What is the evidence that sound travels as a w6amba tdn6 20cave?

What is the evidence thbocpme+ nzo a.b)7.*eat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string top4 owjc4bdf-vp(q8s ;:l0s(pi ywv4w the bottoms of two paper cups. Wh0cvpw8d-qo lsp(f4s i ywj p:;vb(4w4en 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 y*x phe.t5h3r9p5pzt into water, do you expect the frequency or wavelh zp3hty*95e.xtppr 5ength to change?

What evidence can you give that the speed 463i,hp t pdpau3*yvb of sound in air does not depend significantlbuyhp*3ppa 34 d,itv 6y on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?jj gj pu3w.;p5

How will the air temperature in a room affect the l7 bfgxy 8q5b50dbxl9pitch of organ pipes?

Explain how a tube might be used as a filter to redu/y2bv -i 6tbynce the amplitude of sounds in various frequency ranges. (An example is a car muf2nyb -6i/btvy fler.)

Why are the frets on a guitar (F,xida pl+6i ;nnv 0o5fig. 12–30) spaced closer together as you move up the fipfn,a;ii5 o+lx0vn 6dngerboard toward the bridge?

A noisy truck approaculo3.5drm *d qpkv z v1jn8p15hes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more1 55mu3d1 vpj nv8*zrp lqod.k of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacee w(zeu-72nr3 5ktrah ,” whereas beats can be said3nw5rz-7kh eea( 2 urt to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points kh9+cwkacjfkjvg)5 u--ww * .D and C (where destructive and ckc-.g +kvu5fak w-w) h9*jjcw onstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the heaz ynoddszu:ni1 3:7z li6v56f ring 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. 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 czsi1zf5 67oidn dl 3:y6vnz:uould adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave 1 6zy1:.snouo(vepye can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. pyes o1o.1zu y(e6vn: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 ic as( 9fong4maov )hx89vu:53. tkkhef the source and observer move in the same direction, with the same velocn8 4 mtaoa)sh9:kx35f .he cgvvo(9u kity? Explain.

If a wind is blowing, will this alter the frequency o83 ilx x8dwvfv1o+l) ff the sound heard by a person at rest with respecxv )lfvo18xd3wif8l+t to the source? Is the wavelength or velocity changed?

Figure 12–32 shows vp7 7y 28lylehr6ry w9bk ,7ceuarious positions 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 frequency for the sound of the 2r8elc y,7e6p7kh wu79lyb rywhistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the 3kpunh7g62z necho of her shout reflected by a cliff at the far end of the lake. She hears the echo g27nz h3k pnu62.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shig1pyhu3;1 gbzp just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below g;gbhyp1u 1z 32.5 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 waveleng k8y ny0rxwsk 6t*imk8/rw74 cths 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 jcg+w ,mx5q8poust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awp+owcx 8gq5m, ay (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cli(qsahscd up 1 i+f,9)ky,on-42(nxz ksij .ik ff. The splash it makes when striking the water below is heard 3.5 s latak iyh1+((zk9u24.fx) nso p, sndki is,qc-jer. How high is the cliff?    m

  A person, with his e v+w5i+ *nxzdosg 4ja6ar to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels ao*x +v+z 64sng5dij win 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 jml or+6 f6/n*8cc nv)azcl1lmade over one mile of distance by the “5-second rule” for estimating the distance fronm66c8v1lalnclr*+)fj z/ co m a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 4)h gitqr,l(gdB?    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 soune ;shgr48wbbez )-1m4(6thtll (q lfud whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d ur. ih u)mg0kyoe-n ;ohwfv.i j-2.g:B when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add h;mun.e0jr-:io wfg-k)yhu.ovig2. intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equalc)7clx/ouxcse7fe jt4us, :/ ly 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, nos/x4cuc:x oecf7s7ju)le /, tt dB’s.]    dB

  A cassette player is said tonr snf(u)x+vj6e85y2x4inq ouiv3 u. have a signal-to-noise ratio of 58 dB, whereas for a CD player it usf+48qnxui)j2 vo 6n3e(vun 5rx i. yis 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 syb u6 n/tbln)5-p5k;6 poi yihound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphe;yit 6y hp5n5kupb/ilbn)6o-re 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 s4z3 z*tq c/tcetrikes 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, kzfk 81/+eobaw9et7s cqx- 2c while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibelsbcw1t-9zek+x f82s 7 kq ec/ao you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in xjnma-,0 yt1g front of a loudspeaxgm1y,t0 -j naker 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 85vqdd*w2syl1 ;z,o0.cgsjp b5nrr m of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by thisq0v nob 2*8dj 5rwp yssl.m;dz1gc5r, amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave i0d2 bqv5qsx x0 8shmf3s tripled, (a) by what factor will the intensity increase? Increas2xshbfq md x38s5v00qe by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frer qq:pdrmu;3d5wf6 3 aquency of the other. Whaf ma3r q5 w6dup:dq3;rt is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air+nuvs2 4((r0du8/k) eqyg z3yzlw vse that corresponds to a displacement amplitude of vibraqkg e8wzuy3e) /s zy0u2 4l(nsv(+dvrting air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must h z*+ed/uk3mw: iub2+0m uvsjk ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level?s : mwz+ek m iu32ub/jvd*k0u+ (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whe6lml5att, t6wn the sound lt,5lt6wt la m6evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What.7h:pm;ij(cvc a99bv5 ok url is the ratio of highest to lowest intensity i(p:a;h59rcku jm.vvl7 o b c9at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length op d an+e178ltkf the vibrating portion is 32 cm, and it has1adt ln8p+e7 k a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm uqo, fhw,w 5w1jrx 8e:long. What are the fundamental and first three audible overtones i8u:rhwoew1x, 5 wqf, jf 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 frequencn4gc 5m xv4zkkuf5n*0y would you expect from blowing across the top of an emptyvmz* 5n 05 x4fkgcun4k soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the ran4k w .v1i5nzq1gpac1-xls4oh.y1 bnpge of human heph1.inz4 1 kn 5l-v y1x4gbc.awp1qosaring (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonjnncx/n a 9.-xe- 7fa* msd*wxic. What will be its fundamental frequency if it is fingered at a length of only 60% of its xn*n.-msc7xn a x dfej/wa-*9original length?   Hz

