What is the evidence tha1pv1k95tkfqo e kq6d wd5jl+9t sound travels as a wave?

What is the evidence that sound is a form of energy 6 btztvmkv pzt3t 1y7a7f0n7*?

Children sometimes play with a homemade “telephone” by attaching a string to dm4/hz5zf i i,qf:( cuthe 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 sohf5/(, iqduzfcm :4izund wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the f,6 jr q)blhnyr9 ;sf7irequency or wavelqnhs 7,b6i;rlr yf9j)ength to change?

What evidence can yo,)*7 u7zn w-n/awtmw3 trplqwu give that the speed of sound in air does not depend significantly on frequez7wnw) 3a7mpt-u w,q/*ntrlw ncy?

The voice of a person who has inhaled hey2 nf4gw .oru7sz *ix0lium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ ut5jd-kh7d)u pipes?

Explain how a tube might be used as a filter to reduce the amplitude of s k*1vy0yy l9h-0 javn*n6b,lxe:zn c-s ;xqhmounds in various frequency ranges. (An example is a car muffle* kan;*6 x cv,9ely ynq-jmb n0xzshv01yh- :lr.)

Why are the frets on a guitar (Fig. 1p7p7tr+:neug82p4k(g i* xb jqkw a6c 2–30) spaced closer together as you move up the fingerboard toward the br(ua rc+7ni px2t p74wqkjbe gk *:pg86idge?

A noisy truck approaches you from behind a building. Initia/oxti8k mpy4* lly you hear it but cannot see it. When it emerges anp t/8yk4mxoi *d 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 saidd4q7v(ftfxpv 9q -d/28 sst eu to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Evddxvt9 p ss2uq(tf48 -/q e7fxplain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the6 s1o.o-gnidj s 1r1j6yeb 6mg points D and C (where destructive and constructive interferencms16g .6nrijoos1jd 1ey-6gb e occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wutp0t-qo43g qntu 7pglh ka52c1jn.8ith 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 electronical1p- u5ugqp2nnqo8 t k al34ht.ctj7g0ly, 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 beuhn2s4k,x exl9bvx, / thought of as a superposition of two sound waves wiex, l,x/2bsxkvnu4h9 th 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 and1eym +qx4adq2 observer move in the same direction, with the same velo q2x a14qey+dmcity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard uydi0.f79z+ xnauzeq318y0qqu1 j h sby a person at rest with respect to theqnh+au 8xe 1uq917f.y3iz jzdqs0 0uy source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chi1a.;h,p 5khr luo hu/*mmt( iyld 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 th u,mhtr hiyoma/;h(*lp 51.uke child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length okg2r /4jak(zd f a lake by listening for the echo of her shout reflected by a cliff at (k/d2za4 krjgthe far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jus4a1 w (geardn.t 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 4a(1gd.nar wein seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air :: a4r4ngwn ilv j- veh)9bl3yat 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy cy/ht: *u7b y:8j6ww0v gcbdcq 8pof; day. Without warning, an engih cp:b:vq86bdyucf 7 0t/w8y* wc goj;ne 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 (qzmi+ r+bue, 9a(retwhen striking the water below is heard 3.5 s later. Ha(e +( 9mr iqe+bzt,urow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrd;8x35a hzn kkt.- *xl0gktgrete pavement. A moment later 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-t.a0 *rzk dtng38lhx5x k;kg. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distanvi ,g:5x,f-btc-je bz ce by the “5-second rule” for estimating the distance from agi -:, exbcz-,tb 5vfj lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at tf,c ftqr a./s/ 1kn ccs57o-fvhe 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 who2cm i e7 q3(:0gktu3tim5v ;xboiic+ese intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousq)5;vv op4z2f6b hwfc riu/-jly at a certain place, what will be the sound level if only one is expv rqvpi;jbzfc)u 6/f452 -hwoloded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplap z980qfz;l sune 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 captain shut down ap9lq fs0 z;u8zll but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hau/2 qm9og0pofaj,,;8x g4zb z1 eznljve 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 apz1,en0qxzlojmojz8u9 4fb,2 gg /;a nd the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speak9 w9kzs,bvmfcm mo51d1yz uo3us w*2 .ing in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered onwfzwms321o mduk9m 5sz, y*1b u.vo9 c 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 earfa7 ;*j8k tkhptjs6l ta-v1f :drum 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 tjbi01eqjr+iwk 2jj d31 zv:;phe more modest amplifier B is rated at 40 W. (a) Estimate the soje+wij 3b1dkzjv:i1 rp0q2 ;j und 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 meter regi;alpiyx9yit f2s) g ;w,9a he2stered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. h2l)fw t aays9p gyx29e;;i,i
(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 zun g c2 qk61s/ g/j75zu1qo6woabuz5 dB. What is the ratio of the amplitudes of two soundub 1uqgz ckg jon/zu56/7oa z65w2 1qss whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wa+g03ygn33 b jjms8kd xve is tripled, (a) by what factor will the intensity increase? Increase by a factor ofdgjxb3 sj3 kg80m+ny3    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, b- wvbdgs rr-13ut one has twice the frequency of the other. What is the ratio of their intensid-sr3 w1-br gvties?   

