What is the evidence*w zs(c(yarz6w v,k l2 that sound travels as a wave?

What is the evidence that sound is a form of e+9 ka-)hy:v pa0desgu nergy?

Children sometimes play with a homemade “telephone” by attaching a stringy7isuu ,q :*7uvseak( 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 kaqsuuu ,7iv7 (*es:y from one cup to the other.

When a sound wave passes e 4zeb6dsbao0sdg+:; from air into water, do you expect the frequency or waveles 4do a+dbe:zs0 ;egb6ngth to change?

What evidence can you give that the speedvg1g n7 afoq9: of sound in air does not depend signifin 7q:1g 9fvoagcantly on frequency?

The voice of a person who has inhaled helium sounds verya2 :r5 h(rvlr;hh no:x high-pitched. Why?

How will the air temperature u *41jz zjn+dxin a room affect the pitch of organ pipes?

Explain how a tube might be used as w;c6 / mmhgz;g )q0rx06gavrj a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mu;gwr 6mxzgqrg j a )c0;m06vh/ffler.)

Why are the frets on a guitar (Figr in 9x8j+ m3c8ocn(xk. 12–30) spaced closer together as you move up the fingerboard towardikoncr3 mn j+88xcx 9( the bridge?

A noisy truck approaches you from behind a building. vs 8z:dces 0ib e:3c-sq kki96Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. v8ksd3i ki 6:scbe q09zc:-es[Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfer 5w08jk6,uvygpcm g8sence in space,” whereas beats can be said to be due to “interferens wkyv8g0mjup, c5 68gce in time.” Explain.

In Fig. 12–16, if the frequency of the speaker5/2kkdnq4 qq is were lowered, would the points D and C (where destructive and constructive interference occurn5k iq kq24/qd) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areasta2*fmus3m0)p-rcc- g0 j :iez n6jzq 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 detnc j m2q0 izr6-3smug:-eca*0zfj) ptects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a supt6 -e+/im6bmf ;5nr ndaw. 2gb m-tqqaeh3,tb erposition of two sound waves with slightly bdm-6thiman , .q 2b-nrb3t;qwm +e/ft5g6aedifferent frequencies, as in Fig. 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 observer62ol3(0cckn i+hqs kf move in the same direction, with the same velo0skl6cc(niohf+kq 23city? Explain.

If a wind is blowing,9hvmji -)-x ez will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or veloch)9 zvx m-iej-ity changed?

Figure 12–32 shows various positions of a child in motion on a -c bk/ pwe)kc( x23ckmswing. A monitor is blowing a whistle in front of the childc-2pekc/(k)c mk w3x b on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for -z)r8z rshch/ the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate/hr)z8 csr-hz the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thpy-s6pz f x wthq.3:g2e echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawatey- . f:2 q6xphgt3wpszr is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths irj l/)f*z, 8rbwlk+uc jvjl+qz+s, i+n 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 dri.prywr5 y( ro ;3vsap p6ws28dfting just above a school of 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 the backfire is heard wr rp;.prwvp(8325yasso d y6 (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makess (nt3z:md t:i when striking the water below is heard 3.5 s lmdti:s( :3ntzater. How high is the cliff?    m

  A person, with his ear to the ground, see3q9l;jf , azx+g g+uyc er);cms a huge stone strike the concrete pavement. A moment later two sounds amc;z xgg yjq);ea+9 r3+ful,cre 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 disa 85h6qk 0 tty.p6( l;smofnintance by the “5-second rule” for estimating the distance from a lightning strike if the tempsh onp 85 y66k m;inatlt0.fq(erature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at tvzdc4f( htyu1 (-o+s jhe pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound who *xka c2;bz8zkse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired 9/5csg::wx,iyaos )rq94npcf 5o ezn ;w wy a;simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitcp9gi5wns;)x/a fo ey,on :w94 r:aswqcz5; yies, not dB’s.]    dB

