What is the evidence that so*/ dhl)ekldz* und travels as a wave?

What is the evidence /gw5s yoz01ctxb,)y un eq72tthat sound is a form of energy?

Children sometimes play with x wxa:zwvh ).-a homemade “telephone” by attaching a string to the bottoms of two paper cups. a)z.vwxwx h:- 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 other.

When a sound wave passes from air gzb03lqw )9 nointo water, do you expect the frequency or wavelebw093 lgozn )qngth to change?

What evidence can you give that the speed of sound in air doe-5cp9 j su*sjts not depend significantl5 pj-ssjc9 ut*y on frequency?

The voice of a person who has inhaled helium sounds very higj3wlmn u.jbi4,k,z ;dc+ a:wb h-pitched. Why?

How will the air temperature in a )d:g1pxqf x tcg-np qykv5s1v 9o2:2g room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of+hqe2h6i3 7b8tl* qe h uecjs- sounds in various freque7*6uqis8blh3h te e+h q2e jc-ncy ranges. (An example is a car muffler.)

Why are the frets on a guitar 23i i vg* gtog1b2;iin(Fig. 12–30) spaced closer together as you move up the fin;ito *ggi 12igib32 nvgerboard toward the bridge?

A noisy truck approaches you from behind a building. Initia1-22;vdzptnui cvk- 2nxwn )4g f(fvolly you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explai2)2cp-2inv;nw tn 4vfxvg u z 1f-(dkon. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beao1ws b: /y9s6 zv2limokl f4:mts can be said to be due to “i1:o w4ym6iozslfslv m9k:2/b nterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, ysowyk+xajb3+) 1ryh.ac/ *b would the points D and C (where destructive and constructive interferexkyyc o /y.bs r*a)ha1+bj w3+nce occur) move farther apart or closer together?

Traditional methods of protecting the he;p/jf hp8a nwnwh+ c+5aring of people who work in areas with very high noise levelsp/8ah+ ncf;p+ w5wjhn 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 ears?

Consider the two waves shown in Fig. 12–31. Each w d( isl(scdz7+07cgjhave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (bh lc7sdd((gszj+0i7 c), 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 directionr4swmz5tb ,8t5t. hyy, with the same velocity? Esr, m4bt w5yyttz.8 5hxplain.

If a wind is blowing, will this alter the frequency of the soundt 4 lzu.b v fb/8vvcdawdm*50: heard by a person at rest with respect tod vulc8b./ 0mavv4df*w bz:5t the source? Is the wavelength or velocity changed?

Figure 12–32 shows various p;o*4 hdny/lzr 1 ldn4pak 6i/eositions 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 fo/ha 6dk/zd il n*;p1l4roeny 4r the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of jys.c8 jfs na y2t:0lns .0wc9her shout reflected by a jt0s0c.y28lsaj :9nwn f yc.scliff 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 9tya5a;n:u)q zv 1jy42 vojdfside of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly b tjy2zdo;vaja 1)fu9v4n:q y 5elow 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthsigwyohm+3 1fb/w 5tv* in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school 9mb fo.zf- 2zdof tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before tfo-zb2 fm.dz9he backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the to9- dane ybanrs 6hp ;q tdpi3y*3n585lp of a cliff. The splash it makes when striking the water iaa9n lpt n3h 8;rb-55qpy *6neyd 3dsbelow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground,-b52)yr7u4ncbnwu mx sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travenbc4r5n72ubyx -w u m)ls 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 distance by the “5-qy+jfhkfcvvu/ kzw sc*l/:dh6o2c 50ltc- 7 7second rule” for estimating v6 w yuo2h f0t75lk j:s c+k-cc/cv d*q7fz/hlthe 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 p92g5b 1)cjo 2ac qgkjfain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levehb36lfliltr+, rr 51zl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce 8ebgiwy 18nnk/ mh-i8a sound level of 95 dB when fired simultaneously at a cerhn 1-yg/e 8inkiwb88 mtain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four+sq0 y,7jk 1qbq+p mxg equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sxkyb p0+jq+17qgq,msound 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 ratio9n7j -2ntne dn of 58 dB, whereas for a CD player it is 952jde9n7- nnnt 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 soun2+saeqp6)kr sd from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads s+2res )a6qkproughly 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 strln28t4*7oghvcj fa t oow.8i, ikes 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 w:gy)a;9tfa 5ike( y kmodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels ;5y)weayaft kg( : ik9you 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 deu-z dr /d(sny +ij+qpj( ((ykB when placed 2.8 m in front of a loudspeaker on the s(sji+((n p y(dyu -rjz/k +qdetage.
(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 5xqy pdyk(8ji( f/df-nzf/i8ib t2u+ difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: S(2i +y djf8fb/ftxuyk /iz in(pq d-58ee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) e xs1vxmec609xv:6 b dby what factor will the intensity increase? Increase 1bxce9e vm v d:6sx0x6by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twlu:c mm2wyj;koo38 ; zice the frequency of the other. Wha3z mu;w:lo;j cm8 2okyt is the ratio of their intensities?   

