What is the evidence that sjhgt(t w044w/wxc5 sn ound travels as a wave?

What is the evidence)np3of3 pwax- that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to tcj* .t6vfhi 3(do dq23gxo:fihe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–(f6fo32 o. t :3xidgh*icdjvq29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, )0/,nzalzf)gsm f( gmdo you expect the frequency or wavel0/z)n)g(azff, mgls mength to change?

What evidence can you give that the speed of sound in air does not depend signif,vb,9-l/u(st / jrtniumuzh9t. vc0g icantly on frequent/ svu 9rlc ,tm. nuj9t-ib gv/uh0z(,cy?

The voice of a person who has inhaled helium sounds very high-pitched. W y8: h01 4pmgyy5ua3kbju5cqphy?

How will the air temperature in a room affect the pity u he3 yma3dt*iar5)3ch of organ pipes?

Explain how a tube might be used aspy9jl)8se g2k a filter to reduce the amplitude of sounds in various 8s jky2gpl 9e)frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you moveg3ia :e3vl iw8w)n( pl up the fingerboard toward the bridgelw ne:3 v la3ii)w8p(g?

A noisy truck approaches you from behind a building. Initialmu 29kpmpw5g ye; 74gvly you hear it but cannot see it. When it emerges mk2 g49wy;v5u egmp7p 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 bepoq:d *;ebw.- jmf+ nt said to be due to “interference in space,” whereas beats can be said to bwbpjd;t* oe:fm-nq .+e due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thelo wd hv945zodftdrl 0,1cx)+ points D and C (where destructive and constructive interference occur) move farther apart or closer xfodwld +v59t l04c)o, hd zr1together?

Traditional methods ok* k) jvq(hai/x:qjv -f protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. a j *v:/-vxh ikq()jkqInstead, 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 be tiqs4a8324 n+fy1 cc kgkcly9 ghought 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 the two componkql8+ 49y kai1ggy ccsfc234nent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move 7w n7r/cuvrq+ nam +0uin the same direction, with the 7m ununq7+cr+ vrw a0/same velocity? Explain.

If a wind is blowing, will this alter t j ncmrq63y ,plm7hjy93(t* rvhe frequency of the sound heard by a person at yvjml9rp376j(ht 3c*r , ynqm rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions z28e 1qn* siruof a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position,8*ser z2un qi1 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 listend) m+q1fo d.oeing for the echo of her shout reflected by a cliff at the far end of the lake. )eoo+ f1.mddq 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 his ship just below the waterli 04ucyh:r/tx ine. He hears the echo of the sound reflected from the ocea4y: 0hxtc/i run 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 ai8 oajxxe 4.;hkr 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 s+yso) d q eh/e2rm+m mqj)uh)sf;+q9cchool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–3ud;)m erm)cqjq )+ss++h 2qo efy/m9h3). 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 it makes 9 jyt,rprl5lkxv+l)9 qs e,m( mv4 8hgwhen striking the water below is hea el +,8 9gtpl (9v4vmqrr,shxjl)ym5krd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sto76ye lpl 6-vztne strike the concrete pavement. A moment later two sounds are heard from the impact: one tez tl7v-66ypl ravels 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 one mile of diss 7h8 k4fl.cpgtance by the “5-second rule” for estimating the distance from a lightning st 8 hkps4cgf7.lrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity orwda xba+:0dme7l6y06wb9 f lf a 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 ,xb, n 0: qc*hus5n- cozwf:oma sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d0x12orwisu( c B when fired simultaneously at a certain place, what will be the sound lsox02(1uc w rievel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from ugx84 ts:q6l2cpo/gxgz x6it h kekh *,-6q/aan airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Wh uhx/ekoqx: xt,6kgits/ p h2g-q * 64zalg8c6at sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noe+0g5 /0vh/ku-rasj:- ro cp3vxz ji wise ratio of 58 dB, whereas for awj sg/xu- oh/+cez0prjir-v 35: k va0 CD player it is 95 dB. What 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 souxs+fb,jfz-j xes5:b91j j py3nd from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the fbf:jxbp1j j5s- jz+ x3 yse,9mouth. $\approx$    $ \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 ara3 q9ee2 fhk+pea 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, wh(b4 /k lke6zadile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect ez6/(kkl abd4 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 y5vst18 ufhfui8 y1s3i6zc f;meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. f yc1i8ufvu15t8s;yzh 6i fs3
(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 oe8tns2 p/on9en1p c3detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds tpeneo93 21s/no8p c nwhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what 2m n 2f3omn ;y8gl*bruegofp 5d+:*bzfactor will the intensity increase? Increase g 2+*p3no2 med*b zmly8gf; :ofb5nruby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes,ih2rkm 3h3iv,-oksc 3 yy.j f6 but one has twice the frequency of the other. What is the ratio of their intensitirhvk,cij- .mhfy i3oy263s k3es?   