  A person standing a certain distance npcb +()j-vtfud;g/w -l*be 60rufzc from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound 0 ebrz6fvlf (t)-j-wcd p*u+n;/ bguclevel 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 ha z;nb mj-wh9v)ve a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bav bm9)z -hnj;wckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perso2e8r :u q16jf4nnvto /z;wu g,uyiy c+n speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly oquie,z1y8fuv:g+c r jo/w;n24t u6 nyver a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum mt n/jbs5fafa 9m:*8cd)ie nm* 0h)mf 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 w)e 2)jyv+v 3 g*bxzjamore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect atejgy*b x)v) jw2z+a3v 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 13 hn/.1g qh7fw;.ievcgc sd6o*0 dB when placed 2.8 m in front of a loudspeaker on the stage7gd ws*;c v6h .iegqnc 1/.ofh.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sxr 2h;i0aps9- r o:jvk rqln+y0h/ax;ound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose leve /k9xoqsr2;pyax rair +lhvn0 :;- 0hjls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whazkia/pu-twd ,2x j)i fd, sca0puf(fd e/1w,8 t factor will the intensity increase? Increz(j idfppfu wt/ ,ec )10awa8sx- if,u kdd/,2ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemen 1hrdb1+5pn 9hfh/cest amplitudes, but one has twice the frequency of the otherrp1h9/1nechh+5db fs . What is the ratio of their intensities?   

  What would be the sound levf1q(c brxk)3xel (in dB) of a sound wave in air that corresponds to a dis xb1qr) kfc(3xplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what pd qi q keu)a+ .sr0-:u8flkh3k +jcz:sound level to seem as loud as a 100-Hz tone that has a8luaiqf +sz cp :j k+3qk 0:hkdrue-). 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies iu0 84ax1bjus k(f;jaq k9 ,gethat an ear can detect when the sound level is 30 dB? qak8bxg9jf,uk ;e jai4(us 10(See Fig. 12–6.)