  What would be the sound level (in dB) .tml 2p6ado1t of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules oltm 2.pdtoa61 f 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have )v zgx0thofohv/b1 :0b0 cr, wwhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)th o0vb01x vrzwo:g,c) 0bhf/    dB

What are the lowest and highest frequencies that an ear c(bhqd:h .6cg ff 1o rf,55bheean detect when the sound level is 30 dB? (Seee beh,:.5h1c ffdo6fqrbh(5 g Fig. 12–6.)

  Your auditory system can accommodate a huge range of soundg*uwxbke v4oe1 +8.cm levels. What is the ratio of highesegx.+ 4m beou v8*1cwkt to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequen rl5ci hru5zo/;a)d6g nfig,7cy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of ncza iu/l hg 6 o;df75)rgr,5i0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and f tpdm-ki moh13j,w g-*irst three audible overtonei-oj,3* 1m tk-dpwhmgs if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the t1m u/bi8vegtsw 3:r +mop of an empty soda bottle that rgw3mi t/m+8esbv u:1 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 openj b:b*5qbv r 2d 3zma/13kulhw-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pblqb32u1hvbwz:/k5* j dm3a ripes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of .nb*ir9er r xha pr8:-540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of 8r .- 9hax:n* ripbrerits original length?   Hz

  An unfingered guitar string is lfil:k+i9*x.j / rmaccq yo *)0.73 m long and is tuned to play E above middle C r.amo cli+q* jly: fxik9*)c/(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 leng),pf)a 0dbvs cb,2fipth of an open organ pipe that emits middle C (262 Hz) when th i2csb,d)0 pff)avb,p e temperature 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 anc.2 xa2zq8(3zrufu it 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 Exampl;a+x;wa8pponijeg k(7d v+.)e- (av 2fopqnue 12–10 should the hole be that must be uncovered to play D abppaxgd+ pn i.ua(fvv8ea+k );(2eoqw n;o7j -ove 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, andh 3w5w8 (6-xafeqve tp 616 Hz, but not at an56aw wht 8ex- v3qfp(ey other frequencies 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 el f7 hsha6ekh;-x f96c 86d7ub)drl icnds. It resonates at two successive harmonics of frequencies 275 Hz an- l;hd66hekb7dl6c7fc9 8 xrhi sauf)d 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 6hzf0byq :bp2 9wh*ck$^{\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 ar6s6hdtsn :)vae,o/ n*dao+gjbp3 i+ ae present within the audible range for a 2.14-m-long organ pipe aid+ptdne,v/oj sas6g n)* a boah+3:6t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsidczzjb8g),:czt-5t/ si 37qxeg:sy s :0k wqnie and is closed at the other end by the eardrum. Estimate the frequencies (in the :b )sn/ 7zcitsygkq,zx8zwc g53t:e:0sjq-iaudible 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+(ge+eb x bog nfg/* zpw(3dq/ s when trying to adjust two strings, one of which is sounding 440 b++ez// gwfg n o3egdq(p(*bx Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if yks*g-5li;ca 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 operateluy.n jk8z) *83cehinw v qmz(3*9cg ms at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard z3n q*c* l(8cmyign )v38jmewh .zku9by 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 when sounded with a 350-Hz tuning fork )9nx 2*hwen feessj;j; mw*drs) 69*z*wpzcv and 9 beats/s whene xm9*v wre d;)ns2*z*; jsp)z cw *sefwhjn69 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. Tm 3jtknn/(.gny b,*sohe tension in one string is then decreased by 2.0%. What will be the bea/o(,ng* j3. n tymsnkbt frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two nl +3iokuy+ /b 8pdspsa * zmc4imv+ 7:rhf,(uidentical flutes each try to play middle C (262 Hz), budi,u blh p3aky+4vmz(87pu/n r m +o+: fcs*sit 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 has a fmdq;ur9 kd1 z.requency of 441 Hz; when A and B are sounded togethedzqdu9k. r;1m r, 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 1.80 m apart. A person stands 3.00 m fromr( (k,rzwco+*cmu;h l:dz ;+p 4tjvz q one speaker and 3.50 m from the r zz;+cjuvdtrwp l+cqo*k ;:z,m4 ((hother.
