What is the evidence that sound travelsdj v;i3v ab/y,2 94ukqguw lzn83)l lo as a wave?

What is the evidence that sound nm...y jfx/bn is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to they zvsixtp7mj l f be3*6:i*2l* bottoms of two paper cups. When the string is stretched and a chiefzt*2 lj *spx mvil:*y bi367ld 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 into water, do you expect the frequency 7q f0 iyessp06or wavelength to chang qs0 i70syep6fe?

What evidence can you give that the speed of sound in air does nyb,f 6gw ql*6hot depend significantg6l q*6b,w hfyly on frequency?

The voice of a person who has inhaled helium s t)brs*drniox2,;y;8l hcoy, ounds very high-pitched. Why?

How will the air temperature in a roopok3snv ib s w)y-.v81m affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ay w/vb-d; e;r)za(4nrt ;gq7g-tfn1 o th gto:mplitude of sounds in various frequency 7 ov) h;q(gr4/-a gt1;nn-bgwteyfot:;t dzr ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up 0ir4r-p.(pr *mcsm du the fingerboard toward dr(-smr. i pr0cum* 4pthe bridge?

A noisy truck approaches you from behind a building. Initia0z1pr*8,uqia1x m+pen qk.w )c gvkzv;*v)zelly you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” —a*rgw1i0;p*uc,q1x z).nkep v veq)8zv k+zm 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 space,” whereas 0meac/ lt,gqu.)yfv. beats can be said.)l 0 ac .,yfmt/equgv to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wo ,tsj*i*km doz a1xd;5uld the points D and C (where destructive and constructive interference occur) move farther apart os1jo*ad z,tx5i k; m*dr closer together?

Traditional methods of protecting the hearing of people who work i)op* 5p:la.mcu qzvf7n areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more)5*pv:az.fpmq7 cl ou noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig.em*u a y8p t+xi 2kq1skj2jb*5 12–31. Each wave can be thought of as a superposition of two sound waves witj85bj yxmu ea *sq2+pk21i*kt h slightly different 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 observer1ftl // a;+jhen(t daw move in the same direction, with the same velocity? Explai; e+/1a nhdla/f ttwj(n.

If a wind is blowing, will this altery (ka8 sq1yxyhyzi,.7v c6ka+ the frequency of the sound heard by a person at resy7yia,1 (v ckhqa yx6yz8+.k st with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motioq uuz7w78pr 0ah)d kz.n on a swing. A monitor is blowing a whistle in front of t8rku uh7 dz)z qa0p.7whe child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake i4zalevx n al-9 e)5: hm3iax9by listening for the echo of her shout reflected by a cliff at the far end o9)e- ixaezl avni:mxh5 al9 34f the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlineju 5 noo9c,zg(. He hears the echo of the sound reflected from the ocean floor directly below9uzj5 g (,oocn 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 wave, nky 7ikmt5i9lengths 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 orfu/xp a elqb j96(//. 0i iejtr:wx9zf tuna on a foggy day. Without warning, an ji t/0il 9r9wbr.ex 6ej:qax( uzf/p/engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whey+stjw tzl- ar,vh -v.h8v/ g1n striking the water belja/sgrl+vh8.z t1y v- wh,v- tow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strik,vye z ywhy(/(mr/.7yf gev:ue the concrete pavement. A moment lay: ymvryz,g (h y.uw7v(e /fe/ter two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one milnkz:(in:y 5 zk /uht6ye of distance by the “5-second rule” for estimating the distaz k5 n 6hn(ut/i:z:kyynce 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 therwse4/ :u(:j h jel;,jz)dxea 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 whose inqr8ks5mo *ok3;ac4n 8k*p vdetensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslyx; zi7 e07k erf3bk:qv at a certain place, what will be the sound level if only one zeqfv0 bx7;k :ie37kris exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an ar (7 ot.4bbtltqr4xpg yo ;dx-1x63vfirplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captav6tgyl1.ob(4bp-;qr4 ftdoxxt3r x7 in shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal--/v +h rrz3rn wzgf2ig *;lf/eto-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rah ;/rnwiz*g-l/vr 2zr fef+g3tio 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 sound from a per8rcx:si2hwb(occ*rcb i40 dfe+ 0zm4son speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly cxm8c (bi0 0z4ehd c2o4wrs:fc ib+*runiformly 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 eardrum1rf aprh 2:jb) 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 mmopx-wk, fa m 1.zrnr156n+g godest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected-,zm15 nn kw6g.a r xfo+p1rgm in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m i :iz yjk:khwvl;+t,-0nbhk:in front of a loudspeaker on the stag:kl -yi0vtki;bnz k w+ ,j::hhe.
(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 9v oyiq:c*rw *2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: Sw* *qyiov:9r cee Section 11–9.]$\approx$   

