What is the evidence that soune2q r)grfn 0lv:j7mq1d travels as a wave?

What is the evidence thqzwt 79k.x ncsx3tm57at sound is a form of energy?

Children sometimes plays (lhkx.z 0s)y 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 (Fig. 12–29). Explain clearly how the sound wave travels z() ssxyh0k l.from one cup to the other.

When a sound wave passes from ;( n25sip0x -ceox yaiair into water, do you expect the frequency or wavelength -on(i; ps0ca2ey5ixx to change?

What evidence can you give that the+ey*k1wmb6f cufqty vn4w(/. speed of sound in air does not depend signifiuw km4w/yve 16b (fy*.+q cntfcantly on frequency?

The voice of a person whob fk ho+eu-5e16j cmq, has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect o0dwl2l*d 6 oathe pitch of organ pipes?

Explain how a tube might be used as a filter to renhxa:z;- qfj4w t n/:fduce the amplitude of sounds in va/xa4-j;qfhn :n :tfzwrious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) sc+,p2u leat sh 8a p48:p,gyq0pk5cfxpaced closer together as you move up the fingerboard toward the bridge?u0 :+ 4f8a ,g8tyqp 5eps2hp,lckcaxp

A noisy truck approaches you from b-ytsmsxu 2h/f3 9rhwvx mo.c k1;b1m/ehind 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 the high-frequency noise. Explain. [Hint: See Section 11–15 on diffra3 vb ct hu 1mxsfxh/9/w-.kyrm1;2osmction.]

Standing waves can be said to be due to “interference in space,” whereas by qg8+a( l8c2dhplr4veats can be said to be due to c82a (g hpdvry8qll+ 4“interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would theqq po- :94vi+u6rtuo3x 2x qnl points D and C ( q-q u2 6u n+:4i9xlxtooprv3qwhere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearf8o:4(sir vooing of people 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 blocvso8 r :o(fo4ik 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 can be h upbsuc7v),,pp fi:9thought of as a superposition of two sound waves with slightly different fr7, puhuf v isc,p:)b9pequencies, 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..,oa xo9j:ls j/jfbu the same direction, with the same velocs o/:l9jb,.j uafo xj.ity? Explain.

If a wind is blowing, will this alter the frequency of ;qfcvluej 8*c qq-o*rsaa:q :/es)y: the sound heard by a person at rest with respect to the source? Is the wavelength or velocia*: js v*:rq) loeq/cayq8 csf:-qu ;ety changed?

Figure 12–32 shows various positions of abe9+30 zlze jt -qskoq:t p*f-2k (xpz child in motion on a swing. A monitor is blowing a whi-zpzqk(o-zkt f 2be3j9:s+*pq0l tx estle 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 length4f9qn ;/ j-cctbeqsg. of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 st;c.q c-bfeg49q/js n after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below th xqkh cp (1jw7(ihd60a9i7b noe 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 the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with bknw 9dc(p0qi a7(ih o6h7x1j depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ifp;5yzcv ei7 .n 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 l/nqb+r1 yom ..*clvw q9i;vaof tuna on a foggy day. Without warning, an engine backfire9 .* l qyi. lqvo;1+/vwbacrmn 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. +oz s6h8najp 2The splash it makes when striking the whajs8+2z po6 nater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stzp ic4o c* bk+,(cc.l6 z(q aevr8f,xkrike 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 dizfvk+,c4 qe8( (ikr o 6cpclx,z.c*abd the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mi7jj d), pnpsw;le of distance by the “5-second rule” for estimpw )sd7 np,jj;ating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120bq)o/sh ;n3yl 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 intensit x 0 i*)6n 22kzjx:bkulrd,zrqy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound le3 +kv8+ qanj4 aatyb2mvel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitiesky aavqmj 83 +ta4+bn2, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally * -a)vo1o4f1et wectenoisy 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,4fe-c e)t aov te1*1ow not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio ov6lr5c -szz++r2up i*0n ovn af 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgroundrn c +v56in l2p*+zus 0vr-zao noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fr0 r wt*mhz6n92cg+ inyom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rouh w ir*nzc9t2m+y 6gn0ghly 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 eardl/xn96d0f vpd,gw x k-sbtb o03r -c(trum 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 qa6h* u51 h-lt kff/c;xozxp9p 3a99z s0 htuirated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in tuiuhz0stp 1 u6 -fq x/a;tp 9h9* afx95hco3klzrn 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 2.8o2 e0;uc7 gxrm, hncu4 m in front of a loudspeauo 7 mcr024e;cu x,hgnker 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 diffeu4ptkwog mt5phw503:wn. f8 vrence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffetmtv3o f 8h nup4 5wg.:p0w5wkr by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a so. cp8u,lr7a, ta/lsi9z kei+ 4g:tz wlund wave is tripled, (a) by what factor will the intensity increase? Increase by a izp,t4euacsltga9ik w8: z ll ,7.r/ +factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal r or2 v*v)97ufvm upp6 1:;wbv9micej displacement amplitudes, but one has twice the frequency of the other. What is6* m um p;vrpvwb9jf 7oe:v92vi1cu r) the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave :5ut0un0wgbw ebus );in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at es0 tbwu5)b ;g:u nw0u300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem v wvqm ,mca79mmq(n 4q3 pz)8ias loud as a 100-Hz tone that has a 50-dB sound level? (See Fi(i mnq3)9qma,m847q pc vwzvmg. 12–6.)    dB

