What is the evidence that soun/w vqmuhyke.,n,4t / z3o nwe:d travels as a wave?

What is the evidence that sound il d-,ycda6k1 as a form of energy?

Children sometimes play with a homemade “telephone” by attaching orr7j eq0 fc*2a string to the bottoms of two paper cups. When the string is stretched and a child speaks into o7j ocrqr20fe*ne 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 inbbch/ 3:1 jj3ntshdmef :j poof)/r.:to water, do you expect the frequency or wavelength to chae: po ::h1mbojtdf3f .js ch3n)//jbr nge?

What evidence can you give that the speed of sound in air does not depo,ov.iuoe8*3fnumd )1 u l 4cqend significqin3u .e oo4fuc1, mdo*8v)u lantly on frequency?

The voice of a person who has inhaled helium sounds very high-pi (hh/tkoe;evi;i;vbw , gcxnt 2,l;6 kq/ hac1tched. Why?

How will the air temperature in a roomm *gov5n pi ec 2+38t2som0thfue ),c79yiu ym affect the pitch of organ pipes?

Explain how a tube might be used as a filtsq1t a v8wb*qcl77- rgd2aor7er to reduce the amplitude of sounds in various frequency ranges. (An example is7l*dt7 8ravr wsabq7q2 - 1goc a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as -lop ;wh 8ur s:m29wldyou move up -9 ;p8owuwdslr2:mhlthe fingerboard toward the bridge?

A noisy truck approaches you from be0gdq enp3lv 6)d+ 5*wl-pclmq hind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Eqc e-n + gm65*dld0 3)lwqpplvxplain. [Hint: See Section 11–15 on diffraction.]

Standing waves can b0wycsfel 8xb .r 87n88 jhd8pse said to be due to “interference in space,” whereas beats can be said to bx8ey7wn8.8pdsfsl r808 cj h be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the r *isdp w-65igpoints D and C (where destructive and constr*wsi rdg i56p-uctive interference occur) move farther apart or closer together?

Traditional methods of protecting the heariwrkpk8sh p vzym)6 t 0).-ir3eng of people who work in areas with very high noise levels have consisted mainly of effortr z)hs6- e t3pmry.v8ki0w pk)s 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 Fig. 12–31. Each wave can be9 o*g ym vyer h800v6gos3rtx ,n+o/co thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are+39* ymhxv80o,r egt0on6v osco /yg r the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sames6y4ilc fvyt/je1su) xv 9 .w) direction, with the viuj)sy1l9s)e6w cx4.t /yfvsame velocity? Explain.

If a wind is blowing,je7i4o5h x9xdrkz.kq 6la; 8s will this alter the frequency of the sound heard by a person at rest with respect thke 8di j6slz 9o7 rxk.;xaq45o the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A0g*uuzr )sxa81m9diw*e hrv7b .jwgwv6z y, . monitor is blouvsey d6 rjz w u7w 1m9rzg.wh8v,)0*i.*axbgwing 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 whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sa444i0+cku / b4rcmswiv i tp(hout reflected by a cliff a+m4u 4vrpk cta0 i( ii4/cs4wbt the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of h b)-s tw +bcp pu8xclx s(tf80sj1*fc5is ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. Howx)c c bw5fcp+j-(8s sfs8ttb0*xlu1p 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 wavelengt1 lkrq0g2 ke+qhs 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 drifting just above uk3; g-j,*rj yyhxnl:a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire i3j:*xyr, n-kyu g;lhjs 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 ds894odl3 n( +tkr ivwcud/ n4when striking the water below is h4cl+nkwun d43 8toi d9(dvsr/eard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strzk*iwj71q* jwup (.j fska.t8ike the concrete pavement. A moment later two sounds are heard from the impact: one travels in *a(*si.8j ztjpk fqj.k1w wu7the 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 one mile of dist. hm7d5f:x cbhance by the “5-second rule” for estimating the distance from a lightning strike if the tempebf.h:h m 7xdc5rature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sohvn.etj+f; 3*zyq dk m-mpz* ;und at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound lev 2sy;in7y us0ql2he :tel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro r ,k:szvlj3ek2dzrf2;5tlt4 duce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sf,r z:t32ezkk4jl rt vs5;ld2ound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a ce.udr b g pq).3)igij g1;vzo-grtain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What so3g d.g.ij)iugp o 1qg;-br)zv und 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 58 d:ph1 er6*y p t erzu4a;q:wen:B, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise fep1 t rhn*ra;4q: eu6wy:p:zeor each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pers1gtel4ns+ed6 b 2lipwp x*9 6fon speaking in normal conversation. Use Table lespe41pnwfb6l2+9 g xd *6it12–2. 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 eardrum whose area i wpcqpn7 uar*9x-uw:)s $5 \times10^{ -5} m^2$ (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 t(-m 2zn3 9pbwhr yvfu8fee;3l he more modest amplifier B is rated at 40 W. (a) Estimate the soundm9y ; r eeuhbz3p 2ff8-3wn(vl 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 whw ucyy:x8lgwexi r4m4.1u f/xmz/ );zen placed 2.8 m in front of a loudspeaker on the stage.u1wy:/lz) gxy4ufrm.; /xcx8 w mzi4e
(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 ;hp ridi1fq69 dB. What is the ratio of the amplitudes of two sounds whose levels dif19ih;r p6dif qfer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,0 9o: uxh :9yhsj-zptes;+kuy (a) by what factor will the intensity increase? Incr0u y;9u9x -h :+tj:spokezshyease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement 2cp(e+ ( znnrfamplitudes, but one has twice the frequency of the other. What is the ratio of thenrf +ne(2pz( cir intensities?   

