What is the evidence that sound travels wu vn-e;;vx63z 1e onpas a wave?

What is the evidence tdj)iwn a/k. 5one ja/.5u(pothat sound is a form of energy?

Children sometimes play+ +fm +m gekpp,pm :( hqtx(i.hh,c0ar with a homemade “telephone” by attaching a string to the bottoms of two papr,:.mghf(i m+h xea hckqp(+0+pm,tper 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 the frequency or wurmoktr,jlk p 1k at7 q5e1*,al(;8ix avelength to changa* l rkp rqtitlxej1o8,a; k1k( 5m,u7e?

What evidence can you give that the speed of 7bo5ka:wek* hsound in air does not depend significantly on frequenkwo5 7k*:aeb hcy?

The voice of a person who has inhaled helium sounds very 0mq/ 2mccxa+s high-pitched. Why?

How will the air tempevx; iv1i6pig) 5a*fqgrature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to red; 84a1s tgs,upiyvpu8 uce the amplitude of sounds in various frequency ranges. (An example is a car muffler. gyv,uptpi8;a s48 us1)

Why are the frets on a guitar (Fig. 12–30) spaced c ;c7e:3t +w;dxu jngksloser together as you move up the fingerboard toward the bridge?tx;;geu 7jsk3:w+ cdn

A noisy truck approaches you from behind a buildibsb+d7k)o . jt-6* qe ,geir4efk*k hfng. 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. Explain.bkfo*g-4h tr) j6e*fs+ki, e7 qdeb.k [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference ind eq dx82vcd,zl3:/sy space,” whereas beats can be said to be due to “interfer3c8ye, 2lvx/d qd:dszence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wfdb+ eds2 ,p.2nk1359 hbf7oplq myb aere lowered, would the points D and C (whesbmpyo27ff bq, dal+5 12. bpd39nkhere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areaswm lq,+) gwp;pev8l 0l3vde n/ 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 noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds vlm,8env+qlgdp) pl/3 we0;w 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 be thogpt,+w e1d-97ni sl 0rm5um fxught of as a superposition of two sound waves witeu7f +-d lmt9 n1r,xpwmgi05sh slightly 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 the source and obs w.odwam zpl8ca4k -)gvbqi* p7me)*/erver move in the same direction, with the same velocity? Ex ewcvz/a *o mpp*i-b8)4g7d .wmk)a lqplain.

If a wind is blowing, will this alter the frequency of the sound he+p4mn2oqcdf*6aw m4l(50se z d- g ovdard by a person at rest with respect to the source? Igoz o0a cwql5vn2dm +d 4fdp em-(4s6*s the wavelength or velocity changed?

Figure 12–32 shows various positionsr4uc3p ety e5 7ljfnn:v,0;zb 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 frequenc:4cen f lb,0e putyzj57r;3vny for the sound of the whistle? Explain your reasoning.

  A hiker determines the length8.gdaq4; 6jn/ qtekwc 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 af/6gq 8j d;qack4nwe t.ter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ed6- eb5lm8edy cho of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawdme65lb 8 ye-dater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtixn2y044pu5htubg v9xk zr:6i 7l9yq hs 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 a school of tuna on jouh/y ,2 g)jqa foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How mu2,g o) uj/hjqych 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 it 6;e5 9pewu weomakes when striking the we95e wu6 oe;pwater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone st0b qhnu j:k0 ckaiz3jq1njq y:a(+x )q2xf8+arike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in thuj( qj0aiqj1y) n:k+aqb2n hqx:+zkxa80cf3e 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 errfn *mkd7xsm ;ew; :rfwa44 )pqor made over one mile of distance by the “5-second rule” for estimating th:a srdp;mwfe4)4 fq*;kn wm x7e distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of x1;ifjnvrt5q;wgi )+g4a4 nj0 dxh ;ca sound 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 level of a s5cglfn5 j9)wr b-tzt*ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultanj8j6f /;aa wjyeously at a certain place, what will be they/6 jj fjaa8;w sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanep j y.t+c tuqu25;wdz+ with four equally 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? [ ;.twq5dzup uc2jy+t+Hint: Add intensities, not dB’s.]    dB