  An unfingered guitar l:r2 tz xczf11mhh4h5 string is 0.73 m long and is tuned to play E above middle C x tzr hl1:154mc fzhh2(330 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 685 vviq9s u7ig*rwjwiv , p.hpipe that emits middle C (262 Hz) when the temperarp qij*75i sv.wv 8, h6wgviu9ture 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 22h5y uaa;i)pye gnu1/0 $^{\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 hole eoni9qm/zvjxp2:sw z9 9f):cbe that must be uncovem:2sfq9vj epz c:/)x ino9 z9wred 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 can resonate at 264 Hz, 440 Hz, and 616 Hz, be t8rkq)b)e-z x*pjqdxi-:w: w )i(ceut not at any other frequt)p z -*-qq(x)w)wki ecje e :r:id8xbencies 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 resonates at two su9gt g 5wke+3 d5ws(.puyd -bgmccessive harmonics of frequenci+py-bkw sg5t3g ( g.ddme59w ues 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 h p h(e)5pg-hqrqf9dq- 7eg d in3k+/a$^{\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)so rv 5c )6juqie4rz3 within the audible range for a 2.14-m-long organ pi c5u)rojv r64zi) sq3epe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cqgc.z hbj /(z-m 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 wa- gbzzj.qc/ h(ves 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, onekho6ajx*efryl2 ,c b+ *: djijq +r4,o of which is sounding 440 Hz. How far off in frequency qr 4o f+y*kj jjxb*dh+c,ir:62 eo la,is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andv)z1xuxi5 a/t $C^＃$ (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 anothe x);9w3 mz*lg uib.b*mygyy*g r (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when plam iygxgb*w*zy3y ) ;g9b.l*umyed 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 when sounded with a 350-Hz tuning fork and 9 2(x/q 2brg, x,idiguebeats/s when,d x, i2rq 2b/(geiuxg sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Tq1 n* o y)0htm(hryq ;:bfhw6xhe tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the twhr)h xwm1 t:bonq6h( y* q0yf;o strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical a-of .54m7ykyto7o axflutes each try to play middle C (262 Hz), but one is at 5.0°C and the577-t.oa oomafy4y xk other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. 5tgh(vwrx2p9 Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat freqh w5 vx9gt2(pruency of 3 Hz is heard. When 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 standi q3 vkueer8do8 msf p i.*ws1r*18ln-s 3.00 m from one speaker and 3.50 m from tqsiknf 8p 8rm*31 vurd1l. e8eis*o-whe 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 tuner hqqoi galw8.8;ears three l;.ia8 8wgqq obeats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 id)nd; ba:o8km in air. How many beats per second will be heard? (Ass:bod)n8 kadi; ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqs rlz9dbk+g 2 fmt46 n5rrn8b-a3bhl :uency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you m+l m 32 fl45hd-nasb r:rzknr698tgb bove 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 detect i2,8ggj: p zkpg 3gdkfoax:i66 f a fire engine whose siren emits at 1550 Hz moves at a sp :6pg:2gz,3pok af iggxdj8k6 eed 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 towar: eaf+tbr16 ) pjg,oip3 wmz4gd you at 15 m/s versus you moving b+6)i,ojz f14gra wgpmp3t: etoward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. +xejt w h:5)gktv cq2y+;bqa.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)q.+t:yjw;x +gv ahtqkb52ce the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anm,bl*nfqed.fa4 h d6a rhydh6*2.jx/ d receives them returned from an object moving directly away from it 6h/,mr. *dh*e 6qa yl2jdxdfnb .fa4h at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a esvaw47ez8 2i wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHzee4278 vaiswz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a ti qh(tf-kd db1: .:zskav dw71uba was played on a moving flat train car at a frequency of 75 Hz, fz q- :hsidav17kd1k.(:wb dtand a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter us(a g98;dh nnpl2 r4ooles ultrasound waves to measure blood-flow speeds. Suppose 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 p2 o o4l;hrnd9 ln(a8gif blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves o l+ro3 dwfp*;uf 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 f) i1qhzi f1w*4 idgn*xrequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loca*qn iz114 xh f)*igwidted, 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 land7 orpw98z njh- if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speedi1l; yrduv(1lvey: p/hfhc5 2 of sound is 310 m/s (a) What is the angle y irdhlh; 152e(1f cuy/lv:vp the shock wave makes 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 planet wh:9o87b8lvru82f0 lfg cv klwv ere the speed of sound is only about0928ovbfl8fgl7 r v8kwuv :lc 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 sy/hgmih 7y9z) trikes the ocean. Determine the shock wave angle it produy)hi yh9mg /7zces
(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 ncc)(yb7y 2md)via2 b $/theta$ 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 h**nvh ,wd:;mlaooi( 1.5 km above the ground flying faio*nh *h;dmw, l:o( avster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. 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 rvzdnhjgy* ,w v7:4 pc4.k( w93iqm cwpulses downward from the bottom of the boat, and then detects echoes. k im4d h cg7, qc3jrvwyp.:n(w 9vzw4*If the 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 ol6l:ipwb1 lz t.8ehbj70b,tx ctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphgs2:y :5yml v3sxvr g (:3,p bybwm(zgony. It consists of many plastic pip(px2v53::lb rw :y3b,vy(gmg sgs ymzes 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 souw yfx1-;bv1 ;pouj hy)/o )jfev0vo/ und close to the threshold of human hearing (0 dB). What willwy -;yvupuhjo f0x1v/j) b)eo; 1 vf/o 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 are8png o)bj6ah; heard simultaneouslb o;8g n)phj6ay?    dB

