What is the evidence that s k;:eps4gtcq5q4(sq;hc abw6 ound travels as a wave?

What is the evidence that sound is a formmap+ g,nvj/n vj+3iu9 of energy?

Children sometimes play with a homemadqm/vk n49h: soe “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 heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the oo/n4 :9vsqk hmther.

When a sound wave passes from air into water, do you expect the frequency ora.+jfdp-*b sa wav-pb*+fd.j sa aelength to change?

What evidence can you give that the speed of sound in air does not depend sigh h-;y;m z*bdbnifican;d* zbhmy;h b-tly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. j72 op hs k,(gzzc3pd7l.:auu m( hd6wWhy?

How will the air temperature x7qoo/9cx,f828h ahyz6uey ;zg bq 1uin a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the auc6 xm/+2dgs 4u1.rzu zxl/lmmplitude of sounds in6x ml1x s +//rglu udcuz.m4z2 various frequency ranges. (An example is a car muffler.)

Why are the frets on a gu4+znq - sc6qr nmujm8.itar (Fig. 12–30) spaced closer together as you move up the finge 4m.8cu+mnz- nrjqqs6 rboard toward the bridge?

A noisy truck approaches you from behind a buildin yo /;gojime.5g. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “bomjo. yi/eg;5 righter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spv3bnu ,a*jn (sace,” whereas beats can be said to be due to “interference in time.” Expbau3n,(j nv *slain.

In Fig. 12–16, if the frequency of the svmoc/cp g91k r.v.rl ,peakers were lowered, would the points D and C (where destructive and constructive interference g.p9 ocl, vm c.kv1rr/occur) move farther apart or closer together?

Traditional methods of protecting the 1pm 0pqtlr 6xr 3csq,b(ot+4is jk- 4fhearing of people who work in areas with very high noise levels have consistedt(psms-xc6 4pr4bqk+01t3jfi l q ro, 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 ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of z1.tdyelc;(mygmo u+ 2s 8nv: as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), az 2 u8l+md(m.cyegnosv ty1:; re the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsk)r( s *ojzjarh;2i9b erver move in the same direction, with the same veloj bh k;)ra2zjr(*is9ocity? Explain.

If a wind is blowing, will this alter the frequencyvk qn,ag8w )oolq.xd448rz -j of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chan oo-q4d n 84g,8qlw rz)a.kxvjged?

Figure 12–32 shows various positions of a c ;0bfxhft z w/,ch7s1lhild in motion on a swing. A monitor is blowing a whistle in front of the child on the groxlh0fz1h,b/t 7; fwscund. 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 wej7;7 r zqoj1vxw4i.sx4qx4lake by listening for the echo of her shout reflected by a cliff ow74 zxw x4q 1v.j;7rsqj4ixeat 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 his ship just below the watqm:b7xd(o b 6derline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s lamd(qdbo x7:b6ter. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths hpiwea t iy(gz7)qage5+*:)nin 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 tahw+92 0pkh/ n2r6 c(snoebwguna on a foggy day. Without warning, an engine +npg 2 wh6s/nr 09oahebwc(k2backfire occurs on another boat 1.0 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 fromu d,o2am4:c76o9lf mtih; gwe the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later;7mg6l odhmew:fi t249u,oac . How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the)rr5-zb 7uyh5v jxp fjr4 i*-l concrete pavement. A moment later two sounds arihrfu5j- yj4b7zlpv*- )x5rre 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 one mile of distanh tsj5/.z rv*f- t itlrma.hxf:sr l8rg1:)j3ce by the “5-second rule” for estimating the distance from a lightning strike if the temper*th3rt.rhtvfx-fz5:/ jgjl l :a r8ss)m ir1 .ature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain leve7p s xk)95a: vzxc;ukwl 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 whose*spe gur3rt q(j( x-n. intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atg og6xi2bcid niwlk 5 m2u72(z3u1/my a certain place, what will be the sound level if on bg 7 (mu wgi ou5223xyzmlk6c2/in1dily one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equall27 y 3c5b0 ebyj0pgxfyn 1yl,zy noisy jet3 c75jnp0bgyly 1 z20yefxby, 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.]    dB

