuny/q.gm*xmd(ve 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) Wha moxzgoc;j+dlgk9 nz; + 6./(fph7 zzpt is the angle the shock wave makes with the direction of thezp/ ogh nco 6z; f.zmk++7dp(9xl;zjg 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 ijzyh8g )6p.ra planet where the speed of sound is only about jhg.zi yp68r )35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oceani*: pse yupo28. Determine the shock wave angle it produceop 8:2 sei*pyus
(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 dkp 21cqt(mgh opcua1 5r2i5:$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead a brk,)ahcgsi+553ls+ thsr7a nd see a plane exactly 1.5 km above the ground flying faster tk7r,ac+ +r 5tblghsas3sh i)5han 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. 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 soyuxs rrazr vt*oa-o)u2zf(, v 7n1y0+und pulses downward from the bottom of the boat, and t- u *so+f()7vtyrzoz20unr1 x,ayar vhen 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 t 4 lm -gxdbon.(k9.0cp6tvfbx here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called q(-(-bv7izj *2fc2 7np :jdwpn xqddca sewer pipe symphony. It consists of many plastic pipes of vari i-d2jfqjnwb vcq-dx: dnpzc72 7*p((ous 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 makes a sound close to the threshoiacgl;ek. fd8jq ,8 t wg(4x7mld of human hearing (0 dB). What will be the sound level d8 (e 4a;jktgwfgl8. ,cq m7xiof 1000 such mosquitoes?    dB

  What is the resultant sound level /z nke30:ij ezg *ed.vwhen an 82-dB sound and an 87-dB sound are heard simultz3z:k/e e.nvegid* j0aneously?    dB

  The sound level 12.0g.l97lfb 0fen m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equall9bfefn.7 l0 gly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The o(2s*aaz nh)e; ij/tdpower output drops by 10 dB ana)ia(/j hs; eto2z*dt 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsb mw f*tq3)()exk7,j a0 ti v,fpnks*t. Assume that the sound level of a jet airplane engine, at a di0 ),sfemxj3a),*b 7iwkvtkn(qt p tf *stance 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 gal5q(cv -rj+y6u s 6dnvcl8y7yin, $\beta$ 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 tjq lp86 m.sqo5 9vh6bbo 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 points with a 0*g3msqkmfs 3 fundamental frequency of 440 Hz and a mass per unitkm g3mfs0q3*s length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical openu,syrawvk4 f3x:e o -+ 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 +-: a v4sruwy3f,xkoe 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 ll(0k2ctkw 5vvqs8-p;v x*mxstring of mass 2.10 g is near 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 resonanqs0x8k-(v*tvv m pxlk wc2l5;ce (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as i;xm 9jzjwdb*s-4 v5zone 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 rang5 6ytirr5/ibpxn( c e ngeg865e coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency / 8bg6nye5(erit56xcp5ginr 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 the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train yq9 u:l21pufuis stationary. The conductor on the stationary train hears a 3.0-Hz bea:p21f uuy9qlut frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as ityz /bkia0o-4 ddt0b d5 approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Hzo0b -yd dbki5 td04a/ow 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 the ditb;x 0-4p jcn wa6n: /xgqk0yhfference 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 st:ykq64xa ;c t-0wghp n0/jn bxraightaway. How fast is it going?    m/s

  Two open organ pipes, soudex*si6 dt7 7 3bhq+londing together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m londt3+i*6e 77bolhdqx sg. How long is the other?    m

Two loudspeakers are aeps ( q:-cddwnlr-lmo0+*v7 r t opposite ends of a railroad car as it 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 th* rr l +(npvq0-wedls o:dmc7-e 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 inu)ce6 zliu 9v5bu x l7.v4,hhq the 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 au)9 eh5cbv v76ullzq.i, 4u hxnd reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whilef(h lqq:jb6vh 9gw+p a6p o8onqh m650 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 freq p6q 5blp0ojq( qh 6w6+:hog nh9m8avfuency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as* sny gbe-e3v9rt164l kulhe1p0 xdj0 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 the1h 3e ep-detxvl0sgn4ur jb l09k*y 16 echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send si95,lzxi v5 y; 0xlhpsfgnals 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 resonatinxl055 vplyz fhx;,9i sg. 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.duvl2 ec( 156chgds4wp gl2p can be compromised by 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, and 2.8 m high. Calculate the fundamental frequencies for the standv14c5 2g(l2esdp uwclp h6d.ging waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” i*9w8c, l zj r1ktt wctkbk02n7nvolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand.tjl92zc wkkt 0 n*, c8rk1wbt7 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 (ovkzwivul0+,:s :v 3/zau awat a frequency of about zsklviv o/+3a: u:wuvz0 ,wa( 1000 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 grouyf*)sadg,101laq h lx nd hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude?h1ys*l1 )xlqdagf 0a,    $ \times10^{4 }$ m

  The wake of a speedboat is m6 5x kib:6x wgza3i0r15 $^{\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