What is the evidence that sound travel a/b ne asw6:)1:o7gs3bdzcb 8yze (ths as a wave?

What is the evidence o5 2(eikwc k:fjaih+-qj fk;2that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string tou/9uphd;fn+x l ,27 c thh-rzw the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig.72h rht-/u lu+fp c;nw9dz,hx 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from bsxq0jw7,: 3q,vxeq h:u1sdw air into water, do you expect the frequency or wavelengtw :xs:,h qw0sq db,13qeux7jvh to change?

What evidence can you give that the speed of sound in air does not p fzhzzn 4: 8kbt7v7r4y (,ljqu* *lrbdepend significantlyz48zby:q7 (*ll,p*7t 4rvzujrhk nbf on frequency?

The voice of a person who has inhaled heli xhlz5*m sjg85td29yo um sounds very high-pitched. Why?

How will the air temperature in a ,;* 5 em*:mf g*oyevabkmajq-room affect the pitch of organ pipes?

Explain how a tube might be used as a filter tpxdqt7n t136t+/1) vtg bzmfs) 7 -nx l7uygfio reduce the amplitude of sounds in various frequency r yip)73lq uf/- t1 b dts+fzxxgn6mgn t177)vtanges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closa(rj0v9c( e jber together as you move up tc(b 0erjav9j (he fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hewf/m3+ du shxk1 ,q+*mgrts4 mar it but cannot see it. When it emerges and you do see usk/*m xq1t+w sgf 3hmdr,+4mit, 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 “intkuc 75nt-xq* ,lycrinv/ 92a d3*a*fqydrk2terference in space,” whereas beats can be said to be due to “interferercqk vn/fl*5uiya t-c *27drty,9k2 aq*ndx3nce in time.” Explain.

In Fig. 12–16, if the f 18fw wo/j1:mazqdc- lrequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togethezo1:jlq8am/wf c1-w d r?

Traditional methods of protecting the hearing of people who work in areas wp0lhxw8 kt g5m /u98crulmq-s o 2*0mwith 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, th/0w hcmtg*wx9l0mq5p8lk2r -8 smouu en 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. Eu0qgv;i 0 ;t,027tb)atmxtfnuxx i 9oach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in t0a; 7,tubi) 0xi9;2xgmovxt tqn u0fFig. 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 observeo a5 d:m+5wx/mpxh8 rsqp6 :yupa:8p or move in the same direction, with the sa6 wyps:x q m:am8:5 8xo/pd+a hrpu5opme velocity? Explain.

If a wind is blowing, will this alterkkx+k9 h)z3w czb8, (y:w wdsr the frequency of the sound heard by a person at rest with respect tkkzd8 +h:cz3) yskw r(,b 9xwwo the source? Is the wavelength or velocity changed?

Figure 12–32 shows var- ,ota6frtx cbv53az8x)6i);q uslor7ou dy ,ious 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 xo;)osali 6yr c 6v)5fbqdu zat8urx-,37 t,o, 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 la s7f3s jeuxc2)tv9h k.ke by listening for the echo of her shout reflected by a cliff at the far end of the lake.cx esf2j7)9u3.tkh vs She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side)2vd .11:qiefynr lol xl:(xahdk y-9 of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly ball o xf y.n1he9: y1v2i)rqd(-xk:dl elow 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 wavelengths in air+h *m7)d3hw lna digf( at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is dri suba a/28:atd :4thzwfting 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). Howbt t8uw2s/a :dh:za4 a 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 whene;*l -w v9m9qxgqgyd - striking the water below is heard 3.5 s later. w-l-gqq9 y e mg*9xv;dHow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tshspdbs ,;a4+he concrete pavement. A 4p asd;,h+s bsmoment 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. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dis sy i rum5er9tqdy*b6os. ul;*(dj5( ctance by the “5-second rule” for estisj.lt*ubuo i qdy(cr55(e*d m6y s 9;rmating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of z/uru.mhh7 1n+lbe2i 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 soundj;d .7jcpcfl jt i*-0v whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level 0h)h smqz*qj6q1 16h put itx,of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.])m1xq01zht6,jq tp*6hh iq us    dB