  What would be the sound level (in dB) of a sound wave in air that correspond7; svjeafkrc+57l qz/s to a dispcl/v fz+ rea7 j;ks5q7lacement amplitude 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 a 100-Hz tone that s ayhx0np1+q t;)*pep has a 5*xs q0+thpy )p1enpa;0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear canrc+l8gqns6 *n detect when the sound level is 30 dB? nq+l 8r*gcs 6n(See Fig. 12–6.)

  Your auditory system can accommodate a hu n 2xmioq igk2t5(9j3kge range of sound levels. What is the ratio of highesjgo 23tx k(knm92q i5it 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.jvb (dvx8mt): The length of the vibrating portion is:vxmtb(8 jv )d 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 s7phmq qp; 9lvk/t)ld gbcz q,309ms 6the fundamental and first three audible ovqk6m0qt hm9l7d3lpc, ;bsgzps 9q v)/ertones 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 you expect from blowing across t27td5t r*b)w 2d:pucrp+fl xghe top of an empty soda bottle that is 187tl*pf 52: rurc 2wd +tgp)xdb 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 11,l7sf lm;i-wbt lhjrange of human hearing (20h,1i 17lbsj-fmllw ; t 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 5 1ko)7i2jql yi;q*z4 5z muw7zdretbof 540 Hz as its third harmonic. What will be its fundamental frequency if it i;id)miz q5 jwzub1*ky7zt2e54 loq7 rs fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abox)he1su+ rs9r +vz2 ztk) sm+m3ohcj)ve middle C (330 Hz).m))o 2ru+rmcez s )tjh3hxk+ 1 sz+sv9
(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 lengi n hu*ym65a5jth of an open organ pipe that emits middle C (262 Hz) when the tempera6mi*5jny ua5 hture 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 a(a4 *j2hk)wg ogcgaoewso + 9*t 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 shgq*gq-x3 niiayb8 b 3 +;8svanould the hole be that must be uncoveredb8ag g-n; 3an*+ xy8sviib 3qq to play D above middle C at 294 Hz?    m

