What is the evidence that sound tra 7- xgvg6um)o7a,pxv 7r*gxfdvels as a wave?

What is the evidence6wqnb6 u6 - wry mj(gd4st(oy6 that sound is a form of energy?

Children sometimes play with a homemade “telephone” by w2.gws) :8z4gphw)fvdp do-u attaching a string to the bottomsww.vog2:p) ufs w dg 8phzd)-4 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 other.

When a sound wave passes from air indhufc );c9bu7to water, do you expect the frequency or wavelength cu cu9 fd;h)7bto change?

What evidence can you give that the speed oo1-15gppwg y/n rodz4f sound in air does not depend significantly on frequencw5opd -og1zry4 p/1gny?

The voice of a person1d)medlioi)/ dgexg*( ;t4cfyn sc*. 0 is:u a who has inhaled helium sounds very high-pitched. Why?

How will the air tempo t8a 0ce mckfgz8 g0w:v;4k)zerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun*8g 1rsc bhm00ems zi4 q9c;s7uktdm:ds in various frequrmmz7 sb;d e04kut10hs* ccq8ig:9 smency ranges. (An example is a car muffler.)

Why are the frets on a guiepxp 8 a9dl*f :qzurtf;)- x;dtar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bri8rpl f-9pxu f )xd deqt:;;a*zdge?

A noisy truck approav3jc,q3.m mooches you from behind a building. Initially you hear it but cannot see it. When it emerges jm 3o ,.qmcov3and you do see it, its sound is suddenly “brighter” — 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 sp;0o z xdghn1byop zjff-k5e5,, pn0s6ace,” whereas beats can be said to be due to “interference in tixn; kenf-j0p6fby,zds5oz ,p 5 1o0ghme.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wojuhiaachp/ 0c. q ie m(rp1)+c 65wae6uld the points D and C (where destructive and jp616/hi+hqeai 5ae0 m)u(crpac.cw constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peouvzv f+a/- onm/,h25z ux ktc:ple who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electroni nu2 hvz:v+u t //,kazf5m-ocxcally, 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 suppcyd x2 ,qpq7-gr *l0herposition of two sound waves with slightly different frequencilx 2g*q rp-qp0,cd 7yhes, 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 observer move in the same direction, qi7+a wled 317tlu o.ewith the same velocwl7 .eu 3 tia7l+eqo1dity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard egeac h(8w ,gho g1ye)-ev71o by a person at rest with respect to the source? Is the wavelength or velocity changoy8geo1vege7 h w- gh,e)ca1( ed?

Figure 12–32 shows varidh,u8jj h.s+aj 4 4kfaous positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the hijdhj ,hu.4k fsj+a84 aghest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lq0b: 8 io2h as-xtrrp6ake by listening for the echo of her shout reflected by a h :x6o 20 qr-bar8tpsicliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of h r a83-lguq.siis ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and dos 8u-arli .3gqes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavef ws8cjv)icb b)7amz +c 8b3:clengths 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 drif zh12d36jc tvoting 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 c6 2tj1 zv3dhobackfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff.vp:-yvd5 x e6lrlj u4+ The splash it makes when striking the water below is heard 3.5 s later. How high is the vxj l+du465py-r:vle cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tfb1l:o3u,epv f5s9fweh+b nf jh2 8 /whe concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the, fh19bf:o+w3sevbjplf u8we 52 f/h n 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 dist)/ 7/b .nniwqvhr6bjlance by the “5-second rule” for estimating the distance from a lightning strike if th nwrijbvn//. 7l)bh6 qe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity o9 hn/m73hru1txk1/ 8bdmtv ktf a sound at the 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 soun*m 8rw74b yjj981mwhpdut 6jnd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firev fdw+(- 8-ih iizpue-d simultaneously at a certain place, what will be the sound lev+ui8-h -i evw d-f(zpiel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancegodz.iv8 pk-7 from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level woup8dkvzi7. og- ld 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 ratio 5me:oy yojx)jpbf.jsg(e(9*of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensiti jy* o.j x5em: 9(jeo(s)fbgpyes of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking i; h+o6kb/h/9 zvgm ft*elqt*in normal conversation. Use Table 12–2. Assume the sound spreadgv+bo i tq f;k6 /ehm*9htl*/zs 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 strikes an eardrums/a . aq*zgo6d9oe2et 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 mod 4xr,88ipjgzcest amplifier B is rated at 4cgz,48rxpij8 0 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB mejhq3-02f re.cvbhef. p 6r-nvter registered 130 dB when placed 2.8 m in front of a loudspeak-r.fn -06fvpvh2e.ecr j qb3 her on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. o2.,fk)sjjo9ffmu 1 9wu kj .qWhat is the ratio of the amplitudes of two s j.q kfk1 fo,92mo.wju9 ju)sfounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whas +qwt9ff j)+caf hw o8w/u*-at factor will the intensity increase? Incr+j8 /f-wastw ou f*hfa)c+w9qease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal 9cwxpwlom k, f+iyhe()oe (kx8g9t (2displacement amplitudes, but one has twice the frequency of the e gt()mkep(2 yh,f (kwx9c89xl+oiow other. What is the ratio of their intensities?   

