What is the evidence that sound tra) 6kydkpi3p e,w;) whrvels as a wave?

What is the evidence that sound is a fdp1fj;4o (de korm of energy?

Children sometimes pl4wfxm.bs (gixe al14rput7n0 kz:*,zay with a homemade “telephone” by attaching a string to 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 ot,0(lxz n szb.a441e tkmg :*7x wruifpher 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 wan1ntdyjqal g sf))7hkr+9q: : ter, do you expect the frequency or wavelength to chanjfnr) lt1hq7s)a ynk9dgq:: +ge?

What evidence can you give that the speed of sound in air does not rqjk/j f ;1xah f63-godepend significantly on frequencjx; -k/fag h3q1orf6jy?

The voice of a person who has inhaled helium sounds very high-pitched.mok8 :jkxr o,)ji+0ch4rtzc e y7)3c z Why?

How will the air temperature in a room affect the p+ + 0fmu 4ameuvkx1jk7itch of organ pipes?

Explain how a tube might bewuq;dg w gu)1n2;/ob a used as a filter to reduce the amplitude of sounds in )2aoug w;wd q;/ 1ungbvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–hd. xla7dhe.gp3 an9930) spaced closer together as you move up t.a xpn97.a hel9hg 3ddhe fingerboard toward the bridge?

A noisy truck approacn :ge,e 1gye/mhes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of t nm1ege,:y /gehe high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacy g. ogmfv*lm*da+5 q:e,” whereas beats cl: q+m dgfomv*.g ay*5an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointmu)gg )fca (gyoygj07:ei:x, s D and ifu0:gjxcg)a:gyo( gm7y e,)C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods ., qh.lns3-; au2 9qy gxk fnvq(p3ocgof protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noioq3k ghnfal;q-, 9 np3vg.s qyc(x2.use levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave qd+9oaed7 t fgva8 8a*c.we 5ncan be thought of as a superposition of two sound waves with slightly +wf dv*9.e t5ed oa8cqag n87adifferent 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,ocb 5hw(sfsi.- mnl1 and observer move in the same direction, with the same velocity? Expl(,-lcos .fs hib 51wnmain.

If a wind is blowing, will this alter the 9b 7 ha47 yh)woqzoqp2frequency of the sound heard by a person at rest with respect to the souhwpy 77q2z94)obq oharce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitoraqk06 lkky/t2) 6tgki is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the hia 0i6tk)/ gtkk y2lkq6ghest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by liste*8p9 )/h2exv)atiurz oc98ft m6hnpyning for the echo of her shout refly u2*cei)8ppfhm 8/9zxo)at 69v hn rtected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below t:x*6f*m+cex,mczz gi he 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 tecxg *fz:6*+ ,mmx ziche 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 at 2-qz bfm4 m(654j ly(lgh ns)jg :smm0p0 $^{\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 od3e;py1n0n*y *oo9c 4mgnyfpyo 9c i*n a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses b ooomy4; gnic 9d9n3pe*0*yncyyfp 1*efore 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 s0f, awyn1 c( thb:k lhht4u8c.c5.pai triking the water below is heard 3.5 pi8lch 1f., ca(.h:ycht5aw ubt kn04s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sto /rhd6q-ftzn+f61 v rune strike the concrete 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. How far away did the impact occur? See Tad6/6rnr+f-1v ht zufqble 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secbz ztq1 . 4:(knfgap92:twjlgu x ik95ond rule” for estimating the distance from a lightning strik1q4z5a t :gu: ixl (bz.t2gnkpjw9fk9e if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitc*d 7,x+vsv lgk7zuy8y 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 souroz5v5mx)l)jcsn.9ds2 h o r7ou .tf;nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneous 2zvc.5glg )holy at a certain place, what will be thg. 2ozvc5)lh ge sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fg3)sn 2h4y tu(hg4h v;/yax yxour 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 one engitxhany yg4);xu y3vhhg2 s/4( ne? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereau:iql6b ;c21e crou4bu h:s;zs for a CD player it is 95 z;ueo4i;rslbc: qu c u26: 1hbdB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in clr+rc6sj z; 51 6dyipx-e6oe normal conversation. Use Tab 1 +6zj6-s6c odlrrxy5peic;ele 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 earyd ,; 5sjukx9j2)d dgydrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest jt20 j +wb2zucizs82k amplifier B is rated at 40 2zw jzjb8 stck u2+20iW. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of a 7k 5qzj9 7bfgwi,hmk7 loudspeaker on the stagw5gf97 qh7 7i,mkk bzje.
(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 de yjm na3xv2;p:(au*dx tect a difference in sound level of 2.0 dB. What is the ratio of the amu 2mj n:yax;x* apv(3dplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by w.c qsolkfb9jtpl6arz( ;m (69hat factor will the intensis pq9l66cj zka 9mobt( r(l.;fty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equacpv9o 1u*,wwt l displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities? ,twocv*91wup   