(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 0htqx*k,untz27,vd z hears three beats every 2.0 s when they are played together. (a) If k *u0tt,,hznq x7 2zdvone 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. How mayexo3l +vtj h /6kj0 0rht8/smny beats per sec3 x0e rkl 0/yjhvmjs+6t hot8/ond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whemok9 s 1ya c042jql5)uwpei/ln at rest. What frequency do you detect if you move with a speed of 3oqea )jkl4s/ ml0cyu9ipw5120 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 engine 2x5kr(q l a xk r0y0 anax0jx5v7y,o-mwhose siren emits at 1550 Hz m0yx2o5r y0k 0axm5q v,7x lxrja n-ak(oves 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 movizvl* xa n6:x2hng toward you at 15 m/s :6h2n*l zvaxxversus you moving toward 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 equippedh)avzqlj*3sn (:s7bn3ad s4d with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequenhv 3jdns*4 nq()3lba: s 7sdzacy of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receijnu hb*ht(s-xpn):x. ves them returned from an object moving directly away from it at 25.nuh)xh-n( tpsbx j :* m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of a;v48qwuqr,e0 mu /7 byle-oc5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz.c wb7 , ao0eu8elm urq-/qv;4y What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments,4pw :+i s i7un *zy3wwbr-/jgl a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identicalg4w7sz /bpyul:j-*inw3w + ri 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-s+7dphq .2fg tflow 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 c+fhd 7g sq2pt.m/s directly away from the sound source?   Hz

  The Doppler effect usi.ly iw cdny,)7ng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of freqg i, b2oqyvz,3uency 570 Hz. When the wind velocity is 12 m/s from thy izvg2q3 bo,,e north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on landtf1b,tjyodn5g w -0 4k 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 speedx(z6 ksjey ,;/pome, po:j :ph of sound is 310 m/s (a) What is the angle the shock wave : s:x ,kpe(pe;o p6hzjmoy,j/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 where the speed of sound ;hh.xwy 5k,mi5ly9fs is on,k.ixyfw9 l5y; m 5shhly 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 b3 siout+3g 0p9; mcfl8500 m/s strikes the ocean. Determine the shock wave angle it producfgp9i3c+ suotlb m0; 3es
(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 thb5v78kcrq.:c i( 4r. hyq wk$/theta$ 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.dmno*2nkee ..ybj;pirq7- 3 k5 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. Soi*3jp; b n.nek m-2qryk.e7dee 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 de2z4un/*e+r6mgun em4 tt- r*jwh j br9vice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is t-nrrgz2 *jn*t69ehtmwmj 4b u u4/+re he minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human auvnrcd4n5 mvw1cyx*4 i3j 3ea1dible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer aaforx4f3ve/.i d qd( z /(.hvpipe symphony. It consists of many plastic pipes of variouerv/aavd of x..hq/3d(i( z4fs 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 threshold of hu7kszl 4quo, q,/sg.e tman hearing (0 dB). What will be the szu/qol. t 7,qgs ek4s,ound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87*xyiyf + 2/:c h68il xcvmu n51toyfn.-dB sound are heard simulvm fh5i y:u8/6.c*fc2i1n yx loxtn y+taneously?    dB

