What is the evidence that sound travels kkr msbb6l1dz6pia*(ux0 w7wb)b1r *as a wave?

What is the evidence that sound is a0 q:emi7.t s ifs6+ynr form of energy?

Children sometimes play with a homemade “telephone”cf p). dkc ,wvks*t7r*2z7sy/pv6nmx 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 heard at the other cup (Fig. 12–29). Explain clearly how the ctf.dn* /pvv) s2kyrpxc mks 6*w77z,sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the ejcnr(mg/1nz foi43wg-c q; 5frequency or wavelen c/gzc 1f;n(5gnwj im4-r oqe3gth to change?

What evidence can you give that the speed of sound in air does not de)g,f.uvu y9lj f l3z6gy 5nv3wpend significantl3.vvy3 5fgzl9) nw yg,lu6ufjy on frequency?

The voice of a person who c63iz23k qtrp has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room aff 1:xn+;; baantl b:ltbect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce t:. jdd;4 hm7xm9sbru bhe amplitude of sounds in various frequency ranges. (An example is sd7r d4m hx.9bmu:;jba car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced xql .txz(v1 y5 dq9rj;closer together as you move up the fingerboard toward (xl9xdqz tvq5.j;yr1 the bridge?

A noisy truck approaches you )m2 nzbgt15xkfrom 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 more of the high-frequencz5n2t1)xbgk m y noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfels,b loj: j:3nrence in space,” whereas beats can be said to be due to “interference ino ljln3s j,:b: time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wourf+sp+ mxgv .:ld the points D and C (where destructive and conp fgxs+.v+m: rstructive interference occur) move farther apart or closer together?

Traditional methods of p.lyjh0:4udmi0o q z.e1k( nht3cg i 7xrotecting 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. 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 ear 7.j (k0e0gmhu:i3cinol.xz1yqt 4d hs?

Consider the two waves shown qvjahn6 83 .7 dgq0htfm0i8 zjin Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in t3dhf gmq7z8.qhv0n08 jj6aiFig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directi) iay0un p)+ h;rh-mygon, with the same +0)iuy -hyganr ph;m)velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bk,e1 e tet,2 uba:vs ,q,gh-nxy a person at rest winehet 1v:xuaq,bk - s2e ,,tg,th respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moti4qtq;s/jikvy wmsj. u ko vnx-(4/f70on on a swing. A monitor is; kjkj0su -4y/ xs/ nq.4vowtimv7fq( 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 whistle? Explain your reasoning.

  A hiker determines the length o:rjx46z qop ;cf a lake by listening for the echo of her shout reflectex;jqor6p:4z c d by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of 6ewi xwi4r2*g 96;8iy 8qxx;maemojb his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this poiiq w2o mx g6emj6a9iri w;xx*b88;y4e nt? 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 air at 2o9yy4xt( vh )j0 $^{\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 schoo d7e5 bkj-i+sb)mpd y8l of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1) 8d7d5i- bkjbpmesy +.0 km away (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:ah-zr -f 6csv of a cliff. The splash it makes when striking the water below is vzrsc6:f -a-h heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pavu6ch +k iu/;ncement. A moment later two sok/c;hcn+u i6 uunds are heard from the impact: 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 og- y pd xdgg61bdi*id:i9g;o; ne mile of distance by the “5-second rule” for ed:16g;yi9*gxb gd ipi-d; odgstimating the distance from 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 1tufxh7m)(*u; ubz1f hr u.x/l 20 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 whose intengn(y/p*f3 q(. gl(llkrfiw k8sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lev:in4fwlmo a 4r8hu/d3ie h0l9el of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, a4d98 4onull/wif3hr:m0e hinot dB’s.]    dB

  A person standing a certain distance from an zrs2ap8e zb 93-0 tc,/fa uzvcairplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thisazv-0s8z 2 bc t/zefuc,3a r9p person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio ofecq1 + l:x ktv4m2m6djfal/5d 58 dB, whereas for a CD player it is 95 dBl+4j5 af:tmd ec l62 xqvmd/k1. 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 ofvv8 7ta;.8tt htgaru+ sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on thev .uar; gavtht8t +87t 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 eardr6 hrlpos9x94g/ ykzs 8a:t4eaum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest a alrh8+,6z b x0nur81mvv;vz zmplifier B is ram6xvz8+ ,1 v0nhr8uab zrlv;zted 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 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 bm4y)+ hoiqt9when placed 2.8 m in front of a loudspeaker on the s tbq+yo4 m9ih)tage.
(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 differenc kqc8 ztm;s06apqt(e pmq.*,re in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ byc*m8qm0as qp k(qtez.,6r p;t this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a souyg3l) 7g3.3jyzqbwk m nd wave is tripled, (a) by what factor will the intensity increase? Incz3wq m3kbygyl.g3 )7jrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, b2p7+gf*t5kd 6i )he1hi klwlput one has twice the frequency of the other. What is the ratio of t f1g)hliktwkp h 2d5ei+67pl*heir intensities?   