  What would be the sound 6)1vasr 0y h mh,dpvh7p .u2hwlevel (in dB) of a sound wave in air that corresponds to a displacemevu).a6hvw7h hr2, dsm h0 ppy1nt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a:x5 pf;z2af7t rm;msk 100-Hz tone that has a 50-dB sound level? (See Fig. 12:fz7r2t axspk5; mm; f–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sc u;pk v8z4m79t9gxgn ound level is 30 dB? (See Fig9 mn4xvpku9c ; g7tg8z. 12–6.)

  Your auditory system can accommodate a huge range of sound levhacb*20dw3ccs 7irf.lj0l- o j)kw8kp va8x. els. What is the ra 7fcsaj)-3 p 0lc vbd.lrcawi0o8kxjk2.h*8w tio of highest 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 vih6qn ,*w8vswd4 ks oo:olin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, ansvwws4n8,k:q6 h* od od 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 and i 9tebfbzey m6x.,+h .first three audible overtones if the pipe+ .6,bft mi.h zbee9yx 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 j,1uw20f: 9 s/sl ookvt s6p tc3yy9dxwould you expect from blowing across the top of an empty soda0ofltx do9vc12 syp3w ,ssy9/ut 6kj: 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-tube pipes cy8g0o;qgz8k, twet. spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of tyzgt ,cwek80 got;8q .he lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has gc8hxwli30r 4 vc vouhy1x7c,o+1g,k rd 3d2ya frequency of 540 Hz as its third harmonic. What will be its fundamental xg0v, i yovhc 4dg + ol8d,xh3ccy3w2rr7u1 1kfrequency 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 E above middsx k m.8jgdb zz2 znh4e+.a-2tle C (3nmz-gza8es .xbth242 .d+ zj k30 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 pipe that emits middle C () ek xz-dy7b1a262 Hz) when the temperature is 21 z-ekdy7)axb 1$^{\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 m1t 9go +tzyqz9)1zf z$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examp6 h.3epf.f l1:vwf3cixc e*.ph wnl+ds r*z*m le 12–10 should the hole be that must be uncovered to play D above middle C*cee:w.3f** 6dpfpwx rs. l3hv l znh1f cim+. 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,7-p2yfnq b5wiy: x-vs and 616 Hz, but not at any other frequencies in between. (a) Show why : s-wivfbxnq-y52 7pythis 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(il4hxo+nyjjss8)h+wsr 9 kx5 gs7c 0 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and x5s0lhj(xry98sigcwk 4soh) n 7++sj 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 )ay-cbf3d k5mw pszw)w7 g6b 5$^{\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 wiyarmi ,j8xy8u )cg:-zthin the audible range for a 2.14-m-long organ i: um8zr,) c yx8ajgy-pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is2 1shp vy/b4- kcmei4xd5z1u6bryx5o open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing wa 41 dvop51c5x-/yexr6z hbbmk u4yi2sves 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 beatfy: ).:fbtl*xr) ,xq: f2 vhqhl;v ieq every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otheqx:yt).xf : rhlqehfv,b)ql;*f:i 2 vr string? ±    Hz

