What is the evidence that sound tra*d t0 xck g)xc x/6)pfvuu1hp+ccn u1)vels as a wave?

What is the evidence that sound ou0ga, 0t:zx:wc1pghd:r * e bis a form of energy?

Children sometimes play with a homemade “telephone” by adp3qg66q/ 1 naro qz 6am3t-yfttaching 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 (Fig. 12–29). Explain cmo -3pa qqy6/af1r3 gt6dz6nqlearly how the sound wave travels from one cup to the other.

When a sound wave passes from air inrz ,btmv *d(5nto water, do you expect the frequency or wavelength to change?,ntzvd *r (mb5

What evidence can you give that the speed of sound in air does not depend signt2v74;u+jxa tyj w i0cificantly it4auy0 ;jxcjw7v t+ 2on frequency?

The voice of a person who has inhaled hoq bwmp5aalg -u,9(r0elium sounds very high-pitched. Why?

How will the air temperature in a room affy. y(:amgwq+q vq)u q-ect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun12gab ad-g1g psf0 lz:ds in various freqpglgba-adf120zs : g1uency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together aswifxyrh):ul)t 7 +. eg you move up wxg+. hy))i7f ru:le tthe fingerboard toward the bridge?

A noisy truck approaches you fro y*00y c91g g/fgbloqnx:va;um behind a building. Initially you hear it but cannot see it. When it emerges and y0f u1/ln x*a9;vqg:by yc0gg oou 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 to “interference in space,” whereas b.ysmp( zm*,cpyetjq +sn ;*6clc0 8vu om*)fe eats can be said to b +v s*e py c*6,nm0zcpf).m*oq ecyl(j ms;8tue due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would- ,v,i*sgs*ic8o p rso: tgcl6 the points D and C (where destructive and constructive inti: -ssgg6 t*c vpr*lico,s8o,erference occur) move farther apart or closer together?

Traditional methods of protectim+wty yrmvi. .6o*b 1-h;v iypng the hearing of people who work in areas with very high noise levels hav;pvrvywi y. h6.yo *m1t-i+m be consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, 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 .f / jsfwn() oit6z-:k*bsqmk in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with sliqzmnbi*k :s6o- fk/ (jt wf).sghtly 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 an - 9vx1tl0pipv1q /kw5g+sp lrd observer move in the same direction, with the same velocity? Explain1/lvpw sq kg 9vtp5+0i1lx- pr.

If a wind is blowing, will this alter the ( jhl:eh,j2pcfrequency of the sound heard by a person at rest with respeceph2jh,jc:( l t to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a s2r f(v-uqt xw.wing. A monitor is (uqf .-2tx rwvblowing 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 whistle? Explain your reasoning.

  A hiker determines the length of a lake by liw)ph,p*-qs zhstening for the echo of her shout reflected by a cliff at the far end of the pq-pws,h z*)h 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 hjlkk e.;m3)o(o- opn uears 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 t-ol e ko)o(;3p.nkujmhe 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 wavelengthsup7/n 8nzx(jx 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 aboveza dq k2apt/6 uj 07w,9)e3yvrh*vo et a school of tuna on a foggy day. Without warning, an engine kt)6a 97j /p3u*qerhv2y ,evotd0wza backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it,6q0( ) w(qllnqf codi(vq5jp makes when striking the water below is heaqo f)qd(5 0ljc,(lvq qwpn6i(rd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pave7llm / q)op)j vc0erl7ment. A moment later two sounds are heard from the impact: one travels in the air and the other in the conc)7/0v7 lmjl) leqrcporete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dis(r q1/58w/ca) uz:jdkp qajup tance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) qwcpu u qja15rkd/p8za j/(:) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at theitwm ww8qo qb9 *y;k/2 pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensicmc gt,w,o,z4v h,0gx ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whsn0nv+z) 6cmb en fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hcbsnm 60v)+z nint: Add intensities, not dB’s.]    dB