  A cassette player is said to have a signal-to-noise ratiml9m3j:a;-a mub5 tgb o of 58 dB, whereas for a C9 5:bmm 3 ljagub-a;mtD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpkx*slu;:mjx- ut of sound from a person speaking in normal conversatio xxu-*;:smkjl n. Use Table 12–2. Assume 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 strike 0t9wu c6exo zmowu/(9s an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifie9otf3bo7m4x u ak6n6k r B is rated at 40 W. (a) Estimate the sound level in decibels yuk4 bmko76t 3fx9 6anoou 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 regi3 bq/ja1 mufd4stered 130 dB when placed 2.8 m in front of a loudsp adf41b3m u/jqeaker 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 differe (r,cb9x, +)xranxuomnce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whoa c+nx( ur,x9omb),xr se levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is yb yn u1r;l,jit9f,jfls50r3 tripled, (a) by what factor will the intensity increase? Inc1 ,, l9fsy0 bl ryr5;3nfjijutrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudhzr5+c+qywvm,;xba+6q x ; kses, but one has twice the frequency of t+,sxz 6;h5kqm+by+;x a rqwvc he other. What is the ratio of their intensities?   

  What would be the so bg4wk lg04 5n5u-qh2 xmv(crvund level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrhrq5v40 g2-bwvl5ck4nx m( guating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what g*c3 1ghk yb .l+;r1qmp2qrbpsound level to seem as loud as a 100-Hz tone that has ghbpmy.1 kb3c 2qg ;lpr*1r+qa 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when tb4+ 33 wxkv3:( :8hbtdvz- fbdxfdk0vrnnmf)he sound level is 30 dB? (See Fig.df3xb- 8x v0f w:rzv+3f dhnbk:dk(3n4b)mtv 12–6.)

  Your auditory system can accommodate t87wuo itnd), a3luu :a huge range of sound levels. What is the ratio of highest to lowoui8 )udu,a w7tln :3test intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of t(qf 3xh-kbyiju3x 9t)he vibrating portion is 32 cm, and itx kj tb-(fxy3hi)u3q9 has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm l.5+u/ky c6eng zc-y plong. What are the fundamental and first three audible overtones if tny -cpgzye/. 6u+l5ckhe 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 the top 7mc+tvs*bm95mbb: ;oi* rz ag of an empty soda bottle that is 18 cm deep, if yot:m; b*bmvbra zgmoci+57s9 *u 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 spannyro obgf6hs .k 19 v5d+92c5ex8pqpns ing the range of human hearing (20 Hz to 20 kHz), what would be the range of the len6k8 n1xrpbodype2 5gsshc+9f o5 v9.qgths 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 twk t ;8*/p5/qs; y v:2cgoazpha.qnidhird harmonic. What will be iy:g pc2.o5a;q qap ;nvzthk8w di// *sts fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7)dv pv uqmj1k(rsl-0 93 m long and is tuned to play E above middle C (330 mqlp s-)01j dvur k(v9Hz).
(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 opey(xogu6s ym;:n organ pipe that emits middle C (262 Hz) when the teo(yxs;6 ug :ymmperature 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 20 a h-:)(nmqh *.szqya2hyio8s $^{\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 f3;p+o3bki6pbp( * ij weh76ixd0 jsshole be that must be uncovered to play D above middle C at 294 60ib+3 ;sj6s k(p7ejwdp*f3hopbi ix 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, bizvtm) 5 evf/5 ,n ;*gq 6jw:stdeen*wut not at any other frequencies in between. (a) Show why this is gnm nw5tt5i)*dq;fw *j,:6eesvevz/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 bokwos irf6 s +3aer:1b8th ends. It resonates at two successive harmonics of frequencie r1a3kw +beos:if68rss 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 r-:ykj2 6/dl b ym6vb gvvou+ych*4g* $^{\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-longx,m2 ed qfb 0;f.um+kg organ pipe at 20 .,xbmgedu m;+ kf0q2f$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximav hlth 0.)ng- wr-bgs8tely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrt-lgn)b0 whr gs8vh.-um. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of 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 adju jr-)myrg,5 fh8m8t vust two strings, one of which is sounding 440 Hz. How far off in frequency hm -,u8jr y )gvf8mtr5is the other string? ±    Hz