  Your auditory system can accommodat-dfl /d wd-+p 2v(pwp jyl+(lhe a huge range of sound levels. What is the ratio of highe /v+dp+df2w (lhjwdpp-(-l l yst 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 frequency of 440 Hz. Thel ato*lr2pre k76 aw x0/l1th8 length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be x68orapl 7ellrh/1 *tk0taw2placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three (py1 8*xv arn 8xgo,hj c(bl6aaudible overtones if the pipeoncx j vgr68 l1a(*a,xp8 bhy( 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 of ad+xy y*/3rww /pjj px0n empty soda bottle that is 18 cm deep, if you assumed wpx/ 3+ pjyd0/yrx*wjit was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range,u. o; 28dnunfe8 t1sy;w.gw ,pa hraw of human hearing (20 Hz to 20 kHz), what would be the2 a8d.,8 ustaweh1u;nwnf py,w. o;rg range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as u a0r (sh7 e)u+y.ooreits third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% ouh+0ey() roa eo. urs7f its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above kaca7of 1:. nbi5ud.cmiddle C (330 Hz).ofn .7. :5akdiu c1bac
(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) whwwu0vr7z6b l s,v a)oa0h*4zcen the temperatz4vwahsb r z6),v70*0 alcuw oure 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 duk87 e-ei x*xat 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 Example/ cdp *q ,awsir,:4jtrs+o 1jb 12–10 should the hole be that must be uncovered to play D ab41s t+i:jj/bra rp,qc oswd ,*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 resoif0k;(dso vn1vvi3fy,+v1g ka-ojs b +z ft(9nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipeo vnvks(fkdj(09 zti-v a +g; o+bff1siyv 1,3. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is ovlt-a kuow5s)u z so g(9,doee;i)/9ppen at both ends. It resonates at two successive harmonics of frequencies 275 i)e apd( - uv)okz9o;ws9t/lo5ge s,uHz 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 m)g h /u( 1rmjccmd my:v6dc(/$^{\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-long :e 0n2y*wtgxdorgan x:0 e2gydw t*npipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatenep 6;w)ncoy46mm5yk +zsx d,5* vzgfly 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 audib 5y*dzsk, emm6+cy;6 wfogzpv54 nn)xle range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two s+imttx4a13 n ktrings, one of which 4 t3itnkxm1 +ais sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz*acqp-9w g8djrj4ij-/k,j t k) 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, while another (brand X) z .ypf- iy*tqq;egz)pna4j* ,c n,6x ioperates 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 played simultaneoui4*yzei)yn6g -qxqt* apfz;,jn.cp ,sly, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a ;gp4 xqyb x2h4350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency ox y24qh p4g;xbf the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenc(v wojw3r,vt) - *fmyvy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be yr)v-tm 3w* jfw(v,ovthe beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will js dl eyh+u/,*ed v0f8be heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°Clfh*0+ed uv8/,de ysj and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Ch ) nji*8dv3yd. Fork B has a frequency of 441 Hz; when A and B are sounded 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 i d*yn hj8)v3dof 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 spe1vxbc;p zq +p*aker and 3.50 m from the ;zx *cppq1v+b other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano 6: v8lki2mvyx 3ij 4grzb( ex(tuner hears three beats every 2.0 s whei 8legr3j ( v zim(bxv4ky2x:6n they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound /w r4tg-zif;vj06qp*pi8ta ro tun ;6of wavelengths 2.64 m and 2.76 m in air. How many beats per seco oiruigp; t0/tq-fn jvz r8*4a6p6w ;tnd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ6/zyj gh uprbbp iiz381-,ehr5p;iu5ency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do youi81hzpg6pu -/z5ui r py3ehb5;, rb ji 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 frkwoiz v6 ;;1piequency do you detect if a fire engine whose siren emits at 1550 H6w;;vzkipoi1 z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yoe2b 2sh 71gp9f .ydnmzu at 15 m/s versus you moving towa9es2d.1fby gh 7 pm2nzrd it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one i 4(wypf7 tav59w/cbb*f j8 hens at rest and ta hcbbj9w (*5w7/4fve pfy8 nthe other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 s,mbg7v* ny)bztn ,3.7xmyke kHz and receives them returned from an object moving directly away from it at 25 m/s xv)77mmzyn3 kb s,*bnt,.geyWhat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, tyy1 m;m.imva2 c6 w1zahe bat emits an ultrasonic sound wave with freqaz2v6y.y wm c1a1m mi;uency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat-2x.com75tcj7h 5yemdu xf u 5 train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if thtuyx575.-dx hj5mmeo27 u c cfe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter us/ )ov 5srgsk4(xpvb*des ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz,okpv x(s4gs5/dbr *) v 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 frequency f4p0qp16ohm8r6fwa c $2.25 \times10^{ 6}$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 x:*kfp4wznc9 frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who 9 4pfz:xwkc*nare 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 f qy yqp:9y,5 pu8p+ytits 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 soy; 2h-.jy cj qrf-gmm,6aihi; und is 310 m/s (a) What is the hj2m-;amh i6j- gq;ifr. cy,y angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmos*ym z6c, zekcwxci )/3phere of a planet where the speed of sound is only abcc, z/c*mwe3zk)6x y iout 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. Determine the shoc/23gx*arer-hmmb e)ecjga9 /k wave angle it pr9/er2aa-gg rjece b/*x m m)h3oduces
(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 hy0,l,yonmif (ga6 jd+u*zx:$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above thef7t:l, y(cb 2xo*acw n ground flying faster than the speed of sound. B2o7bwt(c n cl:,y f*xay the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward,( 0*ar7 wwn pw/nmzgo from the bottom of the boat, and then detects echoes. If the maxim,rzg m /n0woawnpw( 7*um 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 t*7uy8-bkqlu jbg7ro9 he human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pilmum6x)u*hkj *hi x,a -( yvo*pe symphony. It consists of many plastivjl6ka oxu( m*mhiy *u, *xh-)c pipes 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 5.0u(d4 x5*p9ih1 kpqjyw m from a person makes a sound close to the threshold of hum19d*q4iykhpu xw( j p5an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whva1ja2vm: zq ,c f:p yt57l0mjen an 82-dB sound and an 87-dB sound are heard simultaneously? :tf2aa0 jp: 7l5,z1 m cqyjvmv   dB

