What is the evidence that sound tcjc0+j2.f4gxdks:8 q aaj xn3ravels as a wave?

What is the evidence that sound is a fo2 (vh 2ydui:tvwfh14hp+xo 9h rm of energy?

Children sometimes pl **1o wmosfxi)ay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be hemsx 1*of)o wi*ard 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 ex7:ji e2pqjic0pect the frequency or wavelength c 20ii:ejpq7jto change?

What evidence can you give that the speed of sound in fdi5i1feq *r5)y gw 2pair does not depend significantly on frefp d1 giwe2 q5*y5ir)fquency?

The voice of a person who has inhaled heli0izr9bbyp0 mg 0r:m p3low0: hum sounds very high-pitched. Why?

How will the air temperature in a room affect the pitchmaekv s7u.u bw -:h(:q of organ pipes?

Explain how a tube might be used as a filter tf r52p5cwuaz3 6 wsy+uo reduce the amplitude of sounds in various freqasp zu5w63yr wc5 f+2uuency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togeeg54q cc,4o* lvgc5 jwther as you move up the fingerboard ojlwqcge 4cc,5 *v5 g4toward the bridge?

A noisy truck approaches you from behind a building. Initialiwj2v 8c.hbw(-8bo w2z :dn glly 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. [Hint: See Section 11–15 on diffraction.]ci( w z28 n 8bvdjwhlbowg:.-2

Standing waves can be said to be due to “interference in spao6afnwp 4* mo9s0ox,o ce,” whereas beats can be said to be due to “int9s 6*moaoo4,fn 0wxpo erference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points D bg;my,w41ta) cebd4 sy,cy4 g and C (where destructive and ca 4 1)4y gbyy, c;4escdmw,btgonstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wo() a 0pmfcduw -gs+f4lrk in areas with very high noise levels have consisted mainly of effod 4+p0l mcsu-af(wg)frts 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 be thought of as a sxv rlgr05y.w;-1uuq1qe1io guperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of 1 0yu qlrvwig.gx15 q-oue ;1rthe waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the o(.o-ne9mih ou t6gd 0,lc6vnsource and observer move in the same direction, with the same velocityno06lth g( n6md9vou-oc ,e. i? Explain.

If a wind is blowing, will this alter the frcftq ppz( .z-3jt+fg5+w,vvpequency of the sound heard by a person -v(fj3z, ppf +qctg5zv t.pw+at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mv uz x 7,d580r,om8m cug+bii5o) anodonitor is blowing a whistle in fro 0 vroud bignodmu5+a ,88 ic5o,7xm)znt 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 l *nhji 5pe t3g2br a2m2wtd(a)ake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimta( *3mtein2hw)5j2apdrb 2gate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hey31xiwsd3k2* c-z 10 jessl ug hears the echo of the sound reflected from the oc - c2zdsx*s3ke11u3w j0 ilsgyean 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 wai tri kbf x**c*8q1nl7velengths 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 a0jp bczfi(9v5 foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–3(5c9fvj0pb zi3). 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 when4a t-5hn45mq5s k jhwh striking the water below is heard 3.5 s laterwht hna4j5-s kqmh4 55. How high is the cliff?    m

  A person, with his ear to the ground, s uv3d5/xb s8qlees a huge stone strike the concrete pavement. A moment later two sounds are heard from the imd5 bqu lx8vs/3pact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of d: + zrcjtufx-2istance by the “5-second rule” for estimating the distance from a lightning strike if thejrzu2-xc t:f+ temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensityoy9:lxzxsz)iq0 +c *l( c;c an of 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 a sound whol(++ zbn q+o( kyawwp7se intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers cwa;o-ywft2t( rk4 u),r 5 ,mxyd6xbw 0e)mfsproduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitiw)mff sdrr( ,xyowuyt-xkc ;6 e5a) m,tw402bes, not dB’s.]    dB