  What would be the sound level (in dB) of a sound wave in air ;zc9qj pr5v2eo 7qkd8 that corresponds to a displacement amplitude of vibrating air moleculesk vze5c rqd9poj;72q8 of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w0g fm eyonx0,o4t-6iyhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 1-n6egmy i foto 0,x4y02–6.)    dB

What are the lowest and highest frequencie -izn-(q au6lns that an ear can detect when the sound level is 30 anzq6(u- -i nldB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangexn4ybp7zl8hy (4 v-ye of sound levels. What is the ratio of highest to loweyyb487 4- ( yzvhxlpnest 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 fundaf d :dr6sq+ymro.(dn+ mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 d rd qofnm.y+:r(sd+6g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lon 6nr:8fil ostm2(f sk/g. What are the fundamental and first three audible overtones if the pktmsl2:/fi( rn8os6 fipe 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 2 pj8h.ds)nd-m -fzf6 /wck :khatb 3van ejcwks dm3vd f.6th anph)z8b-/ k-:2f mpty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-px8 ifv0b j/y5tube pipes spanning the range of human hearing (20 /yx8pj5v0bi f Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strinn1ru w),klouolaki9-v f:+bcz /e/ q 5g has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingeredi1llf,:/ ba uoquze-kowv5 n+rk)c/9 at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tsif7u5w* ,kek uned to play E above middle C f5u k s*,w7kie(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 organ ps/fsg4(vr hq(erp5ud:2f j+v ipe that emits middle C (262 Hz) when the temperatu +2fsph5f((4v:jrv d qeur/gsre is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 p33gd: 2k fb.laas +udi,e a5r$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exz9 wr k3pa7 fwo8uz3)oample 12–10 should the hole be that must be )oza3f8rwz9oup 7kw 3uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 2 )ng*ydumzl /b) c 9g(+mo9mhcg.pa-q 64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or 9l ny)cm cbg*zd.)/h9-mu(ggq+mp oa 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 resonates1 ,p8j; wmdc,j8 krvjs at two successive harmonics of frequencies 275 Hz and 330 jds pm18j,c; ,r8vjwkHz. 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 5hinrd-b( hnm +c/qb 3$^{\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 l xfrov9/fml: f)ve8j2z-o-t-long organ pipe at9 v tvf-z: f/x-ojo 2lf)rlme8 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long):gdnz (u i0aj5jq c6vd ;q.zy0+qiwj . 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 your answer to the information in the;d0(yz.n 50ajq:j6 qdzjic)i+vw qug 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 tryi-/pnqf; dskla )lv m4ap;2yq,ng to adjust two strings, one of which is sounding 440 Hz. How far off in fsd)l 4mfaa knv;p/q p ,-q2;ylrequency is the other string? ±    Hz