  A cassette player is said toeni+ga d :7fpjxrofs37c(,o5 have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Whatno:j,(o ide c3p7ra7 sfx+5g f is the ratio 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 )7tib-zt)jfx hlp6 u0 speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over ut)bpf h lti0 7z-6)xja 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 str:fuk .wm7m-u gikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B isykded +7o iv m)d,9n9p rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3 oye+dv99, dm)n7dipk .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 mc 7 uvn 00ayqcscyf;qx u(2uydm9m:(a,xwb9 .eter registered 130 dB when placed 2.8 m in front of a loudspeyc,w 9va db m7u(0faxu2xc c(q0yyqsu 9n;: .maker 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 detect a difference in sound level u knz2 o 79y.n.onyfg(of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:gknonzyu2o .9yf 7 .n( See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is thwr;6s pis y5m x8k)i(ripled, (a) by what factor will the intensity increase? Increaskh8p( r)56 issmwy; xie by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but oqj3xtt )( d4-mev s/srh-cr64u ) nytjne has twice the frequency of the other. What is the ratio of th4 t-rreyq ujdh)4 j 6/tctvxs(nsm-3 )eir intensities?   

  What would be the sound lepyh7k75): ia3yba onhpa us-go06+ rd vel (in dB) of a sound wave in air that corresponds to a disppa:n b k7i 3hraay -67pd+y5g)ouo0s hlacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve)0spkeb gj c-s;p ih.(l to seem as loud as a 100-Hz tone that has a 50-dB sound level? 0pi kgcpeh s -(s.b;j)(See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sounah cs 7l.s1, 4:,9bhyw p6 9rsun+owf p(uagbtd level is 30 dB? (See Fbuws(19f9opsraa4 y s:hn,t76bpw h. gcl+u,ig. 12–6.)

  Your auditory system can accommodate 3ahm s7v6,er c tbj(iu rz.l9-a huge range of sound levels. What is the ra arz(m-u. hirslj36vc b97te ,tio 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 haskw+hj1r272k9t gv tm wu)5i j )byju.e a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed) jh92)2k1.7g r u+ tjvwjbek5ytu iwm?    N

  An organ pipe is 112 : j54dkr;fr xfcm long. What are the fundamental and first three audible overtones kf5r4xd :f r;jif 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 you expect from blowing acrt fmlujm+4(0f2qxz; d oss the top of an empty soda bottll m( qfxdz4ju 2t;0m+fe 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 opeds1 -2kfu.1vnns )azkn-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would bes2ku1f)dv z1.- asnk n the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has ai3*mlev k 7g;ccby-u3 frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 7bgcci;-y kuvl3e* 3 m60% of its original length?   Hz