  What would be the sound .euw;4cmsg h9j 5:zsolevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibratinzoh45 w:9egscjm.;su g air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level 74,m(bw ux.rpv. hk tq-(m mfyto seem as loud as a 100-Hz tone that has a 50-dB sound lt,f(umxbym- km7vr.p4 w h.q (evel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an c g -1 +27gm5be egk0bi1vmxti4ecj+ kear can detect when the sound level is 30 dB? (See Fig. xvgeikj+e t7kg5ce1bm0 g2-1m+b4ic 12–6.)

  Your auditory system can accommodate a huge 0i.m n v0: *vg9yuebm86qboovrange of sound levels. What is the ratio of hig9g.qv:06 mu0 nybovvo*i 8em bhest 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 cylc j)4 iz67,2 kv8-ujl qjgsof 440 Hz. The length of the vibrating portqu268lgkvc)cjl-yz7i jj , s4ion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wha)kc pjj+e31 yrt are the fundamental and first three audible overtonrckypej3+ j1)es 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 across2qaamhn/kgk 4i6g +7m the top of an empty soda bottle that is 18 cm deep, if you assumed it wa 7/6 in4kmgaq kag2m+hs 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 orga5- v;b segfk6in with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range oke fvbi6;-g5sf the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thmr ld3,jt2jx 2zu1de6ird harmonic. What will be its fundamental frequency if i2zme6,j t1xd 2 3lrjdut is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play4l 1o- jszmcol + 4cxd-;2ertx E above middle C xx1e jt4zl -dcl2o;-+4 crsom (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open orfs0jprw99eq 7,rg.q ugan pipe that emits middle C (262 Hz) when the temperatu 9 q79gfjrsq,0peuwr.re 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 *(dm-m4 rgt crdxt,u7 gke;j,at 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 Examplr v37y ce(v;bv/ mqs6de 12–10 should the hole be that must be uncovered to play D above middle cqvr/3;vm(yvse6b d7C 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 resonupnx,g r0s0qz(hhst 8 ,u,w .sate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenciess,tx0 unhq,rssh(w8.0pz ,ug 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 0u:1;xhzo aih+,g;u f :nk)8kw h zkqlp0tlc5open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is0o; lp), g+qh:k1hlcz: 0k f 5n akz8ux;thiuw
(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 *za3t nfb,r,x$^{\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 fvy :7 *j+v3 au6j ajeee(pv9hfor a 2.14-m-long organ pipe at 20 3:v+yjfvajvp a9*eh e(j 6eu7$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is o*)m3a hljc /ob2lsr3 dpen to the outside and is closed at the other end by the eardrum. Estimate2s )blj*ldac3m o3r h/ 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 2.00,,ytrmh pa vo3y+fd 1kq(w-m s when trying to adjust two strings, one of whichtq(-3ym0ad+o wp,, hr1k m fyv is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and ,8 txa6 ppew 7-ie5sst$C^＃$ (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 k:)u - 9hnhnddoperates at 23.5 kHz, while another (brand X) operates at an unknow:n-dd) h nuh9kn 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 simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork a zvxk7 gsz56v;nd 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibraz5zv 6gv;7 sxktional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to thpy l3c q32j:s 10zz :ya,povptju -p3ae same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency hearujsyp:03plp3tz3-jo ,: a2 qayvp zc1d when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes e tb0q:yjwa c33z mu7s,ach try to play middle C (262 Hz), but one is at 5.0°C an3: 3mz0,yub7tc sqjwa d the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B 5):q v07dwit4qtvy f0ne n/wm, and C. 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 iqn 7dv/ )w5 fn :e0yvwt0t4qmand C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from 8 xe.8e7rc :ev1zbnoa one speaker and 3.o8e1nzc7xrb 8 ea.ve :50 m 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 to be vibrating at 132 Hz, but a piano tunerzt1 sq/wdq*w5 *:blf y hears three beats every 2.0 s when they are played to1w/w* l*qbs:ztyq f 5dgether. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beatss5 tzozz(8 3jb per 5tz3sj z8boz(second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sig/),; z3c wlztfbf9cx- n3z/e b4xgp bren is 1550 Hz when at rest. What frequency do you dczf wl3 g,3/cg4t9;fxb )n e/bz-pbxzetect 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 frequency6tg x9oe9 2z/ghea9 ez do you detect if a fire engine whose siren emits at ee/z9 ohgx6a29zg9t e1550 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 moving1 sf:r*mi jz0q toward you at 15 m/s versus you movingf1j i0m*r:qsz 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 equipped with the same single frequency horn. When one is at nfiatb0y326t rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequi3ynbt26ta f0 ency 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 recnbcp-ayn7j*1h ziz8/ eives them returned from an object moving directly away from it at 25 m/s What is the received sound freque- nbh/c 8zpni*1 ja7zyncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 .rosudr1 x5 r.,.x a5w9qmei cm/s As it flies, the bat emits an ultrasonic,er a9.5 w..x mqrs1 dixrc5uo sound wave with frequency 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 wage)exuf zdjq q.-hs/:3q +xeevwx( 6m)01j kas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the s1es gedv(xufjekzq q3xh)m6 qw:.e-/0 x+ )jaame 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-flowg*.3 a bk f,ypn8s;kmq 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 pf.*bna y,m3ks; gk8 qthe 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 usirn,;wv 2q+ 9l jsktf3wng 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 o+mn :/ +hoq r6fg f:mrys18ikpm yu0q7f frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequ y:p:qnq0 8/hsi rgyom1f+k mm+r6f7uency 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 landk/3pu ,t*jj- mz+u fum 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 r c9- l l8*spvfqu+or/the speed of sound is 310 m/s (a) What is the angle the shock wavpc*l/l8 qr vo-rus9 +fe 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 pl /qvdo 38 fxia.w,uz52z* vcdaanet where the speed of sound is z f.a x*q icdvz52a/8uov3,w donly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s ry nk/)0w1r3g 2jc simah*( 3crfe9pxstrikes the ocean. Determine the shock wave angle it progk3(i )erapr1s32 *hwx /c9y n0jrmc fduces
(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 sqs26.bjy k p5$/theta$ 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 aboveglu3)ib b90q b the ground flying faster than the speed o0bqu39 g)blibf sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sona/ m s dlgt84sif;a:9xz9zy1ax r device that sends 20,000-Hz sound pulses downward from the bottom of the boas:9dix/9 s;fa48yg lzxmzat 1t, 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 th* 2z wvwr*(dqqma;ry2 ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display c * 1btnav4 bsk hn1-b1ra5mkd5alled a sewer pipe symphony. It consists of many plastic pipes of various lengths, whiv1rn1 s51ahb k5mtd-*ab4kbnch 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 per5n nfv9n9gnsigh g8+3son makes a sound close to the threshold of human hearing (0 dB). What will be thennv n fgs3hg9 n8+59gi sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are-st,d h+3y zre heard simultaneously? -ystz e3r ,+hd   dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What ih+lxre,b*wke- ,x6 x:y-monis the acoustic power output (W) of the speaker, ass,wr6 byh, l:xe-kxmi+-*n eoxuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz iti;x;:vvm8 0br9ygiyeyzy:5u8h 2b. The power output drops by 10 dB ay m9v:bheyzyr; uiby v 5i:0;ti g288xt 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectdjyultu.- z*0t yd+ k5ive 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 e-tyy ku+u 5jl.z d0dt*ar 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 communications systems, b- n 9 ;qs+lpxt9vpyw(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 frequency xpvj2t,sse +xt/o/5k 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 p)fqxs t yd;8j+1-md 4qxlz*hd oints with a fundamental frequency of 440 Hz and a m-81;zyq xjdx l)sdht+fqd*4mass 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 dr j288dorer8 vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with ther2dr 8 roed88j 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 that is ope0u) )- s5bkhv )wyf:mr:bxgasn 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 th y- s0)bmwf) sxrgvb)5:uk:h ae third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res pot3ikea8dn)z;x* 5bonate 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 ig3 o(kmt/xg;p afj(fqh2v 0fiu y58i:n the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is thep(2fhmjy:8 oga xk (i5iu/fv3 0 ft;qg frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is*0 21n.vfjuqc eo9jk3wz2s3 nhvw zx)qa*6 dq stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approach293 z qedq**j1 0. s6v u2xz vwwonha)fjn3ckqes. What is the speed of the moving train?   m/s