  A person standing a certain distance from an aff5d;m4 i .qsuo 3xml4irplane with four equally noisy jet engines is experiencing a sound level bo4o;mim u5l4q. ff3 dxsrdering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fou b2.9 dmidiosb/;ov7tm;c4hr a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eachus 94i;mdi; /2mo .7vhdb btoc device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a personi 9z: eerf,ue5 rtf,6x speaking in normal conversation. Uxtere i :, 5uer6z9ff,se Table 12–2. Assume the sound spreads 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 eardrum whose aryson9qj6 f2)eo.6 yfvea 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 8wbf*-oq d )ks. z 3)zlxyr+hnmore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would )s+*l3kzo dqh-nwfyzr.) x b8expect 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 reg zhj3wc)p h6)ublq6 :vistered 130 dB when placed 2.8 m in front of a loudsp36v b) l whj)6zc:huqpeaker 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 ex1 a1xgw /yk12.0 dB. What is the ratio of the amplitudes of two sounds whose levels diew 1k1y /1xaxgffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) byq 8i ea2d*wfyqb /gt ;tx9z54qi;t -sv what factor will the intensity increase? Increase by a factor i wz-4i;qygvqts ;5qe* /ta928 xt fbdof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampf4f ) +yxcd10 thr yehfk/3p)klitudes, but one has twice the frequency of the other. What 4 et0fcy y/hdrx1)fkf +hpk) 3is the ratio of their intensities?   

  What would be the sound level (in dB) of cgab 38sg+)16gbazw wf 19m uka sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 bwc3b 6ggk91ags+1w)u8zm a f mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as l.(f (egpz-,tm0ry8thlg; tqdoud as a 100-Hz tone that has a 50-dB sound level? (See Fi z8-.r 0hpl(,qdt(tet ygfm;gg. 12–6.)    dB

What are the lowest and highest / ;o(qkwlw//pe-roa cfrequencies that an ear can detect when the sound level is 30 dB? (Se;kowq- //rlp/ewac (o e Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound level8. p m58lfh,io8,/aduyxcuggs. What is the ratio of highe8c 8,f/5d 8 upm,luaogyxghi.st 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 levuwng/ 0t6(htq: b)imngth of the vibrati/0 mvt6i)t unw(qh:gb ng 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 the fundg;y9d bfn74sb amental and first three audible overtone 74ds yfgbnb;9s 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 bloqgo 2;tf2ijz0wpw/wr + +rke qxh(7m,wing across the top of an empty soda bottle that is 18 cm deep, if you assu, x 7q ji/0qw+2+ rkpwrmzhet g2ow(f;med 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-tube pipes spanni7ul m-xy0b0 ling the range of human hearingmb0i -xyu 0l7l (20 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 string has a frequency of 5djri;a px7 y 7 f-gp,c.c4(ahi40 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of i pax,i ;.7af4j7hyc-cpg( dronly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tune*1(n 8x*3 ghndx jmxrrd to play E above middle C (330 Hz)8d1xngn rmj* 3(x*xh r.
(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 pim:qf 6x becc-.pe that emits middle C (262 Hz) when the texc c.fm6be q:-mperature 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 ) xy1rq7fe2b2;zg;ntxla. 0 jxv tb6w20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mou(jmt/;6lppsskwz ;rz7 gcw* :thpiece of the flute in Example 12–10 should the hole be that must be uncovered t ;kjs s:p* (/m7tgrlw cwz6;pzo 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 264 Hz, 440 Hz, aqc1qx56jg fgc bu3v. 8t;r0wfnd 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clbj u v6rt cf;01.fgqxq8wg35cosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m -z 54vde;4gz;ut5x7xf od cixlong is open at both ends. It resonates at two successive harmon7 4g5v5c -x;dxdiezxtz4f ou;ics of 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 0j ib8jil j w;jjw2v96$^{\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-lon 2 eg )l))cfiu(1ksfxzg organ pipe at 20 (xfe)li)1u2czgskf ) $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It -k-9at 3mqsj)0a(z rr csdx*zis open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing as(jzcq3aks)d-r 0x r-t*m9 zwaves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying tv; sh q+rsk(, q:vect)o adjust two strings, one of which is sounding 440 Hz. Ho)ek v,qvcs+ts hq(r ;:w far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzt jcuzm59h+(n ) 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) ope0yo7z y 2(zs0gd ga5vqw 0yu2;,tkwx:yyfi /vrates at an unknown frequency. If neither whistle can be heard by humagudw2 w0x tzoiy0yvv5y:;z 20,y7k/qs( fygans 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.v0c5gku fg +-ma,:g z6 ( aew;0 gy-ifpttvrt 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoningtvg(-vp5fye +wtg t;0aaz f k,:i0 m.g-gr6c u.    Hz