  What would be the sound level (in dB) of a sound wave in air (h6u x, 2 ogudkd20jevthat corresponds to a displacement amplitude of vibrating air molecul,d0 hxu( 2ukoedgv62j es of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level *vg6nx9gh;qd to seem as loud as a 100-Hz tone that has a 50-dB sound levd q9hn;x6vgg*el? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sojw/-9guo q9-ryswdp :und level:wj ouds-gyw /pr q99- is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommod)j3,i(mh0z,lo zwqzohz lkf+v x 3s;-ate a huge range of sound levels. What is the ratio of highest to lowest lqzk3 hz,-0v(os f;mjz,i3 + )hzowxlintensity 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 frelzp.k+g2o p,0j,;ex u b.epprquency of 440 Hz. The length of the vibrating portion is 32 c .zr0pjbuop p+ ex,lk.e;pg,2 m, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibl+ wy/wb.57cs+enlxv-c ;vti je overtones if the pipe is. ;jv7 +wtxib cn +sl5/ey-vwc
(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 frequer+ gj+x sayu12ncy would you expect from blowing across the top of an empty soda bottle that is 18 cm ry au+jx 1+sg2deep, 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 thec h,oos fwfav3.+km 78 range of human hearing (20 Hz to 20 kHz), what would be the ran8oasw7mv+f,hc3 .of k ge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540d8xhd nob s pbx/6j54 po1md45 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengtn5 j md6bd51o4hpdx b84o/xpsh of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and isnspj-(ypfsd8q:p b (/iksjczw7 6-.i tuned to play E above middle C -bsc6sp7qpj .w 8zi y(p :s-dfk(/ji n(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 pipe that emits middle C (262 Hz)p5ajt6z9:qjf4 bc3 mal9vb wa6 k) (gh when the temperature is 2faambw3hj 9tz6 6 lk: b9ca5qpv (g)j41 $^{\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 s )5a )xn(hjxa)mws j;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 Examplnvm6alvs38h4*k n ug8as q82ce 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz*uh28sn6 v c l34akm8qg8snva?    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 resonato:y6hoce m 4f58ei0dce at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why t5f04d6oihceem 8y oc :his 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 twonq)b( frb/*kl successive harmonics of frequencies 275 Hz and 330 Hz. What is lq )kbfnbr*/(
(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 u4dc)cg gvq)/5n)l ex$^{\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 range for a 2.14-m-longrx142lh4ov+s 7s;1d*rxs4erq sx uyz organ pipe at 20xrs441oyvxs 1q d;+r*zlx7hsr su24e $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apjbes) rd.oz)u )yp:zgo7s9 1oproximately 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 wave)rojygudz9 s)1: 7po b.oesz)s 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 l6(u3 babvwb7ot 13( lo z..+kv kehvxtrying to adjust two strings, one of whichvz1 o(7l(6lbtvek. uvhbw3a+b x3.o k is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat freqqk9gj )agfck81za w /8uency 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 23.5i 4fcgxblxjy zlj*1d u,s7 8*8 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard byglbjflx48 dzs,jy7 18cu** xi 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 beats/s wh:bajyycsx . 4q) qqk75en sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational freqs7 kx)q .b5j4yaq y:cquency of the string? Explain your reasoning.    Hz

  Two violin strings are aqkx k)c d1k2igm-b w,cn5 x-552 txwwtuned to the same 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 Eq. 11–13 dci)5-cwk w5,5qbt2xnm-xk1agwkx 2 .]    Hz