  What is the beat frequency if middle C (26sm ;,jtwyk q tx)1lq292 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 (bra:( nfw5czx d.knd X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency .cw x: nkzf(d55000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork andog2yqrb q*/ng l 1:vw, ub7y,e 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of*y1q :w,, 2/ggebnolvbr uq y7 the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sa xwi ,v:(kzstv 6q(k/1k y5lx-lto+x ome 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 ao (z 6q1lxkksl5tvwkvo(tx-+iy,/ :xre played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be q: bc;.ukrhca515a av heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othe 1c:5.ak5qc vbuahra;r at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of ua kld234ycx7 bh f*n*441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are tnl4*f ahbu xdyk2c73*he 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+qu;gqmy0 xmcul.*q, tands 3.00 m from one speaker and 3.50 m from the othuxg *qq mq+ylu.;,mc 0er.
(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 vibr yzx bn f-h3 :;x8jio u3c*q .p7blmvm7*u,koaating at 132 Hz, but a piano tuner hears tho3q; v ymuxu73 kp8b xib.*h ,foac7j*n:-lzmree 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 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 wavele f)3x2 ,q9xcjy vrem6qngths 2.64 m and 2.76 m in air. How many beats per second will be hear)m,v 9fqq2xy jr6ce3x d? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fir x z ,p,qz93qe:u/msf alrb00ne engine’s siren is 1550 Hz when at rest. What qqm 0e9z/3,f bn0, u:zsaxlprfrequency 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 dn58 mrmfxv 2g/etect if a fire engine whose siren emits at 1550 Hz moves at a speed of v/n2gm85 xfmr32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yo nhftyaemocfychl5 yf/ ;7 sv, 82+1t2u at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the samfn2/somv +f ctcfet2;5y, l8ayh hy71e? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whentpc+r .:) 6j:r -xb9ikq reogr one is at rest and the other is moving to +-i:p :ekorcrrr tx.gqjb96 )ward 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 kHz and rece h*arq:xp d6 )s:n 0t ;njokw5npd+ao2ives them returned from an object moving directly away from it at 25 m/s What is the received sound o+ w6 ah:nn50*kpj d:sdqx ;tna2 )porfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 mp l t;bf2 z(iz9zm6kgqcss,35/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does gls2q6b tzfzp m(kz9cs,; 35 ithe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played os0ej cl( qc.8vu1:a iwps-w0j n 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 0wsj i(plsu j c1c8:wq0.v -aecar approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves tm-xfeu 6wmi*wkld;x8 xr81x/o 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 atu18*/m8x-i 6k xefdrl mxw;wx 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ulthe(9qn (dg-x55 fgxtm rasonic 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. When the wind velociab:o8da,z 8b tim/m*eon/ , mity is 12 m/s from the north, what frequency will observers hear who are locate/ ,, mbizmin8eabo8ao t/d*m: d, 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 ix)*wh ;wrct6 its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Wjz *d)+gmw629q/ g7 uv7yf nfa6jcjg fhat is the angle the shock wave makes with the direction of tf c*f w+7 g fj9m2aq6yguv/6dnjjg)z7he 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 jl8m55-d fv c;ee gpd8a planet where the speed of sound is only ep8md8;lv- 5c ej fd5gabout 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 slrdiw-/7w n gjehu8)033fehihock wave angle it producese fhi) u3n78 / r0jhl-d3wgiew
(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 :jxv*w8js8p z j.yhroe :70xh $/theta$ 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 km8 ;+)sfl0 )ypl eihybm above the ground flying faster than the speed of sound. By the tim;l i+hf8 b)mpysy)el0e 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 devia9p bw;kd7h m9ce that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for km 9h9w;a7dp bwhich 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 nasi0kxy1 16c audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of9m4 warm 3ntz:oqln */ many plastic pipt l/mao*:q3zn9 rwnm4es 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 fr .h)t4yiyrm9q om a person makes a sound close to the threshold of human hearing (0 dB). Whah. 9)iytmq r4yt will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound a8ww1elnu ,:6lrn5 n3ba ;h mscre heard simultaneoua 6, s3nbce mhrn;u5ln1lw8 w:sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. r 8ksfy wrgc/u+p2n8r8w ;+huWhat is the acoustic power output (W) of the speaker, assuming it ru r2 + ;8nsf +hwypgrwukr/c88adiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The80od dxei4q8q q (5rjy power output drops by 10 dB at q 08d oq(iq 458ydjrex15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft tyd.0yt1 5(gd fdjgwgxk95i;c f pically wear 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 radius of 2.0 cm. What would be the power intercepted by an unprotected 1 fx5 k9.c5d;g ygdwgt(j i0fdear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, th no nwu nh0yhp54:my94e 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 fc zn+a 7wis;0k2y w9-h4h+-fo3 qtst6qd tjjwrequency 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 c 7ecgfld+ d4z5m long between fixed points with a fundamental frequency of 440 Hz and a mass percz5d7e+g dfl4 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 vertical open tube filled 11kgnlxe9md :zlvf;/ 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 level is 0.125 m and lm xv 1 1gn;kf/9zld:eagain at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g fr 5ax:; bpzwog(h8u.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 fundamb8a wg5uxz .;rf:hpo(ental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as onghsekk;;b/d6 xu l/0o e 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 comi od l9,ep4i(ic7azlbd f :,x6hng from two sources. The sound is loudest at points eqb :lifed7 c,(9ai6 4hpl, xdzouidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whis /d zb0t;dwy6b5 zvl0vtles. One train is stationary. The conductor on the stationary train hearb;z0tvld06 w vb /5dyzs 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 wh9 yply5n/;y + ndh. grvwrkj1.istle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. H+nn/rh.g.yj v9k1y ;y lp5 rdwow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listlxzf69dto 1* nening 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 straighto 6dx9 nf1z*ltaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. fcxyr)k ctonm*91)td (6r ;psThe shorter one is 2.40 m long. ds y9t)r*m6)cc xp1;nroft( kHow long is the other?    m