  A person standing a certain distanceid(w.r s9)ffj db+ j:a/-fmx qz6jpf3 from an airplane 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? [Hint: Add intensities, not dB’s.] i/ .w+bqx zaj(sj6 fmj pf r9f3:fdd)-   dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB,z (:sbmtdtdh2xv9ig779uup tih7** v whereas for a CD pvmsuxtvti* b dg97iduhh (9 7z2t:p7*layer 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 sound from a)tkc,nv7ia ht ,zozq 8) (;vlx person speaking in normal conversation. Use Table 12–2. Avlxka 7tt,qzcio);,z8n )(v h ssume 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,gz cq7bo7/ohnp .i:d 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 thntf7kh1qmf /, 9/zptj,2ytjseb9rx3e more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn /h2fp 9k f,rm sx9t3 tqnzjt/7, yje1bto 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 dBu7id - cz3ll3y meter registered 130 dB when placed 2.8 m in front of a loudd3l -zl u3cy7ispeaker 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 i2 mpfwtkm1v 23wle1v*f fqc::n sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hi*: mp:1 22kfe 3wfvq1wct vlmfnt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by jkfsyki/i+d4wjq2) 7 what factor will the intensity increase? Increase by a factor of wdfjs/j7k+iqi 2 k) y4   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitude5m/84gx pt5qz, drxgos, but one has twice the frequency of the other. What is the ratio of their intensitiespoz5 g5g/q8,x tdr4xm ?   

  What would be the sound level (in dB) of a sound wavetiiwot: ;1 zj0 in air that corresponds to a displacement amplitude of vi;o iz:0 jttiw1brating 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 120y tg sel/3*v ,awhoh00-Hz tone that has a 50-dB sw ,gvs*l aht0h2yo/3e ound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear ca6r0 ei8gzjgqocgd4ulkd+ *5pvkr hfa2+ 2.0s n detect when the sound level is 30 dB? (See Fig. 12–6..rui paso5 c 6+regvddg0l *+2k028hgkzq4fj)

  Your auditory system can accommodate a huge range of sound levels. What misw(/ g;5*4tnctbw bis the ratio of highest to wb4n*/bt5w(ic ;mg st 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 funddlk 3y(c dv.2cu zjhitn4 -az8)o n;+tamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mnd t y - tl84)i+c3ad.uo ;2kj(czvhznass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental anv /j ylk2q d)-4oxbz3bd first three audible overtonesko4 bvz- ) 3bdxl2qyj/ 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 th*s l*.*x5f 8kb y mkzzpsuvo/)e top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubpbu*sm s /*8xzv)o zfk5 lyk.*e?    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 spannino tjnj-*ladh(m.: :cgg the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes red(htn m:. *o:j l-jagcquired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What wsxsidvete k ,w/)9 +c(ill be its fundamental frequency if it is fingered at a length of only 60% of its original length,c/t)s9xdksi+ v e( ew?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middl4iajl t+6ou/ re C (330j6 r +atuo4i/l Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C s*tyj0 z usbv)-aud1z00lj ;t(262 Hz) when the temperaturedvz)* 00uybsuasljz; jt t10- 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 20xvez5xn/v fckb3v7wdhw b8q m8 lfl26,0 06s f $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece oz xnnhoc . u+kw9.r3/zf the flute in Example 12–10 should the hole be that must be uncovered to play D above middle nuzzx3hw9 .. +/k orncC 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 .e ff/ xmr9b rn(b(t r+fhh1n,not at any other frequencies in between. (a) Show whyr bfemxb/tn9+ f,( nrhf(1h. r 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 opbkw decbuj.atgk0w7p;+146y en at both ends. It resonates at two successive harmonics of frequencies 275 d4w7e+agjku1bwpb yc06 .;tk 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 ayr9p942 ah hr$^{\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 audible ran+-urxk9rlmr q2nfy38 l;cdq2r8h9izge for a 2.14-m-long organ pipe at 20 r rhq+8f 92m;qr9zidu3klry-nc lx2 8$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ie 18yzn7ob6 d4p;exols approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the ;o18lzyo b76xd4ene pfrequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings w4x lkg;k crd0n*uk-(, one of which is sounding 440 Hz. x d0cwu;4gk*-rlkk n(How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) hob /6l6hqgm2.xcps-,e1 ev y r9o5j pand $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatelhogww7lsntg s* :b4: rlu6c0c dq472s 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 p 7 r4:0dgln s2lblutw* sc7q: c6g4wholayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when s.guvz * 4 uh62k30md+vjfcghaounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork.hh 26+ucv0gmkf vagdu.*3 zj4 What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sf58 uol5 69njdjtz,rsame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eql,f5ntou 56s9zrd j j8. 11–13.]    Hz

