What is the evidence that soundonelvpyu r(c47wz lt12l +hc5w in.,*h 6x0f q travels as a wave?

What is the evidence that3j-xo9g )j b.wtf nahpo) 7y5g sound is a form of energy?

Children sometimes play with a h1rg*;zc hn8m56yoaz h cs x4n:0qkcz)omemade “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 wos yzq1 8ch4ch5ng:;nc a 0rz zmxk)6*ave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequee jhdjxwef5gh3 fyi/+ rc0n1an s,5() ncy or wavelengthfg5c/eh(+ 1r j05 wyni3f, ehsd)xajn to change?

What evidence can you give that the speed of sound in air does notj 9k8xi(x 1ina depend significantly on (1inxkxiaj 8 9frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?tzvl5ln o(2aqdr/fdd: 6m48wj, 7nwy

How will the air temperature in a room affect the pitch of oiu/el b1t:(99qmd9 ybx xp c 9huo*ry.rgan pipes?

Explain how a tube might be used as a filter to reduce th*m oofg(1m, h.-eqf.;p1 krrypg.e mqe amplitude of sounds inrf1me (y r,oek gmp o;.f-.1gh.pm*q q various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo60s+pw5ub* ov l 44uff y nsk.vv8shfk v4)6ntser together as you move up the fingerboard to +6hnku)v4fo0 * s8tfy. 4fb5 v4nv6lvuwpsskward the bridge?

A noisy truck approaches you from behint hylru- l-g ,+8kbt+md 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 b 8--t +tu ylkgm,h+rlmore of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said 0 rhbh. mn8sg5c (jp3eto be due to “interference in space,” whereas beats can be said to be due to “interferencrmeshg c8h(n 0 .3bpj5e in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,:klpg5f b8y4 gyvu6;h would the points D and C (where destru4fgl6y 8:kgph5 b;yvuctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work .y*noejtm 6odhdkz8).d g:2y in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronica tdk28) n.6oo jg:*yd ye.hmdzlly, 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–g9l8y,wq /nqjo- qza3w,z d/d 31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves/3j- 9al/,ywnqq ,go qdzw 8zd, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observeh:: jx4imcst:(s)i cb 8cbf*n4 -vlai r move in the same direction, with tnisccic(b* x a)tvm s-fl: :84b:4hjihe same velocity? Explain.

If a wind is blowing, wil io6c 7oqnna4g ya*3(yvv0) qfl this alter the frequency of the sound heard by a person at rest with vgyyn7vfa3o6 (q4) q ca i0on*respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positionscn3qq2 ev80 wv of a child in motion on a swing. A monitor is 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 whistlev nq20c q8we3v? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shdmp(07kzizx. 3,8y fv6 . kch gidlil8out reflected by a cliff at the far end of the lake. She hears the 3li8xhlmifp(87 gy6z0d kikvd,z .c. echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jf gvbq5da+:(; nl zv.tust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of soundv+ d.(fz gqba5 lnv;:t in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveljo oepo/ 6uc 7q*c5 ylbt4fb1n-k5y7dengths 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 foggy day.t) -h:ral kvz.py ;ew2 Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befv:zwkhar -p y)e.2;ltore 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 makew7wdwm 8o7 *fxs when striking the water below is heard 3.5 s later. How high7w7 x*dofw8 wm is the cliff?    m

  A person, with his ear to the gr5y 0/,jacgxhxound, 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 1yahx/cx,j0 5g .1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second r y7cqy*y./jzld 9ydz+c +/v (qcpvd(tqt 3n 5uule” for estimating the distance from a lightning strike if the temperatur. +yl/jzy3d 7ct c95*y+ /qyqq ddptuv( c(vzne is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of p9 9tgg;p5hs; g*zfmo 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 leve txwvr8)x2s9q 1jstx6l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fir3 betmxti.62t ed simultaneously at a certain place, what w3.tbt 26emx itill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpwtzrgn nzxn12j4a* , 8lane 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 njznn,zw *gxra 8t4 12engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, w8-r kxe+e;k3bft uj+g 1 bpv-ehereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for p-v-u;e b1je++e r38gkbtkx f each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in 1ptqe 0au* 0gfkhd.t1normal conversation. Use Table 12–2. Assume the soundu0tf11e t 0gkhpd *.aq 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 area is ke1si lduwp nu7mv2 +;gnk g,06dr3o 4$5 \times10^{ -5} m^2$ (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 isjm+r p9pp5 pk hy:u05a rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to epp590y5:mj ak u hpp+rach 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.k6fwlol5 e0 9s8 m in front of a loudspeaker on f5lw0lkoe9s 6 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 differenceyhh/hfr, k,mro 7r +(eyd( 2on in sound level of 2.0 dB. What is the ratio of the amplitudes of t y,( ,f rn(h/komye+7dh ohrr2wo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fam*g6vo5pa bg5fq dpd vy5+.b)ctor will the intensity increase? Increase pf5p *)g.av556 bvqmydbdog+ by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacy) 8o1gh kxvny/ev2a8fy3 4pmement amplitudes, but one has twice the frequency of the /gx4o2y hv py)1 3f8nve8yakm other. What is the ratio of their intensities?   

