What is the evidence that sound travelsm*wnu9s 1 (2e fj2gd 6hofzy6n as a wave?

What is the evidence ty;)y(iy eok/; hx/ia2 ud;y mnhat sound is a form of energy?

Children sometimes psink918b 3j owlay 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 other cup (F9ibn1 jwk 8s3oig. 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 expecdj,u 0y.x,fum t the frequency or wavelength to chang ujm,d,.xuf0y e?

What evidence can you give that the speed of sound in aphg n590r (gb 6edr ,xtfgv)x6ir does not depend significantly xgb,r g 5h env9t dpx(fg0r66)on frequency?

The voice of a person who has inhaled helium sounds velv)f); y(g9jrnw 8c ,78jt zaj9ygumm ry high-pitched. Why?

How will the air temperature in agswtbzvti4 y nj 6wsj i8,55lc. 61mo/ room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitv x8 y:x9xces55,mc avude of sounds in various frequency ranges. (An example is a car ax vyem958c x:cvsx5,muffler.)

Why are the frets on a guitar (Fig+kwi:1, t3 xdjp5kva,c f dps3. 12–30) spaced closer together as you move up the fingerboard:w,t3 dkpx sdf5v31ki ac+p j, toward the bridge?

A noisy truck approachess.d17qxlh 0o+fkmxflb ) 09uw you from behind a building. Initially you hear it but cannot see it. When it eme l +x0sw9h)d1x uomqf.b0fkl 7rges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due topf )bdka/63x o “interference in space,” whereas beats can be said to be due to “interference in time.” Expla k/ fdxo6b3)pain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin xjr-xdrmfa21(brk(x ,; b6 flts D and C (where destructive and constructive1xxxm kf,6bf(rb2 - dlr raj(; interference occur) move farther apart or closer together?

Traditional methods of prote ;u(d*aqtbev+2u*hk q cting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noe+v b;ut2hk*a(*q du qise 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 wavenu /mu1w3( b saa.j nz vk-jg.0m:pt*ys shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different wgv/n0t:j 3.1k a . ps-muym(*njabzufrequencies, 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 observer move in the sams4t* 72d7.n,w)wwd fhupkv gcf; +apa e direction, with skf* d)fh7.,gw 4 wd +wn paaupt2v7c;the same velocity? Explain.

If a wind is blowing, will this alter oz os-fpz:/h*the frequency of the sound heard by a person at rest with respect to the source? Is*zfz s- p/:ooh the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor 4bmimzd*a3k i 5ngl11 s3ob(yq(e,iqis blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle1o ( *zydkis1ibqb3 35m4amq ,(lieng? Explain your reasoning.

  A hiker determines the length of a lanh8vo87(h it0mw:x +y3beovr ke by listening for the echo of her shout reflected by a cliff at t xt(3vv y8i:bhr87ow+ nemho 0he 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 the waterline. He hears + 26 m ajt1ma-n3kt(uq xh ;fg)cw(gxlthe echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) a(h -(+m 3kaxtc lfugxn;16)at2mqwgj nd does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavel;nq( s hssklgv6889kfengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggqsnaf,h)s)c6 1 d5s+tduy+ a by day. Without warning, an engine backfire ys6 a+1h5)qd+utas) ,f cn sdboccurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frogeqve6 ); v23z5+z, 6xmaxvg0x lbmsom the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hi mg 65 v3ol2 gee)z, s+xxv6vqza0mb;xgh is the cliff?    m