  A person standing a certaio*- ehp,se 3pzn distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, nz 3e-*h,e osppot dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for qu (3vpmqm7tww 8y,d ;-3 b gwfz.iuy7a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 5qfb3gt.-mv7;my,w8 y w 7(duu ip 3qwz8 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power o-o(yl +if 6eyoutput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rou(-i6ofleo y y+ghly 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 strik3o w y2ia5ju:qes an eardrum 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 amplifier B is ra9paw7 i1ipmngq;u5i 7pj olpp: *.-kyted 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 eqgip y1:p -5 loinjipu*; p7 a79.pwmkach 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 dyn*yo vz0ru84ul;qg8ef- d .tB when placed 2.8 m in front of a loudspea yn. y ou8lv*0fg;tq-urde84zker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Wh;xgevgk) q 8b/ k/wyutmj3;6 eat is the t q;8v w)kj e3/ ;ky6u/megxgbratio of the amplitudes 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) h4js2ulhqxuf499ic h5k 7 r,e by what factor will the intensity increase? Increase by x4fjh,ci7klsq er5h9 4 9u2uh a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fr:) r gmy5;falzu 6k-n1xw3zxpequency of the other. What is the gryk6 w-5x l;z )xuma3fn1:zpratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thati *)h wjn6f9x( bd.f mf1*vqow corresponds to a displacement amplitude of vibrating air 91whijmbfoffd)*q.x(wvn *6 molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tcww;6ti7t ;xjt u 57cz(+l.p*lhgnkk one that hl *+ cl xj.7tth6u5zpw;gi ;7ckn t(kwas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highn/elh+r 2j(apest frequencies that an ear can detect when the sound level is 30 dB? (See Fij+h/nal2p(r eg. 12–6.)

  Your auditory system can accommodate a h/i v ux0i zphg;ws 0l qrtby9,b;yj5cz(2o9u9uge range of sound levels. What is the ratio orpxy yt9/ivzjlgh0ouqbz c;sb, i w29(095u;f 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 violio l8y+cv2p 2ecx/2bdvn+jta 3 n has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must 2/2tbv3xjald +8cy2nevcp+o the string be placed?    N

  An organ pipe is 112 cm gu-: qpsq0mbq709 hdx long. What are the fundamental and first three audible overtones90q:x d-u7p mgq0hsqb if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of anyufv*i7,w+jq xtdm*z/8 . sln empty soda b /*n87izjsum xdyf +w,l *qv.tottle 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 orgazpc3 jtrcy4+ wh 58k(sn with open-tube pipes spanning the range of human + 5rhk 34(zpyswjc ct8hearing (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 freq 06,65-hkq tbbvxta rfk2axx6iut7:b uency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered a :b2xbhq67 - fa6txr kt56v,buxtkai0t a length of only 60% of its original length?   Hz

  An unfingered guitar stm my7m 6;3w f6m/ahmf,lpa9gkring is 0.73 m long and is tuned to play E above middle C (330 Hz). lmyk 6m7 /ahw6p,gmfm m3a9f;
(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 opfr,ep 02,7.4 behejma6uma t den organ pipe that emits middle C (262 Hz) when.djum,frp m,bth6e72 a 04ae e the temperature 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 22 vmq bx8p8fv10 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiecdsi iy2u/n(38e;q fnc e of the flute in Example 12–10 should the hole be that must be uncovered to pl(2n/ s3qicd8u fn;y eiay 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, k*6bly lrtnx x*6-h8khq: mw/ie9 me8 and 616 Hz, but not at any other frequencies in between. (a) Show why this is *hmr ex89*qe/xkny6 b:h-kwitl8 6ml 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 bothj stta5 lp8+3r*2g:b2jvrqs z ends. It resonates at two succ:t8 pjvlj bgqt+52za32*r s rsessive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 bhw3 (np7 bvm-64-1vbg iemrn$^{\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 wi380 ,vya8-eidpbml.wk i c i1mk 0ij(xthin the audible range for a 2.14-m-long organ pipe at8i b1xp.,mae 0kw38m -vdiyi0 (icl kj 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm log/gh 8zyi;*i /zfi9b h fqf1n4ng. It is open to the outside and is closed at the other end by 4z h ;9b/iff*1i8niqzgh g/fythe eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 sr10isb+pcg 8x when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency 1sr0+g8 ixp cbis the other string? ±    Hz

