What is the evidence that sound travels asbym6055 dl ij6g ;qgpv a wave?

What is the evidence that sound is a 94h, qnzh hjrj6bly4;form of energy?

Children sometimes play xv-2oa 3)t; pqgvc9ok,5s xp;/ bpc fawith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child spg 5 /x q;paop3csvxv)2,;bf 9-ctakop eaks 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 expec; 68ict oiit4+ lg,wy8c4mb int the frequency or wavelength to changc8 i6mwio4i tit;8nbg 4+ly,c e?

What evidence can you give that the speed of sound in air does no -ld -uluho/ejqt1 f*,t depend significftodj1* q/u h, lu-le-antly on frequency?

The voice of a person who has inhaled helium sounds very high)7(p djoq.wpd9wubzm3 :av (y-pitched. Why?

How will the air temperature in a room affect the pitch qx-c) iimtg wp9a5. 5y0wyli2of organ pipes?

Explain how a tube might be used as a filter to reduce the ampliam0wz0k m a(;p9hmu pin3imyc:6 e 09btude of sounds in various frequency rangewnkhz p;99p(0m 6abuaicmmyi me0 30: s. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clp 6 qr1nfs9jli-jr8z -oser together as you move up the finger896-jfp -zqn 1lijsrrboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear e)8jj dj ixl4z (wvo -g2.u3yjbk7mt.it but cannot see it. When it emerges and you do see it, its sound isljtb.jv8mk u3)gj jwz.dyi(o - x427e suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to ber 8 csv6:1kx+zuw 4pzg d)rb5o due to “interference in space,” whereas beats can csv14zp 8o6r:zw 5+xgubk d)rbe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of theb0 7b;oj rkh(o speakers were lowered, would the points D and C (where destrub o0 h(;bro7jkctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of pu/y1 )4z1v ldmhm)o au7md)gteople who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronicallyhz4/ m g1uodt1))m7udyva )ml, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thouj 0p drslfs/)4ght of as a superposition of two soun js)ds0p fl/r4d waves with 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 observerzse0 2 h0koi,dk t2vi8 :etq51 mee6au move in the same direction, with the8stoi0vimqz1a6e2,5h 2e:d eukt ek 0 same velocity? Explain.

If a wind is blowing, wilanr5v;bgp p+:jz lk5 5p6lc,vc)5zg t l this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or v ;pclztv)6k,nzaj gc5rpp5:+v55g blelocity changed?

Figure 12–32 shows variouskcocw2vy ig9v5rr5 oz6kx-5zrw-84*ux a qc * 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 positionk 8ruo 5xc46gxoazwv z2-95cr*5r vkwq-y c*i, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lig5tgne6,uc1 d,dcde 7 stening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengdndgc7,51u,d e6gc e tth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side.ru a v gqd3fty4:e bu*+c6u3i of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Ass.bf3 gu:cy+3e* rv4d6 uitu aqume 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 inl f 6boy-;.lbpvszp0 3 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 of tu2+f vlk5ktajt7ls +w -na on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Howl+ 7jfvkt5lt-k+ s2wa 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 when stfymha 0c/3 7tariking the water belocf /3 0mh7aatyw is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the 30bhg,+yfp5vpj 6mwd concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and tjm+fp36,y 5d wv g0hbphey 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 distance b8dqwmm-h* vdl:24- i pm3lr i,msd0zby the “5-second rule” for estimating the distance from ldmi4r:p8 ,dhlvdq w23*- m m0z-bsm ia lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitzw3*q nuhn49 ty of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sounkt) w fh jp.7x*mo5ja,d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired si 8pm.a7og+ ukfmultaneously at a certain place, what will beo8.g k7u fapm+ the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane (is/3 (wlwe y*piq43y p(uzmbwith 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 all but w3li/ye34sp zm (y uq(bip*(wone engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sik,ewch hr .j +0io0m+ek./ orvgnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signi rvo 0kwke+., c.+ jerh0/ohmal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power oubowo/yj1quut (p c2e;h6 p54ttput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unifotu; 5y(q/cjeoh6 1o ptwpu42 brmly 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 area is1 /opk :0wd(fnid *-/ aezua+l yi)kin $5 \times10^{ -5} m^2$ (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 -2h 7rzuxi fo3250 W, while the more modest 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 in turn to 7x u-hofi3zr2each 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 2i1 scw8r7:rnuecu. r 130 dB when placed 2.8 m in front of a loud .:7c1rrcw sie8uun2 rspeaker 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 soune2 pevm*yf-5nd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ n 5evyf- 2*pemby this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inte bo i2:e*uz gzo7) l)reuib-hai;z; a*nsity increase? Increase :e z;zob*-) b *l7;h2aizorigeiuu) aby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudekjl;cs8h,+ zlp,l- q cs, but one has twice the frequency of the other. What is the rati,h qp8zj,cl; -cllk+so of their intensities?   