What are the lowest and highest frequencies that anp6qzzb1xg o; rq79pt2 ear can detect when the sound level is 30 dB? (See Fig.6 x 7t;qpob1g2zrpqz9 12–6.)

  Your auditory system can acco xjs ut(h(ssvc: v;*8vmmodate a huge range of sound levels. What is the ratio of highe(scu(sv:*sht8j vxv; st to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violajc6kdv 2j s62in 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 the string be plajjk6d 2scv6 2aced?    N

  An organ pipe is 112 cm long. What are the fundamental and first three auda) -,d 4et+bo9l*k h ytue)fjiible overtones if the pie k)jy4h -+l*ob9ttaui ) ed,fpe 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 blowingt7)d9bozr-p irlk fz4u jb+ 0) across the top of an empty soda bottle that is 18 cm deep, if you assumed itfrudij+ r 0 )zbozl 47tk9b-)p 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 /4iqdah b8abe,7r2 dg range of human hearing (20 Hz to 20 kHz), what w aaih7 g2e ,bdqd/b84rould 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 harmonic. What p2r2gj q f3fga/v;a 5qwill be its fa j2r3q/f5p ga2;qfvg undamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 itcg, ( 5sb-7blr7u 2mnlw/owm long and is tuned to play E above middle C (330 Hz)mtw, l i ug(2b b75s/rclwn-o7.
(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 pip /z (m 1sir9nd mih-9yb6o/uake that emits middle C (262 Hz) when the temperatur9oh/ms-uai6mb yz (/nki r19de 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 a;p k6j15xkww u9ki7aj f *bvh,fimk3nk 4;vw1 t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampts6j(oxz8 r;nle 12–10 should the hole be that must be uncovered to pla jst8nx;r(oz6 y 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 Hu +-bdx:6/xh yqqugpv( llt (4z, 440 Hz, and 616 Hz, but not at ayl(dl 64uhtqx: qp-xb g(v u/+ny other 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 resozgc (j* (q5:;d*3bkfkx,m ),xpmobw lk qrbx7nates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whatq*m5b ,d3wf jxkk:m *qk)(l,x rzxo 7bbc(;gp 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 fmu w2 a25uav07x;weh/sc .m r$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long os:)tgup / , zu+)voiqergan pipe ) ipteo:)vzu/sq+ u ,gat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appb6+mc sy s+e/p;zo9nuroximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the yep+6b +n/zm9co;ss uear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying t a.d* +qeztbpke(m 31so adjust two strings, one b1zm*3+tqp.sdkee (a of which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C :zyg 31h ft(edy5mh2iv ,o*cb(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 operates at 23.5 kHz, while annpvk/r 04 *y 0vpk2fgiother (brand X) operates at an unknown frequency. If neithek02n yvgvfp4k ri/*p0r 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 brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork andrmth0q+3 r:c; (3vc h vnc1xlhtkk9tu2;apv, 9 beats/s when sounded with a 355-Hz tuning fornv9u1c thqr ;h;(, vmc3l3h2k0:prv k +xtat ck. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same w)l:zo;algh6 *qp fy ,frequency, 294 Hz. The tension in one striq,; zglolf*a6: yp)hwng 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 brvz n*k--bwxw6du.l9i6sz )6kx-bcj e heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the oth6li-vwrd-ukz 6nb.k*zj9 c )s6-xxwber at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44upag3i w,aaf x.)9iy *1 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 possibligw 9 aiuaxpa,.f)y3* e 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 person3* jcg,-rlobntc5,we stands 3.00 m from one speaker and 3.50 m from tn5c blw3o- t,c*ejg r,he 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 vibrativxi5szwz t, /xg gp*0-v )r9wgng at 132 Hz, but 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 other g-rt vw z*g,zs9i /p5 v)xg0wx?   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 in air. How many l( fu jm:k.e1vbeats per second will be heard? (Assume:mvjukel .(1 f T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s stmpa92za: t:u5 q4mtmiren is 1550 Hz when at rest. What frequency do you detect if you move wit5 tz :au42m:a9tq mmpth a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stipl kn ,e8;(rgdall1)oll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s ;l gpane,rodl)l 1(8k
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towa c7u suvp1) a1mbxuw 6 /xw:nll23hds4rd you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exacwusp4xa1l2s:) ubclvw ud1mn6 7hx/3tly 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 frequency hom.dw5*a 0jnzs,s6mg yrn. 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 themm z.5a06w*ssd, yg jn frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultra p8 e p165 gufx: v-fsztcse+.*nawx(su*ume4sonic sound waves at 50.0 kHz and receives them returned from an object moving direct1 ez4cnpwe.8x *uxg+56s-am s*( p u:seuvfftly 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, the *0861n wsx+oj zh8ekl9j fmjflf 5oi,bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat heh f,lwfjxm ik*19 8ljj5fe o8+z 0n6soar in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a yg yfn+ jdhi4 6o33:yrga3wb0 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 tr6:4wjn3 ahgby3 i30 gordf +yyain car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Sup 1m5:sa5btsarrkws-7/ 7hu lbpose 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/a7- /bssu 5lwab1kr5rth sm7: s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wa 9d8 qicxdfxij5):8oskb+ h0 hves 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. Whe3evdoxt nnz (ykcb2m1 i*/qmv s52+(h n the wind velocity is 12 m/s from the north, what frequency will obser2mx*2(3qsn hnb td(veozyk+v m15ic/vers 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 m0z:owh erf 4fpft5)u )oving 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-ohsap c,ui(c5y aqx f c.rkji0 5;i6oot:6x/ of sound is 310 m/s (a) What is the angle the so 6ru(ix.oqsoiah-x:0/ ytajp5c ,;kcfc5 6i hock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound pxe,:u)it8dh )a+lr;2u4s e6pt qfipis only aih6 ;2tl:8 uxu4)res+p epft,p)iq dabout 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 850 d.l5ol-2ikw z 0mo:rk0 m/s strikes the ocean. Determine the shock wave angle it produces w2l5: oi k.dk-rloz0m
(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 bku -v56vw mp*q;ds7 v$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan7-rlii8 o kt+n)n1 t/ :izpsmdgi05 cqe exactly 1.5 km above the ground flying faster 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.-i:t k) /z7monignpiiq 1cdt5 8s+l0r 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 28)o cx wgv7hqsjw 80g-0,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is t80gcg- w8)v 7 soqxwhjhe minimum time between pulses (in fresh water)?    s