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

  A particular organ pipe cadf :epm7 i/d)xn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this i 7d dfmep):/xis an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tubeqp: 5t ggvg9.o 1.80 m long is open at both ends. It resonates at two successive harmonics of5g :g.v tpqgo9 frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 +a 1 agg()1u hw43xwaqn9bl 2 ooplb0b$^{\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(cq v) a1ephe+yjj.-f the audible range for a 2.14-m-long organ pipe at 20 (yfej 1ah+ecj) -pqv.$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is ajvz 70 ,sw. bfc4nu/xopproximately 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 fj/0o4 su.wc7vnz,x bin the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat +tp/rb 1sli)3ni bpdy8k)ji via7 4r:7a:dbg every 2.0 s when trying to adjust two strings, one of whi)av+sl n b irbpg k3)j:b7d/ra84i1i:i7 typdch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequ p/b b3-snt8vgency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 20jg+xpa) ( yvfox 3wykHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by y3x w vy)a 0xg(jfo2p+humans 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 bvzv8qtg+wd5;f,x2 (5xa lu cveats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your rea5 v5fxd;tacuvx8w, gl+v q2 z(soning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in oneg6q:h(d yeg p m0+c8ne string is then decreased by 2.0%. What will be teq 6edmpy( hngc g80+:he 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 playa *lt,ok2k/bfgcmnr gx, y(3* middle C (262 Hz), but one is k 3(nm rfcxk**g,,b/l otg2ya at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fop4tz7w.o7lhv*f h x7c rks, A, B, and C. Fork B has 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 together, the beat frequency is 4 Hz. What are the pos .h 74 vtwchflzp77o*xsible 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 g)ze,9e d2boyr sr/4uw0x ga8 apart. A person stands 3.00 m from one speaker and 3.50 m from the otheg8 e2arxw)9byus/o4g ez,0drr.
(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 tuner heae5oz8mx*9j5*h l ;,,iy wfhyo:yoj evrs three beats every 2.0 s when they are played together. (a) If one is vibra*homj,hiyy o5o8 z ;ly:jew x9v*5fe,ting at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m ; 4ez svs)knfrwzh.(m6n j 9yj dk816tin air. How many beats per secje1 4vtzsj6m y.hnsz dk(n; 96 wk8rf)ond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when duvm2s :d ;b ejhpc2wy2 pjp)h-9t9v.at rest. by;9svwpejhv22p:p h 9ddu2c )mt .-j What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you d hg76, yz an7 5;xz9pb.1x:pn pctz., oylhkoeetect if a fire engine whose siren emits71bl9 tk :xg5nxzhzy.p.oo az6pe7hcn p;,,y at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-nob8qbei:i,q 75pm uol. /2dv Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequli qnbqp d/o7 .v2 beou5:8im,encies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Ww(w()zs 69dfn* hx hgqhen one is at rest and the other is moving x*sd ng f9)zqh(6wh(w 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 ul+63- .iy 9(hct 5mm yqqkmcbxrtrasonic sound waves at 50.0 kHz and receives them returned from an object mh5 cim .c q(6 y+qmmy9-tkr3bxoving 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 slq9p:h2m+(vnz b;svx,n gi ;g5u*jthpeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency do:p5g v;t( l9hnj*b2hm ; vquxz +gi,snes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentsw js ,09nqcnk,2hpuruxa,86a, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second qua8 9, jhsxracn,6 w,20k upnidentical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flowc (r:2xdkf: ei speeds. Suppose the :f xid(ec kr2: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 the sound source?   Hz

  The Doppler effect using ultrasonic waves of frecn-t;rb lmyp 434 zp,ui :vzu2-i rro-quency $2.25 \times10^{ 6}$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. Whewmuxd/xlz i5x vj8p /yf*:9d, n the wind velocity is 12 m/s from the north, whu 5/f i,x8d*l xp/vzj:y9dxwmat frequency will 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 speed at 2ta. j8bsa*c n4gt s)-q0 $^{\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 b6r d4r j8yci+:a ho5jsound is 310 m/s (a) What is the angle the shock wave makes +h4robj5iy:c ar j86dwith 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 planet where the speed of s29cy8kem xf5 nfx zl;:s9+ spvound is 9+lp vsk ;m9c8ef5snxzf:yx 2only about 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 shb)b /ko+xfrx qpmq)3* ock wave angle it )k rx3bqq/+bxf) opm*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 da92il ;dxay1hfog..k- sc -d$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly over. *r. ;f ighlyp5hh*pp ;j)e .fw2qhzmhead 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 q e)5hyzpi lp.hw. .pfgrf;2jh;h** m2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sendx2+8u3 xxdwfo g.1ml rn ykm-rkj4,3ls 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)? .3jlmudwlg2n 4x xk3+1rk m8x,y - for   s