  What would be the sound level (in dB) of a sound wave in aux* urpa6ip57g jc 5qi- ns:7lir that corresponds to a displacement amplitude of vibra*- sq:g npiix5auu576pjlc7 r ting air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soun0i3gjv9+k1o7*k zxs :h( hqlxhkr gy/d level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) 7+kjzrgkhyvk :s93hgx x 0i/o1q l (h*   dB

What are the lowest and highest frequencies that an ear can det2ol //*z9uk *z,ooyy fdkrw,lect when the sound level iszol //of yzlu9wdkrky *2, ,*o 30 dB? (See Fig. 12–6.)

  Your auditory system can accig8:mv0vlv x7 ommodate a huge range of sound levels. What is the ratio of hix v8:70v vmiglghest 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 l :.fq9 zgxe;,;;g kcb(m shvhoength of the vibrating portion is 32 cmxg;gv(ohcfkh. m ;s ,zeqb 9;:, 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 fundamental andr -vg .ud fpeipxz//i*2f7t+ 2b cedz, first three audible overtones if*xcti v7.2 z/ed-urpipf+e, zdgb/ f2 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 fr c2w .jn9)phjoequency would you expect from blowing across the top of an empty soda bottle that is9h.2jw)o cjpn 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 p;6k(vlj;lhx0ib e: idipe organ with open-tube pipes spanning the range of humdie6bhjl;lk: 0; vi(xan hearing (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 54j/xvzn 78hhx80 Hz as its third harmonic. What will be its fundamental fre jvhh/xz78 nx8quency if it 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 Eah6:ywjcz yx h3+rg)5 above middle C (330 Hj +ry3 )5cwghxzyah:6 z).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C eo9j ybmpv :eyx7a;:- (262 Hz) when the tempejmbv :yx eoe -pya:9;7rature 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 k .*b,lqoi evv vu.j-+eo46 hnxx:*td$^{\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 thechyfvu 2i22b 3 hole be that must be uncover32u2h y2ivfc bed 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 264 Hz, 440 H -z+3ad)*kbrihgv jp/fs5k *m z, and 616 Hz, but not at any other frequenci)i -g3v5z k*fsrjh*mbp/d +kaes in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open -r ptnc0gud; : )fkui(at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330n(fkr c0ut); gdpiu:- 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 /p 0wdrc hb4i+$^{\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 prese3267lc7e jojbdp 5wkhnt within the audible range for a 2.14-m-long organ pipe at7o7pd j 2wh65kb3l ecj 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apf1 anqr ga lukb6e4ls-x;p/q to)/e*2proximately 2.5 cm long. It is open to the outside and is closed at the other end by the earr)ksx;qp6 /n* gbl2-t4 aeef 1/a olqudrum. 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 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 tryingbu:s39 e s,mws to adjust two strings, one of which is sos39mbe s:uw ,sunding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262yecmlf5* 7tq)ub, a(e 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 .dat 4h33v cpooperates at 23.5 kHz, 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 theyc.avtdp3o43h are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with1u.nlu)h nk8i a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fhn)8i nu.l 1ukrequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensilrm*9hx 4 * wue,7rbnfon in one stn*wfrh,* e7ub9 m4 xlrring is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idenho/b3 2kf u lfpx7xmy(42kdd8tical flutes each try to play middle C (262 Hz), but one is at 5.0°bhf2yuo kd/x2 pkld(xf874m3C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency ofzw)9e-62 kcpcluvv7zex 5 m o3 441 Hz; when A and B are sounded together, a beat frequ6v9)3xulee pzzk w c7ov5c-m2 ency 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 s* q ds7 d,l//qjeawsu aw8kb:-tands 3.00 m from one speaker and 3.50 m from tw:dus *b -7es /awqqj/,l k8adhe other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, bus flglr(da8 l:o) ie; sd:e31jt a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the oe1dfsl8:oe); r( gls 3 idlja:ther ?   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 t b-qf9 k. s/llq,dvm:m and 2.76 m in air. How many beats per secoq/ld9vqsfl- mk:, tb. nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren izgd7m+gn9 a8sd j0rp (;)vp qseuwf);s 1550 Hz when at rest. What fap7nmw ;)ze ps9rq dusgd(gf0v; j )8+requency 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 a fiqa.vlbp:ty9,ux n 8y(re engine whose siren emits at 1550 Hz movesb,lqpy n t8v a:x(.u9y at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in g o2i836cjapns :6 yqp; q/vtwfrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward iqty;a:gs83c6 o v6p2jnq /iwpt at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single brgmem6r35jnn5i9e 8 frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the g n893m6mj in5eerrb5driver 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 ultmr;rx -mk5hk+rasonic sound waves at 50.0 kHz and receives them returned from an object moving direct-k+h m ;kxr5mrly 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,mq7 fos(z4 .ga(aptt. the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Whatpt4t7o.a fma( . qgsz( frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wa *d+2o.lmeq kcs played on 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 the station at a speed ofo*l+ q 2edcmk. 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blo3g;a ts5f blm epim70a 8qaa-*od-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed ofs5eltaq 8a - am* 307apif;mbg 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 fre;sot +.rcqy paex0w:nw4r0,b quency $2.25 \times10^{ 6}$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 freque bh,+ 3o4xv f*2c.hz5/i ozz,ezqm xwzncy 570 Hz. When the wind velocity is 12 m/s from the,4 2 oxe/zzb fzi5z 3,x+hv*.c mqzwho 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 landerx,v,+ dl6s f:1vb ed 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 wher0, )cq -i 2mchx+dpxwae the speed of sound is 310 m/s (a) What is thwc qh -,20xdcim) +apxe angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a pl b/rxxf 9j4e7j5s/m pva;1ekyanet where the speed of sound is only about 35 m/x9jpa eev s7k f//rjx y;m4b15s
(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 stg +fvq wt)d(q)rikes the ocean. Determine the shock wave angle it produc g+)wqqvf(td)es
(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 ov7c us2zjo*/hd)t2ya9pn( w $/theta$ 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 ground fll3 5l)xjhh 87iyskslz vz-6qs/6-j tbying fa3/6slisyvz6hs j 87 l-)jz bhtkx-lq 5ster 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. 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 devicste/gb i377n le that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. Ifeig7sln /7t b3 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 arf(fkk9gb o* o1wex /q/e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonyj;v:i9jd f0bjee7j j7 . It consists of many plastic pipes of various lengths, whichjejdiej9j 0; 7f: 7vbj 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 xd3 xibg3dat3-os 2.iperson makes a sound close to the threshold of human hearing (0 dB). What will be tsx 32 -ixoba.i 3gtd3dhe sound level of 1000 such mosquitoes?    dB