  The sound level 12.0 m from a loudspeaker, placed in the oon:.t vg8 y3 e1jtcdv(pen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direct.g:1 ev(j8 t3otycvdn ions?    W

  A stereo amplifier is rated at 150 W output at 1000 9s(ny*fm*mfd rcs lj(rwg56t e-y4g7 Hz. The power output drops by 10 dB at 15 kftsgl * dg em4n-(57mc6s* (w9yrfjryHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet a2z3r fh* , y., cm1/hgqpaduivircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at/d.rv2zm1,qhcp * fy h3i ga,u 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 communicationnvr-rymq s 547s 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 is9.i) baamxty i wqlhjho-3103 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 fundamergkaeu;k5g.0g6a f zc - 7hr5jntal frequency of 440 Hz and a mass per unit length of0zf;rg-g6kh r5 e7ug .cjk5 aa $6.1 \times10^{-4 }$ 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 verticadaq)kwkq2;m(t 9ssd- i+7 rxul open tube filled with water (Fig. 12–35). The water leveltdxiq ;r79 m d2akk-+wq(s)su 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 mass 2.10 g is near a tube t h6lj qt2o0o/7sa -vfohat 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 fundams6/2f0qo ao7lvjo th -ental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to hmbrra:0j , jln1:h-cresonate 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 m9f ,ra5i:fede+umr r7nf3o- in the 500–1000-Hz range coming from two sources. The sound is loudest ifr+ed7oa5 f,em-3 nu9m: frr 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 one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. T-* c+hq-l bxj,pml2ru,vwo8 h he conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movinguhr wvxhc-+8 m jl-,,q2*oblp train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afterihj;jf4x de; ( it passes you, its frequency ;je i(4dfhj;x 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 ju),q *o h75x6bosdfpyj st by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drop,ho* 5pyxqf bo 6sd)j7s by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat f opjh*.b)b6kz /vpy o-requency of 11 Hz. The shorter one is 2.40 m long. How long ih-kybj/p6z) v*o po. bs the other?    m

Two loudspeakers are at opposite ends of a railroawk2vw .u;v2bud car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers afbv2 ;vw u.wku2ter they have passed him, at C?

  If the velocity of blood flow in the aorta is nj 97d;j1r-o xgm(adnr ormally about 0.32 m/s what beat fro 9a1djx7jd(r;r -mg nequency would you expect 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 6.5 m/s while the moth is flying toward 3qcsf8 uulp6m.2d-b kaa8z h4 the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the 2 -8muc3ubkpl6h8fd4a. as z qfrequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequ-9nz 8yx mteal ju4h*(ency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the n4hexa l y-n8zjt*(9 umext chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send w 72yj/nmto6f 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 m/fnm6o2 t7wy just 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 b- nwz9qd46sqhrz:v yz fl (4(re compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living roo4:v(zs6 r9dq-zf w(yr lnhqz 4m 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 demonstratet2, : gjdn2vhion, 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 practice, the rod can be m2:,v tejnhd2gade 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 7a9g( ui bo arr8r*4rcr7 sk.a mm64hsa frequency of about 1000 . u7ao76 r9mrsmh4r gr8absi*ca(rk4 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 he6,1raxe y-jh, - qzgdjars the sonic boom 1.5 min after the plane passes directly ove,-rgjha1q x,yd -6ezjrhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1kp18( bjea+hweak 7o55 $^{\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