  What is the beat frequency if gg4u17+lve z zmiddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, wij.- zrhu1 .xfhile another (brand X) operates 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 rjz.i-x .uf1hlayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with +0jrtk9 vind x (3qz0cg ip67ta 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency 6tzpi9 0c j0nxdqk r(ig +v7t3of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sam2iee0sxhn 5i8e frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What wi ihx0ne52i8e sll be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will burn :1)q72d id1tc.lx1 rqfope heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 2otqnfcru q1.1d 1:2 pli 7x)rd5.0 $^{\circ} $ C?    beats/sec

  You have three tuninc5g koj+utdk- r2cfx6g 894yvg forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are soc5kyv96cdg2 x-rk + j8 ufto4gunded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the 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 1.80b) a ga:xq7s.f m apart. A person stands 3.00 m from one speaker and 3.50 s:7abaq)gx. fm from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed atut(lgs r :6mw3u.u3to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togtuaw3tsu.m6g u3r( l: ether. (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 aig6a j-;x ri9zvr. How many beats per second will be heard? (Assume T 6i-jx;azg9 rv = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when an 05f8ztjn h,gt rest. What frequency do you detecn 8 nf0g5hzjt,t 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 fire engim (xzqf3kc 7j-ne whose siren emits at q jcfx-3( mk7z1550 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 to5wh1( elc0n krhn-m2a ward you at 15 m/s versus you moving toward it at 15 m/s Are the two fr a(5-rkhcmlhn 0wn 12eequencies 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. When one 6+vb7tl p cc6qis at rest and the other is moving toward the first at 15 m/s the driver at rest hpvtc6c+lqb6 7ears 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 .i t5 v*g* m/slkqoz1lwaves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m. q5mlo*zt*/iklg vs1 /s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at-xq4qvn0osjbdzed f*4 s zt:dv: ,3u+ a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the b:s3 ,:qnqds4*dovz0tbe-xd f u4vj+zat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fbd.pyzr2rqi :tb k: +0lat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station.dit bq:r0 .yk:+zp rb2 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 ultrasoui *ras/k b1e1gnd 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 if blood is flowing in large leg arteries at 2 cm/sab*g 1ser 1/ki directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freqphu:2szz14lb uency $2.25 \times10^{ 6}$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 emitsbg 11p6t dj7qsz7h ) ljm p69bdwl)y1d sound of frequency 570 Hz. When the wind velocity is 12 m/s from the northjb)1 6qjl1d6sw t dyd7p zbgmhp179l), 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 it:ky)3.vbtxxy. n2dp,u gec5k s 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 sound is 310 m/s (a)y9kjf..xp u 8f* b+fxj wrzx8* What is the angle the shock wave makes with the direction of the y fbf+xp z..j wuxj8*fr89x*kairplane’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 a) w 3po)jqpob7tmosphere of a planet where the speed of sound is only pow))ojbq 3p 7about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determig0:-ld g/6.4jstui ldix auk* ne the shock wave angle it prod- tk u/* gx6isliuagjld.04:duces
(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 :i/m; qxzp/:apxwd /oja+ n9 p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead ag ;ab13dvpsi: nd see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34;3a dvi1b sp:g. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downul7c.:rwu lw/y4x) wm ward from the bottom wum4 ) y:wl 7w/ux.lrcof the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in th50uswn t;yb qv-18pyalncc , 1e human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called /plvbca+gyh u u 0*ad(0ewj ++a sewer pipe symphony. It consists of many plastic pipes of var+b+0 y /wah uv0lg(+aeu*pjdcious 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 sounde8gmd)hbn-e : 8 uv1a0bxxu7ccej hu;p-k97i close to the threshold of human hearing (0 dB). What will be the sound lek70xbu8:mv;8-eub )nhxi 97u1g acp ceh-jd evel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and andjgp/ ,f+48xc0-jynvgq6b ti 87-dB sound are heard sixfbydnvg,8ji+-pq0 6 4/j tcgmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. dwd+ii8v/ t7j0w. 5mka jf9deo((d m xWhat is the aco dei/otjfwi9 vk(.7mwxmda 5d08d+ (justic 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 )a)l++jh xtje Hz. The power output drops by 10 dB at 15 kHz. What is the power oe t+alx jh))+jutput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ear,nejj3 qiz 94 yi-i6vrs. Assume t6 viin i3y4q9je-j,zrhat the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communik4; o usvnwx-:adr99m cations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a viol- 6(s5qloll, v j;jcrwin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a n qz6 s;qb1-1sy wf njcaj9u 9*tuv5m+fundamental frequency of 440 Hz n5ufbmjyj vc utq *69 n1+s 1qz-wsa;9and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open t.-shszil9whmb(s . h l td2-w/g9wp0qube filled with water (Fig. 12–35). The watgzb(whl/s 2slh-9 it.0.ws9mpd-wqher level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of massw5-dnc hrkztfva; +z: hc,7 .n 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third h ,.z:k5ctw+ hf-nd;vczr7 nhaarmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tvz *5la 7tukk7o 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 comiwt pc8mht.+;w8mu9.( bhviw cng from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person mow ccthtu.(;+mb. hw9p vi8m8wves 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-Hz whistles. One train is stationary. The conductor on zj9ma)wm4 ek -6zjv*hthe stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving z 9k evmjj6 -mza4)*hwtrain?   m/s