  How many beats will be hear 3au/sy q zpgyhzm,iw50sn3 84d if two identical flutes each try to play middle C (yngz30y 8, /szpw qim s4u3ah5262 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has51,0 9dd)ywnim a gqfu a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz i,i0u adn 59w)1fmqgdys 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 stands 3.00 m from one speaker vg/t o qil7m: q7d+/kkand 3.50 m from the otherdmkl7igkv /:+/toq7q.
(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 1vfj 0wc 5vm sxaorosl )z9f,b 505zjou;6oo:supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played tuoov1zflc9; 0zxo0,:fo6s5 b a jjs5ro5 )vmwogether. (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 m in air/y9yu yb pthh)f2h/v ). How many beats per second will be heard? (Assume T =hu/)t )yy 9hhb y2pf/v 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enm/ /4b0fgurnk ,* g3pt hqzuw8gine’s siren is 1550 Hz when at rest. What frequency do youbggmhr*3t u,q pzkw/u 48fn0/ 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 detect if a firee laai2bkhz-) r-2w9seg,svu0/4 eot+sr: jp engine whose siren emits at w-s+- 2begl4, 0pr:so uats)2e9iv z /ajkhre1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in gaja: apqwt1wp);ae ua+o(+. frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are thaw.pe u ag+1pa;wt(aao j) +:qey 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 ho:(en790 cqg:c sr sncurn. 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. What9n(7c:: se ngur0ccsq is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives t/s9yb00 jekoou9hkl 9w.2 j lfhem returned from an object movil0lj/u0 koy j hoeb.s9f9wk 29ng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, wooe+t b 7mml;12 xf48b zi6yqthe bat emits an ultrasonic sound wave wifiz6x be41oql7y+2omw8b tm ; th frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origin4r5w/ qkl7re ial Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a seco 4eq5irkw l/r7nd 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 uses ultrasound waves to measure blood-fl.wkkl.mrk( g ,e lto;2ow speeds. Suppose tm;o(kkl. ewlgr2 k.t,he 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 )ljj10c+ 9t .ozsa aas,ml er*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 Hz. Wpzth+74v k7j4ytmm g0hen the wind velocity is 12 m/s from the north, what frequency will observers hear who tgzh 77pt4m jym0vk+ 4are 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 if9ie c9 j:q-xn..lwizt its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of 5cme+3a xvrf k bed-*;n0ujo)sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motub xcdv) rm50*joeanf3+e;- kion?    $^{\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 atv*vv; gztaa/.ne l8 x(mosphere of a planet where the speed of sound is l vt/nvv;xe* (gz8a.aonly 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,wfqzu+0zy d 8 strikes the ocean. Determine the shock wave angle ,d0zfyqz +u w8it 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 rchr eiy6 tx4;:)7 krrd ,l.k5,dfurl$/theta$ 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 koujk:bb; uz83m above the ground flying faster than the speed of:b; 3ub jzoku8 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 senwyllt7 9lfyql xw+02e,f /jn gh m/)z1ds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum d7 e/q2mfj1t/ x 0gynl,lw9yh+lfw z)lepth 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 :ctr.f63 tbvfare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.14e jrk wryxu8c(k*m( It consists of many plastic pipes4e1jwy(x(rcm 8u k *kr of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threjlpbqe /p/izt 6-4 l6cshold of human hearing (0 dB). What will be the sound level of 1000 suchlj4zlq 6pec/6i-t pb/ mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are u,yz l gp k3tg3fph*ur5*-is2 heard simultaneously? ptu rg*s *5ip3ku y3lzg2h,f-    dB

  The sound level 12.0 m from a d3zo0 e9ye7/vy,, daj5f tg yzloudspeaker, placed in the open, is 105 dB. What is the ac5z fej yovt d3,0 9ze7d/yyg,aoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W o yy065eeqboz 2utput at 1000 Hz. The power output drops by 10 dB at 15 kHz.2q5 ey0be6 zyo What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectinkt4h fs;qu )kt5w:k6ve devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would ;kk) nh45 fsk6: uqttwbe the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, 8ink unu7, o4e$\beta$ 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 a frequency 16 kiikb,5ln+))ay ddh $\frac{1}{2}$ 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 vi/ g ,h9z5hr pbm,:musyolin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit len/u5 ,bgm mprs9hh,y z:gth 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 tm4*4lafz 6vo:mu mez)m m sjjw- *hqvy(t-90zube 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 resonatmy)l- s-e m0(t*z*j4vj mmof9a zm4hzqv6:wu e with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g isu1ep*/k.t;ox;-gwd qw k ry(s near a tube that is open at one end and also 75 cm long. How much tension should be in tpt (wysx ku/wg oq1e-.;*rk;dhe string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass we+gmn:pacpu 3;g1xx, as observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming f kuk88vrdgo1/ rom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from do/u8g81 krvkone source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationar+8vrmv a7vj6 ty. The conductor on the stationary train hears a 3.0-Hz beat frequency wh+t jv8amv76 rven the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. /rm ( czb9 fsrqzzfb5ml3rx(,y;p2 2lAfter it passes you, its ;/ qb r(2mpf z x(z2s5fl,9y3cmrrbzlfrequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars, w4vydh,su n6e/ w5d)e7mkaq just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fasts6 w v,,5m)y kd4quaewd/e 7hn is it going?    m/s

  Two open organ pipes,*np5 *bbh xk)s sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the ob hnp) **x5sbkther?    m

Two loudspeakers are at opposite ends of a railroad car as it moves r*t shxc f4vt,i; f6ze7z qz74nyo9*wpast 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 (zzf*qtiy, 6vchx t;7o9n4*fwez4s 7rc) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 fucg n+t9un668sc snm-d--xpm/s what beat frequency would you expectd+-6ps fgxns m89n6ut un --cc if 5.50-MHz ultrasound waves were directed along the 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 moth at speed ecmu.uo3/5 d i6.5 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 wave reflects off th i5eduoc 3.mu/e moth?    kHz

  A bat emits a series of high/owbc) rk/7i e frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms l /)iworec/k7 bong. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alinqw-ma j1 gbw11h-w 4pine 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 alpenhoq 1 wn-- 1ibm4jhg1wawrn 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 stxb do.+81m tp3)h lceyereo 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 5ml1 ye 3pdoc.h8x +)bt.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rv(s :;olqc/ u my5 wmszfte7+.ods,” involves a long, slender aluminum rod held in the 5:m qmsz u; (t.+eyvlf7so/c whand 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 fo:aa 9m (hg c 6*uj0gt/z2iljhbr the human ear at a frequency of about 12:l0( abjg6g9hzi hc*tmuaj/000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the d u8h)hn//sb mground hears the sonic boom 1.5 min after the p)m/ n hb/hsdu8lane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbozfduz3 q7,(a pxbtvsy.;o,su 5w o ;b5at 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