  Two violin strings ardpx0i( wdy:)n e tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together?d)i0(wp y n:xd [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tr 9e5 nwo7o:q t tue+s:th..sqcy to play middle C (262 Hz), but oe o.+.wqqt 9s : 7h:t5cnsoteune is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, a d*pnaez6t 1x0jp,l p;3p52yi0t5vod ,cntwend C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequencyixywel tc6;v td *tp,ez,1p5 pad0p5j o0nn23 of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.a dcfc+ r*9pfg)jf7/sp fq- j;00 m from one speaker and 3.50 m from the o*c)jp7q9f/ ;argf-j d+csfp fther.
(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 3:sv dqv zcc892 rgp9tpq 87c/d+isqc Hz, but a piano tuner hears three beats every 2.0 s when they are played togethet vg qqpsps9cqci+9:c2 d rzv7c8d/38 r. (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.d2 1ht;tb7 tmw64 m and 2.76 m in air. How many beats per second will be heah17m2wtt bt; drd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sik/uoq mnkrz1x713 ,re ren is 1550 Hz when at rest. What frequency do you detect if you mo7 3xqnkek 1r,umo/zr1ve 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 a fire envn*n*7wl+gg kgine whose siren emits at 1550 Hz mov+v nwln*g*7 kges 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 m oy/ : d+fz2bxj7ik-vabxgd4c1 .8rwx oving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? 4wr7x+:ky ib .oavcb/fd1x2dx jg8-zAre 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 eqa qj wh4a g-oh.(dgl(/uipped with the same single frequency horn. When one is at rest and the other is moving towar.(hj-ga4/ w (hadqogld the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kbzf *mq+a.g8il; 9ju bHz and receives them returned from an object moving directly away from it at 25 m/s What is the received.ijq mzgu; 8fbl*a+9b sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits aldqb ms- 5zssx2 e+z69n ultrasonic sound wave with frequency 30.0 kHz. What frequencyms6es xbs295z-l +dqz does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played onzq/ vqn5t*s;liu-f p/t zs )*b2zwd:p a moving 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 theqpzwp* -:zu ;l2 q/ts/v)*fnbt sidz5 station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasounddkyty1wb tsq0+gdgdv:v 331:o9*qb q waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound soqg v39 b0q *to t:3dyb w11ydkqvdsg:+urce?   Hz