  How many beats will be heard if t77f ,s*rco oqtwo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other atc7,r o*7fstoq 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; m1-3vgk,:nleitu q ) mwhen A and B are sounded together, a beat frequency of 3 Hz is heard. Whengmeqvlin3k u-:),m t1 B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker au8lk*qqubho)(tix ;u53q c 7x l/v.wend 3.50 m fr3o8)qu(wuq eh*xltv ;qcxik/ 5lu b.7om 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 vibrail z-ofymn c1083uxf;ting at 132 Hz, but a piano tuner hears three beats every c1f 38 0nzmixol;ufy-2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 mzatgr)7d f (1s in air. How many beats per second will be heard? (Assast7 fdg z)(r1ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequent3p zc645wpmscy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you cs4 z5pm3w6tpdetect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still2m13x1oglz u g. What frequency do you detect if a fire engine whose siren emits agglu1z3xmo 1 2t 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-Hz source is moving toward you atiz0ns,eyq1 i ho-7.:5epgf pkzfc6 n 7 15 m/s versus you moving toward it at 15 m/s Are th50ec7,p.7 niq :yzh16oep fnfk gz-s ie two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Woa nsm.r;.ny.gw4gl +s09 irlhen one is at rest and the other is moving towars g0.iw9s rrn ag;+4lm..lyn od 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 sound waves m af/ajz/ f/9-pd .m j4jo.lnwat 50.0 kHz and receives them returned from an od/ffazo jpjmjw 4-lm /9n./a. bject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wallz+;qod xl2cr*/d r/sq at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave qrdc ;qs/r2l*+x/odzwith frequency 30.0 kHz. 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 moving flat 5z-;fz6j3 p4 vb7vzmt+ a wrmptrain car at a frequency of 75 Hz, and a second identical tuba played the same tone while at retz- 5vwjmzf7p6rp3 4z a;vb+ mst 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-floxa7 jadx9ah a(s t)w3+zr3/kk s xib5+w speeds. Suppose the device emits sound at 3.5 MHz, and thdkwbxi +s a5aaxh3rx3 )kj7t+ 9z/(as e 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 wav i7ys:79gu,pa 21l bajf-d viehay a8 /yw90pbes 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 frequency 570 ie 10 ra kcswf*t)zc2+Hz. When the wind velocity is 12 mt k)c1riz*s2+we f0 ca/s from the north, what 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 spe)c/ygqzopbo x-,wj p2-xg7j 9ed 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 e.k+mf o2x,z-xx dn4r where the speed of sound is 310 m/s (a) What is the angle the shock wave makese-2o. 4x +nkmf zxx,dr with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a pl+6sucsmu ux u08 4/ *m.wsqxuwanet where the speed of sound is ouu s8w uwxqxmuu+06s/c 4*s .mnly 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 the8e0ttp3d 1nnuq i5n4 p ocean. Determine the shock wave angle ipqn n1u 0p5nt8etdi3 4t 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 inyc+d- chl0;gerggw 1 /i4r.$/theta$ 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 above the ta4f63 yiowe5ground flying faster than the speed of sound. By the time you hear tyefw6it 4ao5 3he sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 0+x ixwdw2a;- m +fj7spnaqllf- 97aq20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If lf+ -+;x2aplsn-09ai x 7j 7wqfqawmdthe maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves l*/ur(flale03)wcw sare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe s nt78bzz-hlvu.39y5xu2o+ f mrm u*v gymphony. It consists of many plastic pipes of various f-8rou9 g*my v7n xuv32bmz.+5lztuhlengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the t6r ppc:es c vkj8+4s4rhreshold of human hearing (0 dB). What will be the sound level of 1000 such mo+vkr p64rcs s:ce8 pj4squitoes?    dB