  A person, with his ear to the ground,mjwg dbulabx gi8/2p k7*-ic *c8bl)7 sees a huge stone 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. w j agcklpbc88i2* u)7d i-* lg7/bxmbHow far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second ru94byrs ut nfu q/p-57ole” for estimating tq to-5r uy u/f9p7s4bnhe 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 1 0a l):q8y; b:lo y6st9lubm)uswtz1d20 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levii(laz.k lf lgtm3bo72, -gi 2el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound l /l ja7yt)qx.wjt9u:v evel of 95 dB when fired simultaneously at a certain place, what will be l .: xjjv)twy/a9u7 qtthe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eq :f 10y6 4x8dmlmyzlhnually 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 engine? [Hint: Add intensitiesm4f:yz1m6ny0 8hlldx, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wherea prj t umc4+9jbdo f :63gg+/wptwqx+;s for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bacx9;4 c tg6+/w+:jb3 o jwpmruptfgqd +kground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power g9 3,zrmvnssfz: 1 6bgd *my,noutput of sound from a person speaking in normal conversation.9m, g3vrzz6 snms:bnf, gd*y1 Use 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 arbq brsvz2*qbd 6,a 2c7ea 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 25yz mm7 * oc:/aq.bzyu90 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 bm9am zzy/q*ocy u. :7loudspeaker 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 13* 8*,r .)mzxs agimj*1pusq dc0 dB when placed 2.8 m in front of a loudspea*,z8u1ga i *)p *mqscmxsd.r jker 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 typis :+g(a(owmwb;qhx+fa, gq+scally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by o( q +a;asqgfwxg(h wb +s:m+,this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inb8wqoy), ggh +nqw78ttensity increase? Increny, w 8 g)qtq78wgb+ohase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amp68 mpzsxwq5dl 9 -k2emlitudes, but one has twice the frequency of the other. What is the ratio of their intensitie swdp9 m5 exq2k86m-lzs?   

  What would be the sound level (in,/suw5;a mc0;cbv:lpcap. nu dB) of a sound wave in air that corresponds to a displacement ampc5:vc .s;anc,wl p uaum b/p;0litude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soundnk)dta-q4m/iv9 jwyi noy;-0 level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Set/j;904 m ok-dn i qw)niay-yve Fig. 12–6.)    dB

What are the lowest and kd+/yg gz*x g8h; cm+yhighest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) * +h gmy8gxzk+ydc g;/

  Your auditory system can accommodate a huge range of sound level s nqq+dsabw0s6he9d,prhljfyp-3 rg 2d69 7 .s. What is the ratio of highest to w -,d+2 .6plgrsh per j3sqdfqy90da9b6shn7 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 fun)30 ccyuii9ij damental frequency of 440 Hz. The length of the viby)j 9c03iiic urating 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. Wh ujtg:-1dj2sd at are the fundamental and first three audible overtones i2j1-gj t sud:df 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 blowing across the topk+zi u iof* j.,1ioet) of an empty soda boi+oe1o* iut .kz i,)jfttle 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 spanning the range /e-b: zhdu.ap of human hearing (20 Hz to 20 kHz), whatudh-bp eza/:. 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 540 Hz as its third harmone mogg s9i **gqgabvx89b b+ v456mg5bic. What will be its fundamental frequency if it is fingered at a length of +ao5evg99 xs*b*gq b4b5mb6g imgv8 gonly 60% of its original length?   Hz

  An unfingered guitar string 1zmm/vb ,9i nnis 0.73 m long and is tuned to play E above middle C (330bi/m n n19,vzm 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 pipu1fs,vffnn7*j 9xs8me that emits middle C (262 Hz) when the tempeux*vfjsm8n1 f,n9 fs7 rature 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 2b y1ys3oamyr4doh y9jx9du-7;ho) cm:q45 br0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o8uyx yu8 wom 2xn*b))ew9jzb/f the flute in Example 12–10 should the hole be that must be uncoo) enw8j/u8by)z u2wyxbxm 9*vered 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 Hz, aokrs(a0o,4ju; 1uek qnd 616 Hz, but not at any oth ou 01r4k ekoja;qs,u(er frequencies 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 at both ends. It resonates at3b+i7lmn+ q p:a vnd.(34mhs4zrlw qp two successive harmonics of frequencies 275 Hz and 3hmwmv3blrp7n+nsi4 lq:q4d a+z( .p 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 k cy5uogojnxn ,..p,)$^{\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 79)f3ah1xqo zh / iu, *pxrmsjpresent within the audible range for a 2.14-m-long organ pixm u,*oi3/sfzhr a1qx7 jp 9)hpe 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 is cn5d etxh03c8 open to the outside and is closed at the other end by the ea0e3h85tcn cd xrdrum. 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 ev,re 0zavht8 d8ery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in h0r d8te8 az,vfrequency is the other string? ±    Hz