  If the amplitude of 4qfl4 + vqxhuk4n (z7 lt/yh;ha sound wave is tripled, (a) by what factor will the intensity increase? Increase by a fah4xlt;uqfn+l k/hqh4y (v47 z ctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudesoo- qdb5bgp5tz 2, kmxs 4s1df;h;fd ,, but one has twice the frequency of tf dth gm,d5kdox1qfsopbb ;2-;5,4s z he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of aebt269u*acoc1fs1 id o.ju)s5 g)axz sound wave in air that corresponds to a displacg 1u1e95cs. xocdjba6)i *t as2)zfuoement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-He 8ra:9ifson m .u;1llz tone that has a 50-dB sound l9oa1el :i8m l. ;unrsfevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when thm ;kpozvwiq2yg(i( ;:64ly uqe sound level is 30 dB? (See Fig. 12–6.)wz;2 4oim kyipquv; g(:q ly6(

  Your auditory system can accommodate a huge range of sound level+u9 c;wnvyflr . uu0 -l-lc)lms. What is the ratio of hil)l .c9-f; 0lwur vcu+-muylnghest 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. The length 3mp;pp/ sy ,bhof the vibratinp b;/sp,yh3 mpg portion 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. What are 5wre01gy0 hd bthe fundamental and first three audible overtones if theg0by w 5hrd0e1 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 frx5hyw :ghz9.q6zqp6pib 8s :n equency would you expect from blowing across the top of an empty soda bottle that is 18 cmh pn.hsix6y85w9z:bz6g:p q q 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 a a kx o *mrhk4x+5x/)a8rlao9open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range oxrx/oa or*a5k8x 4l )ahk+am9f 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 a8suodz9y.4q1 sl49 ,msbz oulug/r8q s its third harmonic. What will be its fundamental frequency if q4smrq 8lobg/9o d49.z suuy,zs ul81it 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 play E above middle zz l *4:nzhnyovlb984d 7 :veyj*aeu.C (330 H e9v7eb44zn8*:*:zyh z.lnyo duavljz).
(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 organn pj9lx-:5w ms pipe that emits middle C (262 Hz) when the temper lnp5xms9jw -:ature 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 kq+ /m(egsa4xat 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 12–10 should the hole by o/3 z(p3lgaltiy l7-e that must be uncovered to play D above middle C y 7ip-oal 3l( ygt/lz3at 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, and 616 Hz6ds7b8nc x36bg++ q wrmj+pil, but not at any other frequencies in betw3rc+m+i lgx676 bspd b 8jn+wqeen. (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 ends. It resonates at t jyu*ph3/yofh/ 4xip2 wo successive harmonics ojoi/p phh3f*2 xyu4/yf frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 w /hoi,gmsz:tohr21 u5 a2no(,ck agul63yt )$^{\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 rang*r j)qr 3kyu,. xe (y*shasgf,e for a 2.14-m-long organ pipe aafssy ,3*gek r.qy)r ,*ux(j ht 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appr (;vue6gv dsxox(jb56 oximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of jv6vd(s(ge;x6oux 5b 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 beatf: zxj9 5m2ctn every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strin9jtn z2 mxcf5:g? ±    Hz

  What is the beat frequency if middle C (262 Hz)9 b:nvm zx6s(oxun1fz /k2jzk6o3-tbyk ;de0 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 kH)1c e6umhq fy)0(/2 raejpsbhz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate th(j2ab0 /)qe1p cmhfre) h su6ye operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whenrhe6 cle6ssu1 kn5:n0o 1 d3uj sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork.sr 1n1 le0ch3ksuj6d:n6ou e5 What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequeblq1 l:x,06qew6 ahwhi9j m: uncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency hear: bqjahqmwu hlil,:9w6 0ex16d when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two i,zh d1;g ; 65g r4rwxvic2jtlndentical flutes each try to play middle C (262 Hz), bugc5vir2 , gxw4t;rz j;n16d lht 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 Bih3slo u84,;ke8hhk l g,ebby3p2gk : 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 b8hsebeh42lo: g3, g,3p kl8iyuh;kbk eat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speak;um xd19efy*/z1l ;ag oq2pga er and 31 au2d1 exm/;o9 ;pggyazlqf*.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 s0/6 si cmsh-zt3 o.jsaupposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz,sh-/06jtio .3z scams 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 an4 +j qmamszpgda4p85tc8*f w8x0bzb +d 2.76 m in air. How many beats per second +zq szmm5a0gwbpb8 4pa+8jc* xdtf4 8will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engin cjs z8jm9a7n76g9avje’s siren is 1550 Hz when at rest. What frejjjgzm9 7c 87 na69avsquency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if ad*f/ozu7fxy3 fire engine whose siren emits at 1550 Hz moves at a speed z3oxd ff* y/7uof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz,p :hh;t6p0ty v xmt/9y7 f kozi7bal1 source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the a kppft h6,;h l 1tvy7toyim0b:/xz79two 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 wo 94exuxgj (8pith the same single frequency horn. When one is at rest and the other is moving toward thxo p(u8x4g e9je 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 kHz i-l*a2u4euhkwec+ mh;ix14 zand receives them returned from an object moving diuha +;hiel 1e4i ux4w*k zmc-2rectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the batp+kco9d23 x bn emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hckdnpob23 +x 9ear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pl2*jdda3kdv q* cqv,0hayed on a moving flat train car at a frequency of 75 H0h*dqk v *d2qdv3jc a,z, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves tkyex8( h 7xtlji:8um8 o measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the ik7 e(8j:xm lu88htyx 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 frequenc2 o 4p*udoi 8bdlg+2ucy $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocp e j a+nw13x2eykta*)ity is 12 m/s ntxy2e aw)jk3*a 1e p+from the 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 land if its speemga ; smpb.)s+d 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 who l,+)v y . y6dhhkta-o;two(qere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction ;(hlo + h-)tow dvk.yo,6 tyaqof 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 whw-;qzpck.5 buere the speed of sound is only acu.q5z-kb; wpbout 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 tic 01np.yob/ ghe shock wave angle it produci0bg y.n/1 cpoes
(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 t 0k36dh +j--qudgiw a;aex;tkefj, +i1d1ww $/theta$ 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 the grokg3d:jn gezp/ ny .f,0und flying faster than the speed of sound. By the time you hear the sonic boom, the plane has trag3 p .ej0n/n:zdy ,fkgveled 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 pulse,*y+j;a k3vh mafyu5as 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 the mini;5ka 3 va*yjfm,u yh+amum time between pulses (in fresh water)?    s