  An unfingered guitar string is 0qe*dod6 g*db:,wz51g8 * 9fzkq5ud xsv5yj qo.73 m long and is tuned to play E above middle C (330 Hz). z6*goy* qdg*:xwskjod1eu z 5b955qf8q,d v d
(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 tha2l*aq4 dchrj6voe +jm.(p-t jt emits middle C (262 Hz) when the temperah2maqot+pvrj(6lj cj*4-d . e ture 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 5hn ase6fip4n;3hdki 1k1z3s-by(ze at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hol+rmx edak* +*gbg+)j q(k; wqhe be that must be uncovered to play D abokx+dk *qrm( h;+g)wjb*g ae+qve middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at alj 27+;ic iqy-zayd: gny otheliyai:z+g c-qjy7 2 d;r frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It rmmf)mmb(,h tw0 m d w4c2.*xseesonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is xm4.2bswdm)(,0m t h*m mefcw
(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 hh85bg etzw2kwspe /ip:y0ra:)xim+* )f t5q$^{\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 wivyz,m 8hin0 +vo(h3m u n7s0pdthin the audible range for a 2.14-m-long organ piydu8 pvn0 ,imh 7m(z+s03hvnope 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 is open myapthcvj/;*0r o y5)f;n.y sto 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 of Figp);50v/;om ayyf h*jt.nrs cy. 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 two9tj sq76 hk8ko strings, one of which is soundqo6h 97j8 ktsking 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) 8kwhnq4zjtr:gd:.w ny (*r , xand $C^＃$ (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 1b90;; b5 szcaxt;cy1za zfjyX) operates at an unknown frequency. If neither whistle can be heard by 90fztazc5x; sac1z y; ;byb1jhumans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whe+ k2(bh ffwj0bfml d)0n sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tun f)l(bh 0+0fjdb2k wfming fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned ) 1mi ( jv,/ + gaqmpo)pi+5vtvspkqh6to the same frequency, 294 Hz. The tension in one string is then decreis16+p igqv+,t)a 5pvmh /(ovk mjp )qased 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 t7(zfunznyk5vn p6ag /.1z ;pflutes each try to play middle C (262 Hz), but one is at 5.0°C and t a (p5/gn z6.vzknt;z yup1f7nhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequez m.zz1q -aytg(fdl523v36d s3mp heh 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 togethermh fal2zmd z5gpdt 3.16vszy3 3 (-eqh, 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 xlgbfc3k,b691g i u,mperson stands 3.00 m from one speaker and 3.5x,ulki, gmc3fg9bb6 1 0 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 tune: d u3;ihb)tezr hears three beats every 2.0 s when thb)i u;edh:t 3zey 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 m1g)kvs irg3a:c6o tlrw p 98z- and 2.76 m in air. How many beats per secok pvr6t1glw)3:ca9 ios 8zgr-nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of.u,8 omqcff, q +g/ qvifb*w*b a certain fire engine’s siren is 1550 Hz when at rest. What frequency do yif/cqf og,wf.8 b mq*vuqb+*,ou 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 yo2zl4 7 5mis8 cn8 jda+ 4s))wjsisnejou detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/8lazon584idi 7s4wse cs)jjs2n)m +js
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source ilm(8 i5 1t4, lalb)nby8vmbfw7t)lg ts moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freque8b i t58)lwylnb ()gvl1l 4bamf7,ttm ncies 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 s tlo01d)ft) zj/lz.a tingle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emitzal1t) 0df jzo)tl/.t ? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends ou/1(n lvlr3pk,s4+ a wkz bt4qnt ultrasonic sound waves at 50.0 kHz and receives them returned from an objecans vzk3b1 ( 4,pn/ltrl+kwq4t moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As i3chd 0rykj3q9:oj:e q9 a:kxst:try- t flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thee o3kyaxh:dqky9 3s9::-rt: jtr0qcj reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was n91+icvuamzz/d i+r+p3 s.n n played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard93+pz mnna s+ndcvi/ 1z u.ri+ if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. S:3 zctm(jmfpfh 2g3c(7 yjd 8kp 8fg1fuppose 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 flowing in large leg arteries at 2 cm/s directly away from f(pj8c (kz : gmmy38dhj7 321ftpcgffthe sound source?   Hz