  The frequency of a steam train whistl v83/9mtd;mmct (pgehi:n b4we as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was 9vt ;h8:i34/pm ntg(bcmd ewm the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by l2qpr6+ sqhri(istening to the diff+qr6s( pr2hq ierence 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?    m/s

  Two open organ pipes, sounding together, produce a beat frequency/ i r91(*lnxljnbwko4o+3sukw ,kp ;p of 11 Hz. The shorter one is 2.40 m long. How long is the o/pr *oulj4slo+( 1p k3kx ;ik ,n9wnwbther?    m

Two loudspeakers are at opposite ends of a railroad car as itg)8pp kjiuam8rbh3/, 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 b ,8r3paum 8kijgp/ h)from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood floy;jbtv3kvfw9n * 8.m nw in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed alongjv .mfty*8n;n 3bv wk9 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 movr.yfm lnr*/-m ezxm (2:0a zxth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detecz. 0ar*vm e(x-xn2/ lrmmfz: yted by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it d(t/xgnn nr6- 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 next chirp is -nrx /dng(n 6temitted?    m

The “alpenhorn” (Fig. 12–38) was once ug)h fud q*fhz(iv06u-d gze(:sed 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 resonatingg -gfhzuhqu:v (6fz0dd) i*e (. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence (fanms, p1fp: 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 theasfn: p1,(mfp fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, callsorw/nrh2 i ofh6 a9i:/u+g i4ed “singing rods,” involves a long, slender aluminum rod held in the n ou2 6:grhf//h+ oi asi94rwihand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequenxomp0fj4l40 .+ fu kmkcy of about 1000 Hkm .40f xlokf0j4p +muz 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 o+wi6)v 8,cggg3 hu d du(rcwh0n the ground hears the sonic boom 1.5 min after the plane passes directly overh (hcud h6, cirgg+w)wdg3v08uead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo:o:bk2 3 :xig0h9/j ktphgcem4uav9zc h :5vnat 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