  What is the beat frequency if midd.ntrasr c2k-ahx3hx02 t;r :nm /2gj xle 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 opj;9v/het : 9:1 tyjuwrsndat-u0,px zerates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by hdej: ,sn;trph- u:utzt9y/v9x 1 w0jaumans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produc xj;pqbx;q4wreb v +:1c*dk*ues 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when so dxe;b p*ruv+ck;1jw *qx4: qbunded 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 tension i1obv 5+knt- g(lcno6n n one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hinln+ gcvbo 6on5n- (t1kt: Recall Eq. 11–13.]    Hz

  How many beats will 1z 2 gfv/uce-yn7;i/ +jupnr( pdk dp5be heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other 1ugr5(u i+en-nfvd2dczj p7//k y;p p at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B gu.zt) ;keizh)yn- x.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 frequencies are possible when A and C are soun.eh) ;)u i.zy kgtxzn-ded 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 fq)pi: v7 drynyin.1:crom one speaker and 3 n1 ny:vpr.cdy:iq7 )i.50 m 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 bey : ;+ x/tq )fw8tbcicjetj7(z vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are:f/jw ; tzj7 tc+ey( )txc8qbi played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m ingo .n zc;s 77+( 0ebgnm1zwha v7s)qzn air. How many beats per second will be heard? (Assume 1se0gm.z a)7 qnc+s( 7g7v;hwz oznnbT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine3viapz65l: 8c dbf,i)s g6 epy’s siren is 1550 Hz when at rest. What freqlvgis:e 8z5 pbyi 6cdfa63p,) uency 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 frequenm/y gn px/hu5ji sbb9k2 f+s tac8p;7.cy do you detect if a fire engine whose siren emits at 1550 Hz moves at a sp9n hf/py7kiux/b.cjp+ssmg5t8a 2 ;b eed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shif r(23x -ug1u zzfxugya 9,zw gmjh534nt in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it ( 5rx93u1uxjm-y ,u4fgghzn3zw 2gaz 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 thk-6q mm u5od,we same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the ho,qm5 uowd -6mkrns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends k eh km6.7h3ytrx,5 ls+cbx)hout ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it a 6 .y ,ehtrcsbm73)kxkhlh5+xt 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wa3zd/5( lv cydull at 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 reflected wav 5cy(vdz/3l ude?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen- d/gw v0o:k il j/pvdx:f99ggts, a tuba was 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 approach pwo/l gvi9k/xgjd-:d0 fgv9:ed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. rjtl08ru6y4jgvp : w;nne-bg a-97 v)8wsvvm Suppose the d u vj8vsvvb ;t0- nw:r8r)g yna4 p69ml7wgej-evice 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 source?   Hz

  The Doppler effect using ultrasonic 8j(71v7mb5 rqbac atiwaves 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 velocity ifaeu9xk r(.05 +jc simxht z lf0q.d1-s 12 m/s from the north, what frequency rk001+ fqz.tfl.i5ejx c( dmsux-9 ah 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 object5qb0 kn p;,;;xctv vvjy 1dj 44uj+xwe moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of k5 smg )/ .ns02d x8m;pf7ymum o8rk mita/f9ksound is 310 m/s (a) What is the angle the shock wave makes with the ;safxtk my 8 m)58o2 kmpn r9/mfmksud7ig/.0direction 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 ofza e8ap)q-i7t a planet where the speed of sound is only about 35a-7iat8 z)q pe 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} $