  The Doppler effect using ultrasonic wave2o,26igaxoi elbdf;0 s 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 ;tqa-if e1u7j of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,afq; 1-7tuje i 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 iux/ gp t43xn/land 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 wherew 8q;pcu;o f;q the speed of sound is 310 m/s (a) What is the angle the shwc8q f opqu;;;ock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed **v jem;qcz o:1k z2u p8gn6t kfk3e5hof sound is onlyq2zeun1e* 5zt * m;ko :6c8hj p3fvkgk 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 strikes the ocean. Determine the shock wa: i-irqva*05 qjj8e7s6uynf1mr6w k l ve angle it prr 6 -vl8j6 im:n1aq0j* fwry7uqi5esk oduces
(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 g3(;x4ulkrfnwcg*1 / 0ifg ys$/theta$ 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 abo0aox7 ga sa9 +q2wf:8sktgao: ve the ground flying faster than the speed of sound. By the time you h gs8f +o27aaoag t9 xaqk:w:s0ear 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 sox31nx/ywm-ga madfrm h3k6 0/b dbw8:nar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maxim/m 8yfgdba3mawxn6 m/k3h1bxwr-d0 :um depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangeo16qtg0l2y uq? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipx; vxiszg4mczait:d ;q8.5 p6 e symphony. It consists of many plasxq;zg4ixt65d8;pa :vc misz. tic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold ftzg57l.xu59 -lqwpt v z35ncof human hearing (0 np ul t5cvqzfgtx3 5.l 7-z59wdB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB8v hy 3q2 m6kzyz4xi2fqbd 3k, sound and an 87-dB sound are heard simultaneously? 3vyy2diz6b8, km4h 3kz qx2qf   dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105ft,glo c7th)a n9z.bhu/4aj8 dB. What is the acoustic powz,ha84ghb t)l79cn.to/ fja u er output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at jwmt282 6on9e7-r5 u ai4e8d jl*p,am ezgojk1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kH 4a8d-eajwuo7 ikj5*26l9tm2em,jpe rgz on8z?    dB

  Workers around jet aircraft typically w qzjq9pa(+c 4cear 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 anp4aq (jz +c9cq 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 communil4r0od n;zr9i cations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 5cr2c3w gl(u r1$\frac{1}{2}$ 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 3sk.oeko8yisl str+ k;v, 09a0 2 cm long between fixed points with a fundamental frequency of 44ev rkiss ,o0stkl0k+y;. 98oa0 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration 3dx q4z- hwj.rabove 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 levr43hxw.j z d-qel 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 2.1ploqu.p16 d+c v+ ;hkz0 g is near 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 resonance (in its funppco1+6vh.kq ;zd + uldamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reson, oru(z 04i.ngc5wpx nate 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 frc+6u4 vnp:ldf m-b.t hom two sources. The sound is loudest at points equidistant from the twf4u n6+v:- p.t mcbldho sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stulz:3b 6rys5 3hp obc0ationary. The conductor on the stationary train hb30bz3osh uy:5rc6lpears 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 whistl f1uk 3obeta3ky h-q06e as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hbyukea- 3ok t6f3h0 q1z. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dvmr 1(, y fzpx)16xpb9pn+wk 4cw8tacifference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a ba1) (1,t kpzxpwy94mccrxp8+ f nvw6 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 beaom)eb5 g y .q/k,hrks3t frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?m)korky5es/qb. 3 ,hg    m

Two loudspeakers are at opposite enc1.:z3x 9d3uvj 3xnf;rq ftands of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. fnxxq .3; rtvnjca1 :z33d9fuIf the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood g; 52yzsb q5mrflow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along5;rmq by2 s5zg the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the b:jgxft: 9kt zk kpwa,; gi5*b;at 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 k,ix9tzb;w f;5*atg:k: gpjk off the moth?    kHz

  A bat emits a series of high frequency sound0flvnli0nftr /9g ig ; 6o+s,l pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns beforlf9r0s;,6ni0 o flg/t +nlvig e the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals fry:0dw7ic1g2zp /uj j zom one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When playeup1 2wc i0y7j/j:zgzd d 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 listening can be compromised by the p435wr ,e w7utmk x24*nbwddpiresence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencixu3 n rpt4,dm7*4bewdwk25w ies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, caw5r9qxgv 1rca)o. -)m)y,r wb2j aumo lled “singing rods,” involves a long, slender aluminum rod held in the han9wjramg12 b ))-orxy .rv)am 5c,uq wod 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 humk(2wsf+,cizi.vf(t 4 p okl 9zan ear at a frequency of about 1000 Hz ispz24 k (.+owlt vi,zs9(fcfik $I_0$ = $1 \times10^{12 } W / m^2$ 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 th w3tng,3nia *ne ground hears the sonic boom 1.5 min3n*witnga3 ,n after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1.-tr eq+tw,q h:cq v+r5 $^{\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