  Approximately how many octaves are th* tiy92gpa;5lp z*oteys 9cwd)0uhu9 ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a2 j-(jlves4oxw-xdq . display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on(.lse- qdj4x-v xowj2 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 threshold2z-fiz -:xxkn of human hearing (0 dB). What wif x :nzk--z2xill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an v84)tl9pkc hppt3w mgzzzlr1 0+f -m.82-dB sound and an 87-dB sound are heaglpp8 hml4tmr 0v.ztp193w -fz)+kz crd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in t4sv3jh/-k 2hzp 0qqa the open, is 105 dB. What is the3qhhv j apqt 20-zk4/s acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output a4xjvq5rjg5phn: e p 7*oodt;4iv: z5vt 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output o55; pxeo*r:v j7nj54:4 dvqpithgvzin watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ez*r82 ;y1 crp xbv7cqgars. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by a rzg 2r1v7ybxq*8p ;ccn unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,fqda4u u *c-7p 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 freqzrpt -qzky 1208z sqo) pm6e:msis67 wuency 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 g.q cq hqf hs qa44;/9wo+que4cm long between fixed points with a fundamental frequen4f 4wqs +q.; qec9 hha/qoqgu4cy of 440 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 vfo elo8 s70;+sp jn7xw n/ush0ibration 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 the tuning fork when the distance from the tube opening to the water; j7e/w07pfs0+l o sn8u hsonx 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 nearth4n2i a1f:x; 0f*lnz: pkpml a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance1 f:4xlp2ktnam0lf ;n * iz:hp (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was of:dv56+ef4u rxv 67*zfgpu dibserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from tw( g.ksua*sw/us9vhwbh j99 f7o sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the h g(b9uf*sh/w u 9jsa7.swv9kperson 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. On50 8;wb 0sc9ieem hfqye train is stationary. The conductor on the se5 mwb0 c 98yh0qi;efstationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trap )+(sf r+k7lt f2 ,dl;it(vejac0egjin whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume const c, j;+a(tei)0v2jkls7lfe+rfp td (gant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeq:,qp7eb:yn )qpcv o/0 d 2uxmning to the diffex/pq2bq07:,pqcm )ydun e: ovrence 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, so,cd,5ihyk bv*unding together, produce a beat frequency of 11 Hz. The k5c ,i ,bdy*hvshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stz60b lty2w yb:is +u0r( fxep(ationary 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 +l bts6yy0z:ui pr(w (x02fb eposition 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 flow in the aorta is normally about 0.32 co b:5ym4xf* gm/s what beat frequency 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 w5cyomg:4 *fbxith a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whv.(*ifpph bc4 ile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects offi(f h bv.p4*cp the moth?    kHz

  A bat emits a series of high frequency sound pulses as it (/9w e lmv6le ihg(n5mapproaches a moth. The pulses are approximately 70.0 ms apve gwnm 9m6/hl(i(5leart, 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 emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from onecqz e:1r5 ( cdyq-9ljm 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 alpenhoe5-c j1mzq(c: yd9qlr rn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening a 3c 4ca1t ve(fxcbr(3can be compromised by the presence of standing waves, which can cause bv(( 4x refca331ct acacoustic “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 the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “s 5- gd gxagc+s )iu */i0p66olwku9ojainging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked wap 6ac5 gxkl d-9/ggusw 6i*+0)jouoiith 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 hearingj eq+o; *98gq6(d/eygiqiam c for the human ear at a frequency of about 10a ei q yg6+gjd/e;98q*(q oimc00 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 heamol)h*2axb9nqz g;/k2 2ybv crs the sonic boomlko2agy c)q;m*zbx2hn 9 2vb/ 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 0y,uy 0r /mc5wof0bdda kf2s ,$^{\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