  What would be the sound level (inv :5er+cq 8xhz dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.e h+5xz:q8cr v13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tk .u1gjt,kxu 3one that has a 50-dB soj3tuu,. kkx 1gund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that b3jw4: e7fb-x vl nrq0wp27i/ef ug8 oan ear can detect when the sound level is 30 dB? (See Fifjevnb r-f lwbq: o4i2wp/x780 ue7g 3g. 12–6.)

  Your auditory system can 7gurgtb:.uz/yj1rv 9 accommodate a huge range of sound levels. What is the ratio of highest to/ryj9zvuug:.1 tr b 7g 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 fundamentaltq6j z7, h10 pwxncay* frequency of 440 Hz. The length of the vibrating portion is7y6p *h jxwz n0taqc,1 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firarj je9bh;4/z st three audible ov9;/ jea4 bjzrhertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would yo5:fhn 3w ,akoiw:ne*au expect from blowing across the top of an empty soda bottle that is 18 cm deep nk5 : wa*:,h3enwoafi, 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 ranqlto /e) u6/uro*gig; gpb:s ,ge of human hso glbpg; u*o 6i/,/e:tuqgr)earing (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 halv3bp1j+* . ,ai8wjmf +zpsh ps a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengl* 8jwsij pp3+ mfhzp+ v.,ab1th of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long a2 3zhf pdua7i7g9ni6snd is tuned to play E above middle C (330 dahg67u i73s9nzip 2fHz).
(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 llackgf16h t14-ol g.e l,o)emiddle C (262 Hz) when the teh .lcfg1lt41k6l )- ,egloa oemperature 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 20gv yw ) y k3b90ym4*exzh)0hssih7ui7tc *x/d $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 n)(qg3vgsy 1,r aujerl ,g,prpp6+( lshould the hole be that must be uncovered to play D above middle C at 294 Hylqurpl3e(,+ 16,pv)rgn (ja, spggrz?    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, butbm6:3ex;k/ ext btr e) not at any other frequencies in between. (a) Shtet;b b k3xr):6me/xe ow why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates +s4pyt +lqlo-n4 5bzz at two successive harmonics of frequencies 275 Hz and 330 Hz. Whspzl4t n+-yqo 4l zb5+at 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 n9;;pry kzg +lr y4hw+$^{\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 audibltk/ubhv 7 je,9 4rkvl0e range for a 2.14-m-long organ pipe kh vj/94tlekv0 u7r, bat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside8q9wuwyz :0es and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canaeywzsw:qu089 l. 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 two bcd)6w1baw . istrings, one of which is sounding 440 i)bbw1dcw 6.aHz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 vf/n ,p7 qtctl(;0a n.mvz g1vHz) 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 op/;+htxu ss2 i zq4x63bz5 vvuherates 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, estimate the operating fhu;4 /z5q x2u x6vzis sbt+vh3requency of brand X.    kHz