  What is the beat frequency ) xp:tw )bvem.if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates 1i 7;wh 08mvt*.y iywnpcjl:iat an unknown frequency. If neither whistle can be heard by huma7m:jlywi.in;8 1* h vcypit0wns 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 beat h )eysn,a*z j5oj8ehp+7vk7ss/s when sounded with a 350-Hz tuning fork and 9 beats/s wh ekzo v,)8jynj psa7h5* ehs+7en sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to th/1r(:euzr np ge same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heargep u r1(n:z/rd when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two iden1k;vlv 37ip1vc 3jymhtical flutes each try to play middle C (262 Hz)vcmvl;yvh jkp371i 1 3, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequenc l;ib-syw i2o;y of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded bslw-o2 y;ii; 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 s7.bd vjjcyf z859hn*rtands 3.00 m from one speaker and 3.50 m frob.c 8zj9f57 r ydvnh*jm 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 vib7cs,inq,e+ l hrating at 132 Hz, but a piano tuner hears three beats every 2.0 s wq,,7hl+sie n chen 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 of wavelengths 2.64 m and 2.76 q3f4k s7o hif1m in air. How many beats per second will be hear ohffi1q 47k3sd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginewc4e(i prgm 15p*7ln 2-xgr oh’s siren is 1550 Hz when at rest. What frequency do you detec15 op-r e*ci2( lr h7ngpwgxm4t 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. z ,xvvke53o .5ket xmto4r0w9What frequency do you detect if a fire engine whose siren emits at 1 .9 v0xk4mzewte,k oovt3 55xr550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shiftka hkslrjy y17u7383 t in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are tu7k 7y 1s j8ykh3rtla3hey 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;emr,wro3t+pjj k0h 3 single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequenh+j;twk epjo r mr03,3cy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recq+y ggzi 26w6+gb27pns. garfeives them returned from an+2g gz6byr ignpga62w.qs7f + object moving directly 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 f5op 5x- yim,wflies, the bat emits an ultrasonic sound wave witi pm w-x5,fyo5h 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 was played on a mo1bkqiz1 dy6e tcit1 thhx4bv,57i,u -ving flat 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 the train car approached tuzq6x1 i kdi 5ei,yh1bt7v-,tbh tc14 he station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Su1 ww- s+0uqargppose the device emw0sw+ ug1a r-qits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi/e 2c.q3j68 milpx4n4t(i vmtlxql)i ng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. W2:y0fsy6i hdjhen the wind velocity is 12 m/s from the north, what frequency will observers hear who are located2 :y0jidsfhy6 , 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 i-mtsfrnn8qdk- +,cs.uspj0 8ts 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 whedo q*l+ a+o(wtfa j.5mre the speed of sound is 310 m/s (a) What is the angle the shock waveoj*5+wq f dao. (l+mta makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound -hm8pemwtr liu4w;,n;hbyme7 uz 9 4) is only about 35 m/shm4;m znwrh7u;t wbei,e4p l u)y-m 98
(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. Determinef b (iml3qffpds1e( 1e5i5 ll, the shock wave angle it produlfil 51ese1 (,iq5f( db3lpm fces
(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 0 k3+qcw)zfl /* dzzu/ qwrfx1$/theta$ 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 wg c3)i7bk;qb.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Detegkb q)wcib7 ;3rmine
(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 devicvz g:yd-mg.8 ge that sends 20,000-Hz sound pulses downward from the bottom of the boat, and thegy -8gvm .gd:zn detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there i0 o6mac 3r-yw 5nw+djzn the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewe1 , p1hk0vgfcy -mak.er pipe symphony. It consists of many plastic pipes of various lengths, whikcy-1 .1 0emvhaf pgk,ch 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 aphel7rem1va/ 2u 66lar + dqz: person makes a sound close to the threshold of human hearing (0 dB). What will be the sound /dvme1apu:er6h rl z+la7q 62level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB +eb 0;p--n zr aebs5zusound and an 87-dB sound are heaap bunz-;b +es0 re-z5rd simultaneously?    dB