  The sound level 12.0 m from a loudspl51r* yvx2i yreaker, placed in the open, is 105 dB. What is the ac1iryr ylx5v *2oustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. T(x1 6knfog zu+he power output drops by 10 dB at 15 kHz. Wfo+nu16(xgz k hat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typkpu x+x5mxg h6:3c 5uwically wear protective 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 r5u gmwhu3 6:kxp5x c+xadius 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 communi.- si6mpd 0r+yv.(w jjxgrno5cations 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 violin is tuned to a uoda d+w;8 5fzfrequency 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 fundamev v7q6ex4je ) miun-edn0 io+-ntal frequency of 440eoqv)mv 6iu4xi 7 --jd ne0+ne Hz and 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 tube fill+ 1(k9ws-7zk 6in ;eyg3ww -apkjvxufed 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 tubei3;7 ynk+z6wg pk 1sjuf k(ww-9-a vxe 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 is near a tube that is op8l(9ebfjq6uda6 7. z2kmidteen at one end and also 75 cm long. How much tem7l9dfeu 26qi6akdzj 8t(eb . nsion should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate asgip7836,rvl g ywncm) one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from twohg.7f5o;bv uq6g (hpp5f fej . 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 p e ghbfqgj6;oh..5p5f(vuf7that 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. On*q5t3 (fgiij)wj6m gs (6a0 mklzq8jie train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whajiiq)mgks(wjmatj z5(*gf l 6q 08i63t is the speed of the moving train?   m/s

  The frequency of a steam train whistle aiw)lv 3,xdny: p)x*qb s it approaches you is 538 Hz. After it passes you, its frequ)n: di yp)* ,wxl3qbxvency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you ccol;r6ar xwkk 3d hhm/, (/7qhan 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 ihka,mxrw;q/ lh 3/( hr6dk7 cot goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency ,f5v xgy 1y (,gi.nq0 khtooe)of 11 Hz. The shorter one is 2.40 m long. How long is 1ienf0yg y5x(vqho ) .,t ,okgthe other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s,4uwwv59 r fehtationary 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 a r5wuf4h,vw9e fter they have passed him, at C?

  If the velocity of blood flow in the aorta is norma u:ri6-vcsgp-lly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were diresrg- i c6:uv-pcted 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 whilmfhkjj5 jg)(j y:k0k:) bk4 aue the moth is flying toward the bat at speed 5 m/s jm) j )kaf ::k5 ujb4kghyjk0(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 the moth?    kHz

  A bat emits a series of hixbcw )h wnbry.2a1o01gh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abouoxr .yan12 c)h1w0bb wt 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used :al1tw 4cc /qxyq20nzzq7) gd to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharacy4qt)qcq z2d/n 7:l z1x 0wgp (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 co 3* o4f+gvrwb(w9gsr tbew4n8mpromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the4g+wfw 4*8be3sv r(owg rnb t9 standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, cnp, kx1z ss+sv, (ew6xalled “singing rods,” involves a long, slender aluminum rod held e kwx6psv+n xz1(,s,s in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For 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 thres n2*beo u(if3chold of hearing for the human ear at a frequency of about 1 o2c ifb3u(ne*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 ground hears the sonic boo.)spds jah ;b,l 3rwze147jssm 1.5 min after the plane passes ds37j.jehs z)bsrs;l41d,w ap irectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat*eg6a1w 4eg mr 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