What is the evidence that sound travelsf8(uyu0u k--euc)0kng9bg8 qg9 q klx7y ur8b as a wave?

What is the evidence that sound is a form ofhn-0hs5ff ) vj energy?

Children sometimes play with a homemade “telephone” by attaching a string tode nyj8emx)c;5,i*c z the bottomxn,zdi;e jy58) *ce mcs 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 to the other.

When a sound wave passes from air into water, do you expect t)au ffy :6 .iyrxzkg48xp3kbc hi5j. -he frequency or wavelength to cij)ypzy ci-k r. 6axb.x u3g8f5:hkf4hange?

What evidence can you give that the speed of sou qhixyhuy7 l09u.bd . kel84(snd in air does not depend significantly on frequenu d.ui. yl(h h84kqs79y bx0lecy?

The voice of a person who has inhaled helium sounds very high:2sg iaolo37+ ofco(g/ wic-r -pitched. Why?

How will the air temperature in a room affect the pitch of organ 1c /bxza, t1bqpipes?

Explain how a tube might be used as a filter to reducdetkc63 (zpg* jol(h0v)0(x8dgghm he the amplitude of sounds in various frequency ranges. (An exampl)d0xcg 8kjhm60( 3tzh( (v dpl*geogh e is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you k z ;m)1ybdzlep kzg1+73 6gkw0fwwd)move up the fingerboard toedk) f0l) z13;wyk+ 6p7z zw1kb mggdwward the bridge?

A noisy truck approaches you from behind a buipc(:u 8viuxcj m7e(1qlding. Initially you hear it but cannot see it. 1eui8 m7p:cjvqc ( (uxWhen it emerges 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 belv.n4o;k4u g*ogv .fd due to “interference in space,” whereas beats can be said tlv* .k.fdg oo4gu;4v no be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointtyedl.b6h ;b (s D anthb (ly6;b.ded C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people whowe8gde7r4exz 7,, tfwe u k22y work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient n7eu g,de7k wf2,t4xzwye re28 oise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave canmdjgy wb0+7uqd xy fb -o94e54 be thought of as a superposition of two sound waves with 4f9j +7qybmeg x 0ybdow5d 4-uslightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if i+)u+4sq7v)wa/etb .oi l a6lkk 5gxs the source and observer move in the same direction, with the same velocity? Explain.) i aig/ewtuv5sq+6x7k)ol.k+s 4lab

If a wind is blowing, will f 9uq,/orro+al 7:5 hojkp:wu this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelengoo/hjlou ,qr : r9kfw+7:au5p th or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitob2m c; nylipt78-tu 5ar is blowing a whistle in front of the child on the ground. At which position, A through E, will the child heabtm p;7l2tn-i 5c8uy ar the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for th/bpu r ,yu:7 qjk5bv3re echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lakvbujk uybr3 ,/rpq5 :7e. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shd k68f . 1ntim9xvunb3syx2 z,ip just below the waterline. He hears the echo of the sound reflectedk9v8 tb236 nmd 1fx.xu yzn,is 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 not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a93w2wdex0xmjl*pac 4cb 3y i6 t 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 *b8w hbr*4t ynw/u9 dxdrifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another b b9 ywr4*hdbwux8nt */oat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash i ze7,s mws61set makes when striking the water below is heard 3.5 s later. How high is the cls1s 7mez e,sw6iff?    m

  A person, with his ear to the ground, sees cn.xe(jm1*:d rw5/no,7 vc buwjsw l 2y,lrd5a huge stone strike the concrete pavement. A moment later two sw5c* conuvrbwe1: (slnr .ld5 ,d 7 wm,/j2xyjounds 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 Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over jn74 p1:fd*oxr3 k jk8o 9fylgone mile of distance by the “5-second rule” for estimating the distance from a lightning strike if t1of9j:x p fkd83 n4* g7yjlrkohe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levyhfswx2r-4 +tg6a zn* el 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 sound whose iypc9o1x 6baxahm +xen iu8.9 n1ks3m*ntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneoukg.vsn0i n5d7 sly at a certain place, what will 5.0vsng7dk in be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane w-ko aqd u0a ue1.f(le5ith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experif a(d l0a5ok-uue1e.q ence if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh402ita;a.r4-tn6 /dd d/t r bppgsnneereas for a CD player it is 95 dB. What is the ra 4;dn2rd4b0- spatna/tgp id6/r.ne t tio 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 norma)7cdum : ve,dbl conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. )v cudd:be,7 m$\approx$    $ \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 eard1,yu+,0rzft rmr m+cfrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more mo*z8y k5zb-)mjobyc3z53 gmowdest amplifier B is rated at 40 W. (a) Estimate th8wymmb g3boo 3*y-5jkz5 )zzc e sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 mr8idsrw.si5qa ;t yf edm(4/( in front of a loudspeake s(rr.5/mdfya;eti8(4i dq wsr 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 wk93c1 jz*h v mdhmry 6dw1g.*detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by *1mjwd* 6 dh rh9.wk3cygmzv 1this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trmuk9wr(0)gze ipled, (a) by what factor will the intensitgrk e(u9mz0 w)y increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displace 0 rl14fshdn4k i0+rawment amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitird+14ha0s nfk wr4li 0es?   