  What is the resultant sound level when an 82-stu0.s eu4if0of2tv2 dB sound and an 87-dB sound are heard sfouit 4f0s202seu t. vimultaneously?    dB

  The sound level 12.0 m froq-b:py60pxulgnky- 7s+a et.m a loudspeaker, placed in the open, is 105 dB. What is the acp-y: 7 0pk6-e.xgaqub sl+nyt oustic 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 Hz. The power output dropshm,lq*0tz(l c b lcqm,lzth(0 *y 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices m70e 1 (twtnpn92td mlover 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 effewtt7 etn(2pm0n m1 l9dctive 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, vqy*g1io h5t +yxz0)rthe gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to t38 ok a+;hecga 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 betweentc i*b ih+)ls)r bfo(1 fixed points with a fundamental frequency of 440 Hz and a mass sh lfb )ro1( *)iibc+tper 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 48xsn))* ii7f- io:ohijx mxuinto vibration above a vertical 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 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-sn*o ij47xi mf )ohu)i x:xi8 of the tuning fork?   Hz

  A 75-cm-long guitar string of masg d*l:nqi8cc 3( r;aixs 2.10 g is near a tube that is open at one end and also 75 cm long. How mucdnxiqic:8;l c *g3(r ah tension 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 was o9s/1sfs9 f8lf zsgx)s bserved 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 the 500–1000-Hz range coming from t7b k dc)m: 8ov56irmxfvn0,vy2yf6wvwo sources. The sound is loudest at points equidistant from the two sd5r6oymv nf 72 8v,0xyw:fi)c6m vkbvources. 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 frequency of the sound?   Hz

  Two trains emit 424-Hl 7padgp d91n4pk,t1o z whistles. One train is stationary. The conductor on the stationapdn,g4 lk 11p po79dtary 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 ap;x (lx;w( gi1wmx rn*pproaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity) ;wxr*wl i(xmg(n; xp1?    m/s

  At a race track, you b)kpl* 5ff0b3c (ux)3mk 8gvsw w(smkcan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cac u3p gmxwk s sf(b(fb mvk)k*3850l)wrs. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frn zeanq9 o0xv 83v: n*e0swdc,equency of 11 Hz. The shorter enq,:vd*no ns9e0xavc 08w z 3one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pa(zf x,rz-i va(st 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 ,vifx( azrz-(they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s r1ez; xb/daja*dg3/y what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along trjbae x 3 1*/adg;/dzyhe flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a motl5,4 dh(h.en ,tvso fph at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that,5ho (sp tedh.nl,4fv wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. rl r/ u+(iutkwc3o+ m2The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp retrr3ut+ck o2(i+/ l umwurns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) e lt1;/5ta uxsu 11fppx5 vo(swas 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 resonating. The most popular alpenhorn;5(1/ls ut1ux pv axfts5 pe1o 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 sterehi vka: :- 6w7fmtz3d 5qmr9qho listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m hk-rf6 qt mv 5zhm9hqwi:3ad:7 igh. 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 te +za0sc,1rx rods,” involves a long, slender aluminum rod held in 0 az1rx,+tecsthe 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 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 m0k (xn)qnqf3 at a frequency of abok f0nx( 3mq)qnut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 21 u oet1z d:zkfzev,r+)xev*ql8 09d g.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whateezql,g0x8ke:d 9z+u r1tzvvfd1*)o is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1 xhmkvzn 9)4i75 $^{\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