  Approximately how many octa2n0rel2on)+,qnmw g b ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It conk 99cdb ua)xm*sists of many plastic pipes of various lengths, whicmcbd) 9xk*9ua h are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thres50imwqlui +b1er)w + hhold of human hearing (0 dB). What will be the sound level of 100) 0beliwi5 u w+rq+hm10 such mosquitoes?    dB

  What is the resultant sound lpi uss *6wad0 iag ;k./g4zjh-evel when an 82-dB sound and an 87-dB sound are heard simultan/a*ds. hg-0igwu4ps ki zja; 6eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105)vd /prk2ng2x.g . jyr dB. What is the k2g.)nyr vd/pr.gj2 xacoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is c- s;rrkh+paz1j: d) i jb kcm0f5lf+7rated at 150 W output at 1000 Hz. The power output drops by 10 dBmr kdj+)c0apzri b1fs: h; 7cf+l -kj5 at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears0ca)x t ngkue c2a79c -0idv5 h08ifhp. 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 2.0k fta 07cdc5hiin ex-ca )v92u8ghp00 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 sys x-drrre6j); lt )k;chtems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned t.mm8ux3bz: dc o 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 be: /r.mx n*knbbtween fixed points with a fundamental frequency of 440 Hz and a mb ./:n*r xnbmkass 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 opehvj+ pb-za)k5y1dy2 jn tube filled with water (Fig. 12–35). The water level is allowev5j)k+2j ay b- h1zdypd 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 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 tmsw9 a*tn-xt4s pj29s9:htlvhat 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 fundamental mode) with the third harmonic in the tubm9ltxh-2sjtsw* 9s p4a tvn:9e?    $ \times10^{ 2}$ N

A highway overpass was observeqh660* d(nmune+fuyc: zah: ed 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 q ,ei bgf(: l6s;qbur9500–1000-Hz range coming from two sources. 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 po9, ui:gb erf l(b6sqq;int 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz w5jx 7oveo o:ljzm8 o/1/ dg)gwhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traijgglj7xo eo8o v5/m)o :1d z/wn?   m/s

  The frequency of a steam train whistle as it699ov0jbnrtm;oobz 0 approaches you is 538 Hz. After it paso6rnt bom v09jz b0o9;ses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the s.thfxkp4w ni9z*mk q*3 l;yp +peed of cars just by listening to the difference in pitch o9ht4;nwk qklx*fy 3mz*ppi+ . f 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 fast is it going?    m/s

  Two open organ pipes, sounding together, produce gt32a a.vfoh7 a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other? 7tof2hv.aga3    m

Two loudspeakers are at ..v /wurcq(x0xi w pe7opposite 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 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, cuwix pe7/.rq0( vwx .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 beaty /kiu )wv21m+maqm o3 frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from th3imq mw u1+2a k)my/voe 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 ps ue,7nb36ws aryn4cj+u / +(4wxw8fo cbh-q the moth is flying toward the bat q 7xewnu 8j /csfanpys cb w464,wrhu++(- 3obat 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 of high frequey(e ochghk3 e1/, 6f5jfpn.xj ncy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about,f f .1kyeehjphcgjo(xn536 / 3.0 ms long. How 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 dhd* vq;kpz :2wh1bnwqm 6i+0a:aw 8r signals 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 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 t kd:p*q1 w+raw:8;d2iqha0w6z m bhnvhe 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 presencesxr21 qdv 8jkt* a-y(x of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundame d18kjsx(- y rvx2q*tantal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singu2 sc5pc.fk**nvj 9 l(,iah xbing rods,” involves a long, slender aluminum rod held 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 aihb ( ca* fv5pn*lj9.2kcx u,s 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 thresholyz8va k dg3/f7 tq1nj-d of hearing for the human ear at a frequency of about kjq 1azn tdg3/f 8y-v71000 Hz 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 :k76vksa1rtx 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Wk xs16 t:7rkvahat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat geox p- 0 ruj3q/k+ls5is 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