  Approximately how many octaves are there in the human audie,ih n*gxfn;yr 4h :0o ia22dzble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of 1esc 95 cth0y-2,pok,dsdr+9 mbllkhmany plastic pipes of various lengths, which are open on bo-dt2r c1ks9lp0 ,mk s d9lhb,hc5+eoyth 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 clifx/a3ayfx- (th* 9b mra /:kjose to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquito :-ja9 yharf/(xk/mxfbai 3t*es?    dB

  What is the resultant sound level when an 82-dB sounds q/34zz or2q9alyhi ) and an 87-dB sound are heard simultaneous) l 2zr/43a9ysiqoq zhly?    dB

  The sound level 12.0 maog2;/f ype , fljt//q from a loudspeaker, placed in the open, is 105 dB. What is the q2/oap,/jf;f /lt gye acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000+ fkjx3 smxd2(+bs 3pq9 tzju0 Hz. The power output drops by 10 d3spu+30zkbsd+j 9x fjmtqx( 2 B at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovrt1vh f6qmrw.a.b i67 ) qxxu)er 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 effecti)r 6x.f axbiv7quw16).r mt hqve 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 sv28 qs4s5lc rvozsh x22sy t,(ystems, 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 tuneqs-mn)nri1 3iz d(+o a/zsoa1 d 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 syp,16yw/s6eoszy./s zi bje6u k+t +32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per units+w1y6zj +66soie se/tu/z , y.kbpsy 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 filled with w l(vg3orqxj*0 5o+vup ater (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 frequency of the tunipqv j5lo*(r30 + gvuoxng fork?   Hz

  A 75-cm-long guitar string of x mg u/i(sq1vm )b1s-rmass 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 1-s rs1qbm mv giu()x/is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t4wq4sdf 1+clm o 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 the 500–g i9w5c2rj+vj 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 j9r5gjci w +v2that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is s,-pe0s4yqrklir 8m v0tationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches.i0rq,-ve s8 ml0yrk4 p What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz.qg6ox(sy3h3 t After it passes you, its frequency is measured as 486 Hz. How fast was the train33(tgxyh6 soq moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listez4 hafaaj); 9rning to the difference in pitch of the engine noise between approaching and receding cars. )ra ;z 9hjf4aaSuppose 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 ad3ttxq:+ot w rzll*3; beat frequency of 11 Hz. The shorter one is 2tld+tzr:t;3*3 l oxqw .40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad 9nsiaytf:z 3 7t3n(j fenpzx.g 44n(kcar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listex(j z. znt4y(gns3 n4:3 7 efipktf9nans 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 12ywkna 3. wefis normally 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 the .fw ynw13ek2a 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 to 54 fhs5 f4z(;r78wrhbgucf cm4m9mqoward the bat at speed 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 th857 h 4gq(r9 f54c hfbf4smoz;wcrumme moth?    kHz

  A bat emits a series of high frequency sound pulses as it app.jq,wxldpqba s v*2 o*c1 /ytf,*(ipproaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat s*o c pt,/pdj q(yl*.qb2p1w *a,i fsvxo that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sign+7x3 nhky z13+-pxib clj :mzdals 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 alyl:3hk3 jn z+zx+c- 7pdx mi1bpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the r56:jb0 a ta1w xgsz8zpresence of standing waves, which ca:zb 1a5x6z srgj0atw 8n cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration7xtla; zs /.mv, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For lx7t.;va s/zm 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 o1,cjtau /.-f-cho0qk2jz6s * so d4vs6vcmba frequency of about 1000 H1to, 0q2dcso/o.ac-6j*su h fc6 4kvsvjmb -z z 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 obsewng 3xwyo0.o 5rver on the ground hears the sonic boom 1.5 min afw5o0 g3wxnoy .ter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ( bn gn*tzudm+ 1zm+0zis 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