  The Doppler effect using ultrasonic waves of frequp v5idj fyd7(5 hb ga8kqfs,v4l*yx73ency $2.25 \times10^{ 6}$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.ovkjc0a/jtc3th 6j9*m 2jg zg.0 .vvs When the wind velocity is 12 m/s from the north, what frequency wil./gtckzmc2hjj 0v3s*0v96og.j av jt l observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spexg e l,s0:ah4eed 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 whedi9pgpn16w(v0wvb (pre the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the aird n96v0ppw1( bgiw (vpplane’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 atmosphe,jme1qk 4jaog nxyn2/xgfv r16a1tnf,/ 7ar-re of a planet where the speed of sound is only about 3,j x/-1avxgfm kq ta1 6f n7/4,2jnoreagy1 nr5 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. Deterhg dndi81h:p9e0nk /ymine the shock wave anglee0nkd1 p hyn/9g:dh8i it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 6l 5kv(tc(61ggsrwk l$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ovzsjo ,,4to,ad7 g )-jq ydcu8uerhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 128acdzju-o,)uq,o7j s t d,4yg–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 sound pulses do ;bfs0v.op yh+wnward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desig0v +b p.ysof;hned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves a:jmed:)3 /: vx7d/zmj yknvvy re there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consitoqh d1xx*6la2;yf -nsts of many plas ;xx1tlyna 6do-qf*2h tic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to th af+ tj+644npif- pkqxe threshold of human hearing (0 ++4fqp 64p-ftn ijxk adB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hea;ju;skg,dxs+ z0rz j8wiyey(eo94 v-rd simu8e0;z, g (;y+kwsx4y es ir-duoj9zvjltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the openv,4b(lvxodprftwv s5 l:9l( /, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it r :5dt(49lrs ( p,ob/lwvxf vlvadiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drop ybq(a ,+/ah- wuunay(s by 10 dB at 15 kHz. What is the powera(,wabu a qyun(hy/-+ output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over1x9szp, hs xz) their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at 9)p1zxs,szxh a distance of 30 m from a jet airplane engine?    W

  In audio and communications systpvx;q(*wubg1 8z 4jwr ems, 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 violishpm.k,zj8-) dpu cf-n is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamtmvu ;31p8 imcental fiuvcmm 8;t3 1prequency 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 vertical open tube filledc 9:syf3 feg.r with water (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 m and again at 0.395 m. What is the fryfcg3 f s.9er:equency of the tuning fork?   Hz

  A 75-cm-long guitar string of m gghoda 24t /6bk-7f 2vhqh9hwass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tensbva 7k-f4hh62h2w go tgq/d h9ion should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass w4n,l ck5yu((jxqzu+7mc h;c jas observed to 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 tone in 7boynq 5i m2utzhr6. ga .2hvn- o1)amthe 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 the fnqb h 6miyno a)t .h.72zu a5vmorg-12requency of the sound?   Hz

  Two trains emit 424-Hz whistle2. 6aw,5siejfh f+ enks. One train is stationary. The conductor on the s+ wjf h5 sfe.2ni6,eaktationary 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 approaches you is 538 Hz. After it 3os k2/ivorgc;f*x8 s3 2yltgx41qe npasses you, its2r 1e4oqgfsvo8 32y/sn 3t gxl*ixc k; frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to pe6/)*cynu lot1fo x7the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is p fu6ony1lt) xe7/*ocit going?    m/s

  Two open organ pipes, sounding tppq5upb0u 95on.pi + t;t3cm gogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lo m o+nt p5gp3t;pc.puqi5 bu90ng is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mc6qd. cqyqzto 2v6 vh0 /mu3(poves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, d/ztuv (cqqhqc 3yo pv0266.mat C?

  If the velocity of blood flow in the aorta is nte5caw*75wls., gr 6y2id fytormally 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 cel wdi76t afsglc*ywt 52ey5r ,.ls? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a m/ym -)8 uzrdh(g.yl kaoth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits hu/ r)lkm8-yz y.da g(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 9o09xjw2 hwt cmoth. The pulses are approximately 70.0 ms apart, and each is about 3.0 mwh9w xc2t 0oj9s 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. 12–3 7gc1rut8xs (z8d7dus8) was once used to send signals 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 resona77crud s8d1sxug zt(8 ting. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stand 6ext1 :cqvf-b j0 j;-:nbcdpding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living r0xpb d dv1; je6bc:cj nf--qt:oom 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 roditucrcn6+lj2 d5o (fa(y e;7vs,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,l2r67jit ae5dvn f(coc (y+u;” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of ang2s*ram1vbi lpt,x.y1e p1a- ;3r wubout 11p1,wv3e 2 lxyatuib-*1 ;pn rag.mrs000 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 the sonic bqy)5wh, s( n ssn)p2tvoom 1.5 min after the plane passes directly overhead. What is the play) p2s(sn v,5w sthqn)ne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 74ifpnjc9e,m8axmt m(r 3 y-h$^{\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