  What is the beat fre4f8bo :jjqu. iehy(6zquency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle opetyk4c 4jqs)/4vn n6of rates 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 they are played simultaneously, estimate the operating frequency of 6q)c4jys4f4 t n/k nvobrand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9x y7y znagpfjg5d)-3ta6.yb* beats xy*fbg5y6 zaty37 - gad.njp)/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tens16 ccn 4hysa3k9a0cation in one string is then decreased by 2.0%. What will be the b64ycac0snaa 1ck h93 teat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to ply nfd9d9 8ani 2b0k 9oei3y.loay middle C (262 Hzoi90ek .993yldny 8i2ad obnf), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, (b * spus(os9oxx0/ks B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat fres(s(x o9p0 u kb/osxs*quencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one (vhw6tb7mbycvpfe4 k66vuq71 1f5e t speaker and 3.50 m e(6py1hwt6vuvft 1 e57m6bc 4 q7fkbv from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, 4u,q-qdzor (:g qkzc-but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vkoz (zd cg4:r,q qq--uibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m andmj c6vsrf1at 7fn ch4p-hr8. - 2.76 m in air. How many beats per sec1 8jtr--r.6nc4 pa7fhv c mfshond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a c2: rxfvc*)fntertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed ovn) 2fxt:c*frf 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 f1n nfv/n6zp1gcr-cf 1ire engine whose siren emits at 1550 Hz moves at a speed of 32 m/vg f6nc1r z/ pf1n1cn-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+mk be 0a4elw0u at 15 m/s versus you moving tow ma+4lek 0ew0bard it 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 fryf+ t56 iko0(6e(wxbbb jy s+eequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Asb+j we6ybteboi(60( s+ y5 xfksume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out qft3-prm(js; ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 23f q;s-rjtm p(5 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall abt +8or7pvps 8c0mfw+0)ib *kj r:xrs t a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the refl700cp oik +xs:tr8+pjmwsrvr 8b f b)*ected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wa.- *;spyyaamhi g0(,e irzt;f s played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba p;i ,ys0;(hga iet fz*y-ar.mplayed the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter us(3kcl h.lje cmy ynao.zq,/2;: 5ko jwes ultrasound 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 sour ho.c(aky.e3 ; w oz/qyjl:2jkn5ml c,ce?   Hz

  The Doppler effect usp 4 wuq0ss3lo5ay(*rving ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velo: x2gws)5 xtygcity is 12 m/s from thx:yx)2 gstgw5e north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20)l.91yuv tqxun hb :h lcm -r.1d8x/he $^{\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 speedjm.vt:qlj 0 g( of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of thegj.0: qj v(mlt 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 atmospherg/ c0-:pqv v;5w.va gu+ j9jc gg6fgese of a planet where the speed of sound is onlyv6 g fuv:9vg5/s -qca+;0gcew j gg.pj 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 strik -kto, d1etnnx3yk* wjh17 lr+es the ocean. Determine the shock wave angle 1d+ho,3 w *71nlt-knk yxjrte it produces
(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 4l7w q-c+psci $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andzulxs*jchfy;mf 5n- 1v1y6u* see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the py**f-x 1z5cn jly;f sv h6uu1mlane 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 device that sends 20,000o:im*kwm/vs3 5s(,finv 45ih 2djgju -Hz sound pulses downward from the botto:/mv,kj4fw 5mvih *dg2osjiu5n (3 si m of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the- xwdwo*m*)xi 5;cg mz human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consukq e/d7v dq:+2 gf76mtszyz ;ists of many plastic pipes of various lengths, which are open on bot;6d772zk f yq+d u/gztemqs:v h 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 sound7 ewkootcb 7h;* 22ebb close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such7;ko22we7 bcbo e*b th mosquitoes?    dB