  What would be the sound level (in dB) of a sound wave in air that correspondcm0 m cw a7t:i0ffj.;fs to a displacement .a fmwm07 ;c0ftj:fciamplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as onb;s2qvb5/lzz(2 uv a 100-Hz tone that has a 50-dB szl5o(qs;nu22v zbb/ v ound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thca,5v* unwrvi:7n/ s 7.dxlsy at an ear can detect when the sound level is 30 dB? (See v ./s*yvunwcx r 5nd7,ia:7slFig. 12–6.)

  Your auditory system can accommodatq hm31ecnxu a5wa,m8;e a huge range of sound levels. What is the ratio8q 3m;wum5ha nxa e,1c of highest to 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 length m n*d-plbht-- of the vibrating portion is 32 cm, and it h*hdt-nlb- -m pas a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm zd*sf;yva mw4951 yvw long. What are the fundamental and first three audible overtonesy5 91aw v4 sz*wydf;vm 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 fr8h lpe7qp1p):s5 hedyequency would you expect from blowing across the top of an em1ph8dp7 splyeq h: 5e)pty soda bottle that 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 a pipe organ with open-tube pipes spanning the r14kk hcord en24jmw766ag5qx e-6d flange of human hea6g1ca4 7n- erho26 5ldwke4 mk6x fqdjring (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What c10n5,m f)qlbj sq(or will bf n51jqc, ( )blsorqm0e its fundamental frequency 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 tunehck) ef6y(7il 1lax s7d /s/)x(riy xed to play E above middle C (3a iyer)h/1() 7ik6sc7l(sxdeyl x xf /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 (2h(v+9bkmt o2s 62 Hz) when the temv+mk 9tb(2 hosperature 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 20 3nfz 9*9q z59fozun st$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiecs ibidybxkkz q*0h*kv-.)r .06vz w-c e of the flute in Example 12–10 should the hole be that must be uncovered to play D vi.)brxbdiwyk0s hz-* 0-k*ck6 zv q. 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 cd2r(u2s3nz hcix rw ..8r3winan resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show2i (x.dns33ric.w82hwurnr z 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 iszf8m5fmn2 pw ;.j /shj open at both ends. It resonates at two successive harmonics of frequencies 2758z;2mf 5js wp .hfjmn/ 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 kpu-vuek;i mpu4,) 7s$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible6nr3 /uy o94q.fbo xrrap, z;e range for a 2.14-m-long organ pipe at 2049qza 6np .u,rfo;r3oeb / yrx $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ig-io.wt scix 0+r7nyy74 m1q fs approximately 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 relationship of your answer to the information in the graph of74rfnxo7iic+tg y - sy.10mwq Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat ; +o5d8x(b-zzaj7xg0luis gy every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in fg 7+-o;z xl08a isb(g 5udyjxzrequency is the other string? ±    Hz

  What is the beat frequency if mi))m zhv 9v;scbddle 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) opera1b(bg: 5b mxnwtes at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating fregbx nw5: (m1bbquency of brand X.    kHz

  A guitar string produces 4 beats/s whepe3k:b/h;p d ;hh4bf-/gbd g3g zf t3un sounded with a 350-Hz tuning fork and 9 beats/s when sounded we;dg/hz f - /h t3b 4bu;hgpk:fgd33bpith a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensiobna7akoq4 -mh)0b ln3n in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–qb0 nn) 4o-lah7a3m kb13.]    Hz