  The sound level 12.0 m from a n,d142nip ocp2 c)m )z3btj veloudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assumi4ze, )t2ompi p31ccnvdn )b2jng it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 100, ih8lhmf; ba2h7esj (0 Hz. The power output drops by 10 dB at 15 kHz. Whatfa7jlh h8i,(2se;mb h is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over the- y1xgb:z vqpyhieq1n;k( v d25hew3 :ir 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 unprp zv(5y q2gvh 3h1 d:ki;neq -bwe:xy1otected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gairi slc)7y j(l5n, $\beta$ 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 t fd ;gdnm d/y1,(7buwtuned 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 ae ej.to ans-,cd:brrd2,ac- ; fundamental frequency of 440 Hz and a mass per uaado,-:c-;erbrt se, n dc2j .nit 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 vertici.y qsx/s-m 6rq- 9bc(8ipv vpal 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. Ws86iip/ 9 cv. p-r (my-bqsxqvhat is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one jreiyv 1fuvg4e fg4h* +9ns: -end and also 75 cm long. How much tension should be in the string if it is to produyg4n*j fvs:e hrg91 - vf+4eiuce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsw m ;+cc rcl o:a+2zpufq3+xk/-7vowf erved 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-Hlog5kgk/jvmgn o3p) ds- 82 4iz 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 abou/s- )m2oglkdi8njo35ggk 4vp t and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condu2 .yfzf lswt5mgq-d08 ctor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is th2ql-wf5ftgz.m d 8y 0se speed of the moving train?   m/s

  The frequency of a steam train whistle hp*ontf9fwt 1et ;,r/as it approaches you is 538 Hz. After it passet ;ntr9f/p*o ,ht we1fs you, its 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 sfeteo3ur ;w/,wp, ph +qxf0e/* ,z yhepeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the e,f0eu et/rpyzx* qhoh3w w;+,f,ep/ 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 clz bvb83s q13*b t/wtg 62nzybeat frequency of 11 Hz. The shorter ons vbbtw *t/3 q8lzc3y1zn6gb2e is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rai3is(y;a)xnq-b,xpws 6 ;y soilroad car 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 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,, )s n3;(py;6 qo ssixwb-yxai at C?

  If the velocity of blood flow in;nrh5rsz f*)n the aorta is 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? h*5z;)nsnfrr Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towa:8rzq8z 6js7f7fg5di 3atu ag rd the bat at speed 5 m/s The bat emits a sound waveg8at83f5gz :zsij qudrfa767 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 amk z,y qqdk*gr49 .tj,s it approaches 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 so that the echo from one chirp returns before the n. ,dq j4z, m9gkrtq*kyext chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vill n.+kc, yod6viage 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 6noc dv,k. iy+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 n9 elxgaxkcq0z++o :whj1-* w the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Ckc*x w wgq9n+e-l 0xh1o +:azjonsider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, cb7asnfh* o kds s+ o;5/c6h9aialled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod i 7di ; bksa9*oa fons5/6chh+ss 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 hunv .zuxh50yh.man ear at a frequency of aboxh 0ny.u .zh5vut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observ6o3uib 1vkay/nesek)5 1(m cw er on the ground hears the sonic boom 1.5 min after the plane pas6 () a nuocewvbm1s e/k1iy5k3ses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboats, vwx/ii1w r,1 g9bur is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h