  The sound level 12.0 m from a loudspeake 6;z-y1i4c2 nlc jrm,1gmkgevuj1 sj4r, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, 144jgu gzj,cc-si6 krj y1 lv;m21mneassuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power .7 k33v8sulju6ae fpy w.5iho9bo+g doutput drops by 10 dB at 15 kHz. What is the o+jk 353 glh9eo vpd8ua.ibu6sfy .7w power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wf t* g:/fo 3a/c8edtnnear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective ratoca/ e/nndg 8 ft3*:fdius 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, the gain3kn, t f(fd ) 5v2fxnzmkkw-u-, $\beta$ 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 ta 3 itd 7z;3dmle+c40gmcyr5yo 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 violi/a* wu6ihoe mrv.1e6vn is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass rau1e6vmwe h vo6/.i*per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertic ke(ueiny,i+0n v)sjer u)alln+mj48 w)(q w ;al 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 abov mje);q(+syulii e 0 nvlnn)+wrj4aw8kue(,) e 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 o4 4k 2zb1 vcadha0n vks4gh-2yb/ 1vjcf mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension shbvkz4d/bvhh2a 4jvc1k n 2 4c1-gysa 0ould be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (etjz .tvc1al/91dx9 f$\frac{1}{2}\lambda$) 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 thf 9ml3 tr,dw 3ci--04bg:axxwg bbo5k e 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant f c4ifm 9b30- - t5g brbxxlw:wd3kag,orom 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. Onetp 8ha2q5a yiv +0(fms train is stationary. The conductor on the stationary train heah p +2 qstivaay58(0fmrs 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 train whistl3hv:xzfc cq 1rh9gm3po9 r6d(e as it approaches you is 538 Hz. After it passes you, its fre cgqrhz3o9 v6mch1x:3frd9p( quency 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 just by liste+,tjrjv8g cascu .1:q.sef u( ning to the difference in pitch of the engine noise between approaching andu.8( j:qv, gft+rejasu c. 1sc 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 togethe s(9odh9c) y xg hp;y9qknd,yn.d/7pgr, produce a beat frequency of 11 Hz. The shorter one y oppnh9 gd.h,n)c7y(yd/gsxk d9 ; 9qis 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 statizy :7.08ap 9p5 eh omdkffqeub53lqv)onary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical so0f.vmyu: e lph9ap8ko bzd7eq53q ) 5fund 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 after they have passed him, at C?

  If the velocity of blood flow in ty 1:nvn nc01ezhe aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow vezn1y:cnn 01 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 (m bcjc8zxi0g;qr n2: 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 j8 c;c zir2bmgq(:n0xoff the moth?    kHz

  A bat emits a series of high frequency sound pulsi3vtl*6 6vqgses 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 frlv3i6q * vst6gom one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine dof6n/ee 4v9z) xf:hwvillage to anothe w9n:x)6z4/fd vehf oer. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F 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 li:e zacsgh + /4u/4u1espw+b h-dc/ye lstening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m lo/b +/dp h zu-e+ ls:c e/eaw4hsyu4g1cng, 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 “singing rods,” involves a long, sle)bprtg 9sq; iy.8*oe/yy1xc v nder 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 *c1 e / vqxbr.yy9)i;g8opytscan 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 fo yn /8 o xb;otxi15z,oqg*4ewkr the human ear at a frequency of about 1000 Hz is 14iyt8 oqobe ,/xwkng;*5z ox $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the soni )f.yz8jfo 3+jsvdaw0x,6 k l b3udc/yc boom 1.5 min after the plane passes directly overhead. What is the plane’s al/ a6fobcj0xv+,3yl)wfzd8 . duys3j ktitude?    $ \times10^{4 }$ m

  The wake of a speedboat ts fp.:5,b;v( tbtl kris 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