  What is the resultanty6ih w1/ao kmgjm88ws mjh9-6 sound level when an 82-dB sound and an 87-dB sound are heard simo9/ 186hm s8hk mja6m-w jygwiultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB3kyqick7 i zn ):ls 9ig+;cqc4. What is the acoustic clcn ig:iizq k37)+9y;4kqscpower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pom--y.w0 zf* jakhgfsz- gt3bh n,8vt9wer output drops by 10 dB at 15 kHz. What f a h8 s tf0*-mywkbt.zzn, 9g-jv3hg-is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. Ar efrn:j-si;:ssume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average hrfij: -rn:se ;uman ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications system qv ;pi5g -wpb o(wi4axpfdq6q1fk ,09s, 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 vioc 5+ )ux6pgwoylin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a funyi50lm kfye) xpg+d5v7ko8 7 pdamental frequency of 440 Hz and a mass per unit length of vg7)iyd50 5o7+ykkmfpl x 8ep$6.1 \times10^{-4 }$ 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 vertical open tube filled with wa2 :rd8ws4htfg ter (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 thw r:tshdf2g 84e distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 gn cmexn66;+ cvv h a la8/ak-cczy0.r2 is near a tube that is open at one end and also 75 cm longa0 vmn cx-vc86kc6aza2 y/c+erh; nl.. How much tension should 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 lou3lu c1qzmy,f6lhip 2 l;( *ewop ($\frac{1}{2}\lambda$) 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 k1g2ns2 ax(p q500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To de kg(x1qn2sa p2termine 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. Onj+ 9:tze( y b s(ekzfw/nx2,cse train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other traitjs9 ,c+n2s(:e bk z/fx( ezwyn approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hzx b9scn wsgavzrahij:-t9 s6a6(d 4+-. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume con6: 9v(ab w+6j h nisgaxsa4-s rdc9z-tstant velocity)?    m/s

  At a race track, you can estimat*zh0+gqv 6v dfe the speed of cars just by listening to the difference 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 fagf dvq +6z0hv*st is it going?    m/s

  Two open organ pipesfiq hj/n( oh)qom 322p, sounding together, produce a beat frequency of 11 Hz. The shorter one2 pqqo(3n o2hj)fi/hm is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of g*l oyqx.y qs,r65f u0a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at s0q6o g.lrf qy* x,uy5B, 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 m/s wx(ya5j.1)c ;ywv mqjv 3igjp 2hat beat frequency would you expect if 5.3 vwpyi1y5vjjqma (;)x j2 .cg50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speedxq8 plx3 ojpel r,kj 6g2l.1w8 6.5 m/s while the moth is flying toward the ba38lg.12pexp6j8 r o, jlxlwqk t 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 off the moth?    kHz

  A bat emits a series lpv,xup5w /2j of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. H5 w,uvplj/p2xow 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 one Alpine vic7g g //lj .qdf9g-bdhllage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create-qg 7c/f9hldg/d g.jb 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 listening can be compromised by the :4gh(t tjst+ym xln5;presence 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. Calcu5ygm;h4s: xl(ntt j+t late 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, slc h81a yysu/,xeikv4(ender aluminum rod held in the hand near the rod’s midpoint. The /x4c,u 8v(sy kia yhe1rod 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 threshold1* tzjcgl odryc3;y 3( of hearing for the human ear at a frequency of about 1000 Hz iszy*( l1t 3rd 3;ygcocj $I_0$ = $1 \times10^{12 } W / m^2$ 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 then,k6kbs0u cd3x,b; 1 i v6sjye ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s a3bsj i 6b; v,keyu06sd,x1kncltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is()ib +n9y erlx*b yv5l 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