Two loudspeakers are at z4hnwti w58c s)u/ +-rxqy c/xopposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have wn)/z8/ryxsx5itcw4 u-q c +h 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 flow in thef og rpf(kca5 *0elb93 aorta is normally about 0.32 m/s what beat frequency would you c3ofafrg le*0(bp5 9k expect if 5.50-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 speed 6.5 m/s while the moth is flying towz:;z icq/ul 1tard the bat at speed 5 m/s The bat emits a sound wave o1z /:lc ;quiztf 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 of high frequency sound pulses as it approaches c1bam9 8d sv*+p2+fyi7vbyiia 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 cdb2i9 i+sa7*vym pi+v8fy1bchirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sg0:g ny1n(hjo ebh58h.a3x ovt k0r 9rignals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overho3 9ohn x.n gehv0g5k8 (0a:trb1yrjtones 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 atn a(:pk-j 3flve *t:compromised by the presence of standing waves, which can c vk3ap-afj: n(*:teltause 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 frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “u b,p /da0p48n1dmwhc singing rods,” involves a long, slender aluminum rod held in the hand near the dh1,u c a04ppdw8b/m nrod’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 o, u i2c+t9b(u5u grtjaf hearing for the human ear at a frequency of about 1000 Hz is jc5bu(au ,r it+tgu92 $I_0$ = $1 \times10^{12 } W / m^2$ 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 Ma lj /np:ei8j/cch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane8 :/i/cejlpn j’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 xf07xqf3i cizc 4m93/tjbkf($^{\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