  What is the resultant sound level +sn ka vn)(9rs cbi;f4when an 82-dB sound and an 87-dB sound are heard;isnb4)f9 v+cks anr( simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1k/nf+oo. )voz nb8zg505 dB. What is the acoustic power zbvkg nz o+.5o)/8on foutput (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 power outpuc08v,m tq .1j smpiuu2t drops by 10usmitm,0j1q.vp uc 8 2 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicall8k/pz k,v5duz)eyh)b2k*j ldv4 g0yly 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 intercelyj5g k *zpy2be )lv,k0z/ 4kudhd 8v)pted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thz fx;+a ckaf60e 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 iu)x+hw hpy -h1;ia8o1$\frac{1}{2}$ 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 belpe,gn)sl0g xf 3gor a6-d4h0tween fixed points with a fundamental frequency of 36gxd-,lar)h 4o0nl f gg pse0440 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 above a vertical openlc dys92yogs ) 7fv,(y 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 th,(l9yodf 2ysy )cg7sve tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open a,okx ( -vyq;obt one end and x,- qv( yok;boalso 75 cm long. 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 wegg xq,t 5ny)7as observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourceslgr)qt qh57lndiit49x5q +2p . The sound is loudest at points equidistant 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 othe5tdq2)q 5+n4l7xitrl 9iphq gr. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train cese y98;nuglk iz 060h,0ubr is stationary. The conductor on the stationary train hears a 3.0-Hz beat fre l6y8 u9cgu0e;ez b 0,rnhkis0quency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a st3ej(chsa 5 w 4h(p-,)hehg* uj,bswgs eam train whistle as it approaches you is 538 Hz. After it passes you, its frequency g, h h3uegbe4 cs(awhshwp,j5* js(-)is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate thu**l0 q- gipyye 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 stralgy qyi0u**p -ightaway. How fast is it going?    m/s

  Two open organ pipes, soundi4o :6 u7ojxof4a,6fg wn3)o8 kzntuywng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m l 6x u3jo74oa4nygozw 8nfkf : )otw,6uong. How long is the other?    m

Two loudspeakers are s9u-i.ft 0hg7mxv d 3hu7 xj ix+5qjf(at opposite 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 identical so7hj- 07(m gftvu xdxsi5xq ji+9.fhu3und 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 the aorta is normally about 0.32 m/s what beata)eprm5h5i2a 5t-r3 jjwg1ll frequency would you expect if 5.50-MHz ultjia ga2p1lt 5r 3 )5m5-rhjlwerasound 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 kd5q p**ude331ue(c+tyb x giat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off q5+ke1ddug cp*uy*i3t x 3eb( the moth?    kHz

  A bat emits a series of high frequen54f1.qi 7vtoz b/fpswcy sound 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 stp5f/qbwif.v 14z7o 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 b)diy / sne7fn+y1kvg +;f*5cp qpbt* Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used *f ;/tb) g*yk5y+p7bsfi1qedpv+ cnnto create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the4 ok:p.lg3 v,9k6 uhp uogf1if presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room hfg1 .pu: 46uko3foi,k pvgl95.0 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 “singz4 3ya/qz br5//qlmthu -f7nf ing rods,” involves a long, slender aluminum rod ha3bqfyr zu7 5ht4l/ /n/f-mqzeld in the hand 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 human ear at a frequenc1;0* khc3h( flnuwwv py of about 1000 Hz 3w*c pn(lwkf0 h1u;vh is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears qukdl 5b0x v2ox;,6h-5kbhlsthe sonic boom 1.5 min after the plane passes directly overhead. Whaqhv,lb k0l;h5d xsxu2 6-k b5ot is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbox tpk0;k05kcsb26 mtf at is 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