  A guitar string produces 4 beats/s when :+gix8tehg7y sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequengtxg:i8e +yh7 cy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the)ki i -av/*qqb same frequency, 294 Hz. The tension in one string is then decreased /qi aq)-vikb*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 identical flutes each try to play middle C kocrih05 y6q6 sui/ 1l(262 Hz), b1cl5 6u/kiis 6oq r0hyut one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freque:5vxrqaq6b1f8b g 7iz ncy of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded to: zqq8baiv5rb 1g67 fxgether, 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 spejnc 5*soas20sojzn-: aker and 3.50 *s ojcjsa5-02nzno:s 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 pi56uy8rp*: tn:nyqco7+gidf hano tuner hears three beats every 2.0 s when they are played together.yi7nq:dhg*+n u p:t8ry6cf o5 (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 soundt0/bfo w 4n-go of wavelengths 2.64 m and 2.76 m in air. How many beats per second will bowf4 bto-g/n 0e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency muz8 17mf h7mjof a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with aj7u fzh178mmm 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 engine whose si9:v+ kua r g(ztiqvo 5/ocvq06ren e govvqrkz +0(iao 5/c6v9qt:umits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift ckm lv);h6 v8ay1bvmw- n8v1e*jct6ain frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sb*mlva vw86v8;c1)vnje1ky -ahmtc6ame? 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 singlo 3:(vs5vccg qe frequency horn. When one is at rest and the ogov5vcs3:q (c ther is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounlxvo-m + q)5end waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/m -n5x+qve)o ls What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed +iz48dt5)bovo- h.f8gszz yg g*t9ttof 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz.z v*.9fgo8ttz -s 4g5t+odyg) hi8ztb 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 movz0ep-kt73i kt ing flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the r037ikptkz- t eailway 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-yyb:4 ;;k 3eqdmxvei 3g h85zoflow speeds. Suppose the device emits sound at 3.5 M4ohd ye3exki8:5q ;3yz;bv gmHz, and the speed 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 usir sd3p1d w2/v.zmpbs*ng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frb /y3p:x2nxx b 8kw+:olk,cwrequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rn: ,xbbc2op ky 3xwr:x+l/8kwest,
(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 a +a* 6f z*tfa v0xs9np7, ainmm0ki.bif its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What qo:(a yte1lpwk/ 6h4k is the angle the shock wave makes with the direction of koa4 :ltwqk/ 1py6(he 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 entersco7c8ae 8ztwrjw-8d*l+e cs0 the thin atmosphere of a planet where the speed of sound is only abou0rs 8c8jwe lo*e8-ta w+ 7cdzct 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 ocean. Determine the shock wave,omt/5jg(v+g+-jcb (z ys7suwnetb 3 angle it produces ((tg mbgts,j y+s /- 35e+vzow jbu7cn
(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 xh259 zvjmo5 z$/theta$ 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 1.5 km abol8p ehh 1y09elve 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.el1h9y p08lh e 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 souvrcs w 9wr.jl 8y0u.*jnd pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for whi*s.rv 8.y0wwc9ju rljch it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in thep13sxm 4t3 vxbf5hd2*m2aly-o f(vs c human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a si;m x2sdk9 ,b ,qtcp1bewer pipe symphony. It consists of many plastic pipes of varioq,icdpm t1,s;2 bbk x9us 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 soun4ft)j8o o c8qqd close to the threshold of human hea88c qo tfqoj4)ring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soh. kwbd /jxc 6 ll)q*5h .5;wj)a/wlfkh5zlg cund and an 87-dB sound are heard simultaneoushz;)lq ll 5 dwc . )/w/j hkkxh6c*bfw5l.ag5jly?    dB

  The sound level 12.0 m from asp6) df6vutq6rd( 4w v loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming v66ddtuv frpw(s6q 4)it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at lc,f xb5fwu* l91a0kut l x7d91000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? 97cu0 9wtxkd 1*l bffa5 l,uxl   dB

  Workers around jet aircraft typically wear prot-yz -c)mdw+et+h3r0+d/xiye( o np wbective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average hy yzonew++diw/e)r -h+dc-x pm0 t(3buman 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 gaiwv t2zjrhk ov) tu;**5n, $\beta$ 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 ag 5fy/hz/n :ff 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 3y.s9nc / 5xzwd2 cm long between fixed points with a fundamental freque.nd5/s w czyx9ncy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertica9t 6xzawdb 88m0,1 lv/vkzrrdl open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the wate06xzw8vdral,t9 m k b1zdr/ 8vr 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 ofzd*a i0 -su5xw 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 reiwz*axu 5d-0ssonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed toj8 nj,8m.us x:pybz.s resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tondm528bze/ ekd e in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moke82b/ed md 5zves 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. Of;kemnrj* nz0sn,z1h( p4p:ane train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed pkhne:sn0 za p*z;r1j 4m,n (fof the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it m6 tb.0 -vhtnrpasses you, its frequency is measured as 486 Hz. How fast was the tra trm6bhn0 .-vtin moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by list72k*qyzb fax(sz b4e8 ceg-m)oy 3gt;ening to the difference in pitch of the engine noise between approaching and receding cars. Supy2k ac ;xb-g*zb)gfot3q s e8e47ym(zpose 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 tdalz q:xm:w70b4jj : 7lzavmt8i,c p9ogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othe7 7cldj pvbxli, 8amwqaz4:0:zjm 9: tr?    m

Two loudspeakers are at opposite ends of a railroad car as it5nms 7 plwm940egywg)kpn : r/-7gnjb 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 s7b 9m w:nngnpe-)r /glpkg4 mjw057y 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 normbu +zjxaw 51(yally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that thjy5b xwzu1a+ (e 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 while the moth is flying toward th vyw+a elp24qi 1tmg9/e bat at spe 9y4vltqaewp2gm1+i /ed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mothfxbmgs750/ p xbn,or ;. The pulses are approximately 70.0 ms apart, ao/xbgfm x;p05s b,r7nnd 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 ;m: enr*q htho+e4(uyfrom one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns (r* o;ey uh+th4neqm :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 2l b3ed3 a -89glsgtg:m7u7hn gir by,be compromised by the presence of standing waves, which can cause a:st,mb3 d -g7auhgb7g3 rle2 8l9 ngiycoustic “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 “singing rods,” involvccrv, .awpjdnz (2 /3ses 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 mar 2 j(,sn/.zcpa cw3dvde 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 qsamw3h2 t5e+ xr/)un hearing for the human ear at a frequency of about 1000 Hr2 +/x53umq atn esw)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 theb1jvgk /pt.8)m kl 3mg sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude.klvt1jmg m38kgb )/p ?    $ \times10^{4 }$ m

  The wake of a speedbaqlz d82*;50ycok8tb r1 qtdcoat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h