  How many beats will be heard if two identical flutes sux awyx;;)4zbw fqf:s - 96wmeach try to play middle C (262 Hz), but one is at 5.0°C and t4z - fums;wsax yf6q)ww;b :9xhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hatfj e4mix /(5xs 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 toge4 x /itmjf(e5xther, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker and 3hmkyxy2(:+ l i(2xymlyi :k+ h.50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tu7,6wa 5yjkc,ejw a0f*f o di7sner hears th 5j6, ,few0wjfs7kayod*c 7 airee beats every 2.0 s when they 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 mva:i gw:msm,6 in air. How many beats per second will b,6sgm mavi::w e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eemy-t6lp5:mra/3)zv zavh0zpzg 8h ;ngine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30pavzt;ge-v r) /pa lhmm8 3z 50zhy:6z m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency pij3jgg:r1. mdo you detect if a fire engine whose siren emits at 1550 Hz3 pjgr1.jgmi : moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frc)ay:rq7 6(pt dv *jdxequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/sc7y pvqx :dr)6j d*(at 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 frequ aaf gg ssjkpf49u/5d9gn*d;. ency horn. When one is at rest and the other is j9/ *k94fdg.suns;ggpad f 5a moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultbw1l e+rn25t vrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What isn e rb51tw2l+v the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spee*nlokzhki.-- d of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the ba*-.hz ok- lnkit hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played omlmab54rx 1 h5z)wm;3a di9k un a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the stati4iza) mhax 3l59bwuk1dmr ;m5on at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spldc nu7/ no:u9zzz7k ;eeds. Suppose the device emits sound at 3.5 MHz, and the spudn9zz : ;ol/7nuzkc 7eed 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 frequezammzzi2s 9ig/i -)k( ncy $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 127 ktm)i(-i2*xbzcceh 3 wz)jg m/s from the north, what frequency will observers hear who are low tzc)c3*-mhgiiej) xbz(7 2kcated, 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 foyme;u8 979r cp+wob 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 sp0 7) w22ffgtgv ra) wkinbs(i8eed of sound is 310 m/s (a) What is the angle the shock wave mak )f7btvwi 0r)(ki ag2fnwsg28es with the direction of 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 o m0 3a h89.thm/vzub*enccx, planet where the speed of sound is only about.c9ec tmo0u/ 3a, bhzn*xh8vm 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 strikft5k*)qxe/d)eyr h 6 jes the ocean. Determine the shock wave angle it produc5krh jd*ee)y tf/)q 6xes
(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 1y mzbr04dmuv5 qjqh4n /s5w.oa zs2,$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.x5u6wezb.1it j8 0pvz zvk9/p5 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. Detzw8ziuevx .pb/9 0vt z51 jkp6ermine
(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 s/2i p.ti3k w:g2ko vefound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to wor.gokt 2 :ekf2wi p3iv/k is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octavewv0sl zh 7fh:8yx1.e1,g o,fz nm1udp s are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calledrz2cfve -4n,a15t vq vpuv7nb r11* xh a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are oz*vphaqve rbn1c 42r f1vt,v5nu- x71pen 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 threshold o/y rpcqa r6uc1,bid.9f human hearing (0 dB). What w1acd, ir/9r bp.6yqu cill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and azzlyzylb8qst,5n/bj384uw5)b 8su et +: uovn 87-dB sound are heard simultaneousl,3 b)utz:j l5 y+z5lvb/8s4zb uy8qws8 nt euoy?    dB

  The sound level 12.0 m from ,bv-hlmlg4w)oj qzm8 1mx,: jzy f,(x a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally ij ow4(-lfx,)l y,:xjhb1qz m,gmv8zmn all directions?    W

  A stereo amplifier is rated at 150h,w zur83a 1rpon )7ks W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powe31a) n,7hw up r8krszor output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theic lt: kg6har7g3wl (s0r 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 s(r gwc6:k0lha ltg73radius 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 syste+sww o exqe xi+wm2q5( /9tkr.ms, 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 frequ9ibu,bf n8cx ,8;su d7omv, vpency 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 cmv8 zv+/iib/h-bxyr; k long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length oi-xvyz /8 hbr/bv;k+ if $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wah;zxa 7:)r;sxce b.9-ail ;e kaj uui*ter (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125):.akxbure7-zacis; 9; uxa hlji;* e 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 noyes(.i e1,m sear a tube that is open at one end and also 75 cm long. How much tension should b.1em (,i esyose 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 )dbzzp9ia1zs /gdmw4bj -,(ffull 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 ak2jddj :*kn-5gbpyh(ks m4sut7w09 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 tht :u*dsjg 7m k4d(abp -hnskw92j05yke frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor ij98mk f7guizt *v) u.on the sta .7 i8j*9u)vimug zfkttionary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachesa ; il3a c0j,ppstzu,: you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant veloci;lj,uazca0p 3ts, p:i ty)?    m/s

  At a race track, you can estimate the speed of cars 1qqu 7)nh tw;njust by listening to the difference in n;q hun)qw7t1pitch 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 going?    m/s

  Two open organ pipes, sounding together, produce a bemys;u( y9 q-qrat frequency of 11 Hz. The shorter one is 2.40 m long. ;qmy9yr- s(q uHow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past 5nybuf:38mag r-m1tu a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers havtb53 mg8:-ny af muu1re identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what be4u/y qihu0it:r y*8wj at frequency would you expect if 5.50-MHz ultrasound waves were dire* q8i:uu0 tyiryjhw4/cted along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while4m g.z d 4xatkjm6)3dm the moth is flying toward the bat at speed 5 m/s The bat emits a sound xkm6d.4j z)ga dm 3m4twave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency lq1u.( bp29d jq (run wdddyq)/k2u*wsound pulses as it approaches a moth. The pulses are approximately 70.0 msduwn2 9r/k *2d(ubu1.wq ypdj) q( dql 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 signals from one Alpine vi nvh/;,zk fv8nllage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sou n;8hn/kvfz ,vnds. 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 compromise+hiiqd s 7 rw6aq:k.3 f6j2iiwg03 umed by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consq.j iurdw 3i7+66sq imhwg3e0i:a 2kfider 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 “singinkf /csye(q+3 kg 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 ro3 y+kc (kesfq/d 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 o3i dm8p bhc6+sf hearing for the human ear at a frequency of abou hpm+di8s6 bc3t 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 ground hears tf9g g1ap * y7ngd*gutdel35 j(he sonic boom 1.5 min after the plane passes directly 5ltd*ygfnuj793e( p1*gga gdoverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 d 8) obnv.od7z$^{\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