  The frequency of a steam train whistle as it approaches yo8 5o)w:a blxs* yk4jldu is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (a4lk)d jsy* b5:xo wla8ssume constant velocity)?    m/s

  At a race track, you;n,)f-ozco ab can estimate the speed of cars 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 fast is it going- ;fo )o,czban?    m/s

  Two open organ pipes, sounding together, produce a beat frequency o2cr,pmn 0v4o q-.pbzmf 11 Hz. The shor.0c o,m-pp2mz rv nb4qter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroadg- x/ yr*bcn+o sg.1r)h0xbplfj1l2c 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,lscbf0 r*jhbl1 +xog12 g/r-nxy) c.p (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normallxsk )447jypgc k.7; ;qhaitvjy about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves w4j.4h ;cj)i7kt ; 7aqgxs kpyvere 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 6.5 m/s while the moth is flying qt9*-xyp+ mb asq+ dr7toward 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 thbdsrm-+7q9qa+y * px tat wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound prs+i* f6+r z/6hicyelulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far awayi h6z*6/rflyseir++ c 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. 12–38w i7r8 vogs()n) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were us87nov )( rsigwed 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 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 bywcn xg.++h8lpqm kc7 7 the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a livi8q+p+k.7lcw7h g xnc mng 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 demonstra w( ozg7kkt/ rzgf ;ic93*ay)xtion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little pra acw*f r o(/t ig)z3zykg9;7kxctice, 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 at a frequency of ab 3j8ia7 *pqgcz69 oiwyoaqiz wpo 69 i8c*yg3j7ut 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 observer wpazzntjoi8ii ,a9+*-u s*b* mi43gw on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s 9wsiz t,wugb 4-iio*p83za*ain mj *+ altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i7az3te3wh. teq4j zft*tx l). s 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