  What would be the sound level (in dB) m (q0:gr m:0qxqoegp7of a sound wave in air that corresponds to a displacp0 mo: em0qx7q(rqgg:ement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sounk( 5:kk9stuouf1 l3iy- vg r j/h,7smbd level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fo,vb(1/r57tl g3 if-jku9ssk hu myk:ig. 12–6.)    dB

What are the lowest and highest frequencies thblrij7ax68e y.cvx1:at an ear can detect when the sound levela ejl81 yx.6v brc:xi7 is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levelsv +b y(vr.-kqb. What is the ratvv(-+q kry b.bio 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 violin has a fundamental frequency of 4p mw-89c+g- /uyai kim40 Hz. The length of the vibrating portion is 32 cm, and it has a m uk9a8/gy- -m wii+mcpass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the funcp na-c1nf n/-damental and first three audible overtonesf-np- n/ccn1a 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 thbi b)ffv89 m)vlnep t7/q3 w)op of an empty soda bottle that is 18 cm w7fqn ip l)3bb)/t89emfvh)v 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 w vd6zv sxar*zra2qu+axcw ,.z8fz */5ith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths.z+ ,zr* r*z28s5 vqxuaafva6cx/dwz of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fre5e4( pjpenvqd8hc)xbkga(c .in41:c quency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengthkpb1)n qi ne( a:4xpc(djgv58 .ch ec4?   Hz

  An unfingered guitar string is 0.73 m long and ;*pd 74queyxf*:ir xy8ofhk ,is tuned to play E above middle C (330 xik xyqu*:e7f,84pf o* h dyr;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 openy+96wr rhhg;g organ pipe that emits middle C (262 Hz) when the temperature is+6wgr 9hrghy; 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 muc9piiqkk j 2,lv)rg -2/c*x$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of6ubc* czv 9q+z the flute in Example 12–10 should the hole be tha+q*zv6u9bcc zt must be uncovered 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, and 616 Hz, but not baeth m2j : l8h*q-:q/bbay9 iat any other freqmtjhb8 e* 2b9q-al bq:i: ayh/uencies 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 resonh+ rw0prli b rzv+yp,25e).pykh )wt4ates at two successive harmonics of frequencies 275 Hz and 330 Hz),b.ihwk)l trw5+pzey yv0 rh4+2pr p. 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 lk*ed /tau jqe(uf: 9,$^{\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-lo7 5np4thcp(9g k: mcnqng organ pipeqtkc (549g m 7:cpnnhp at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 c6 3, aduswl pjqg9( + .a1x8yafi5dqdvm 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 thd.if (q8awqu5 + xjs6a,ld3 vady 9g1pe standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tqtworu91ofqsf e4m p n8 ta8.:1*def.wo strings, one of which is sounding 440 Hz. How far off in frequency is w opf.t* .qq r1a u41s:fnm9teedf8o8the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)w3sx6hb40dg z15yg7yjh r:j f 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 anoh e)ex tfq,a(+alvk2;e + (gkqther (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 occe( kh,eq qvela;k2 g )(+axf+turs 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 foqsqi+c7dd29b t,/ vkswvm6;u vb6zt5rk and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your r7 b q2tku;dv9bzmvt/ is cs,wq6 6v5+deasoning.    Hz

  Two violin strings are tuned to thcf4i4 72qv zsae same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beaszq a2vi4 fc74t frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hei)- i)h0o)p jidguf3 jard if two identical flutes each try to play middle C (262 -i3j0hupi )) o)d ijgfHz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencb9d *dln j3 g,sj-jxp;.h2dmay of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sg*n l phj.xj2 ;dsdbd,9jm- a3ounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are m7b2;igfq jjp) 4dl6 n1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other.f) j;6l2dpig7q4mnj b
(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 70rhl(oe1prt n/3aq b 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, 7( 31letrh o rbnp/a0qwhat 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 waa9u;2y/q gsc; ak4pbdvelengths 2.64 m and 2.76 m in air. How many beats per secok4 9sg d;qup ;aab/cy2nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine+2cbkh rr:(h 7h*gtmjxj3b7) n jq+qe’s siren is 1550 Hz when at rest. What frequency do you detec hrg7rmq)jhbxb7ect++j2: hj(*kqn3 t if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginqi,1 ; 2wg0rby sy-toiu (oac)ua1oz( e whose siren emits at 1550 Hc,aoq )su -u21y;(t0bigw z(iao yo1r z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sour(yqiq 11e e5 o5+8hteghq5bxe ce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sam5bieqe8hq1e 5 1e5+txg hq(yoe? 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 equippqj5l9usguq) 4 cnn96aed with the 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 6u5sg4qa9)nq9n uj clthe frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends o/)u ypn( q; 7dzjulta-ut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received plz/unt;(dq7 -y uj)asound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the 6+;kh/1d3ojfpzthlp0caj xg s o//)xt5z ka 7bat emits an ultrasonhp; g/ktpl dk)3a f1coa/szxt+x6 oj5/07zjhic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playeaw h j;ms z 7,yya3e9+ecyb):rd on a moving flat train car at a frequency of 75 Hz, and a second identical tuba plmazbh ):;7yy,er9 ejwy cs a3+ayed 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 uses ultrasound waves to measure blood-flowdk* kz n79vkc2 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 f k n9z27dkkvc*rom the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequent+c ipx-5zfp)m ipd(9 cy $2.25 \times10^{ 6}$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. Whe9 kj apve0-v 7my;eey* cn6at1n the wind velocity is 12 m/s from the north, what frequency will observers hear who are ;9 cenv16* a0a kym7jt-ey veplocated, 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 ifbr.3 w3ukk ,iq 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 Mal lmhlx ;fy*/3ch 2.3 where the speed of sound is 310 m/s (a) What is the a/m3xl*f;lylh ngle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the 3fi7 w/m ih3jr( vxazl9ntp4( speed of sound is t(a9 33rw4mn li xj/h7pi(vfzonly 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 strikes the ocean. Determine the shock w*lxv90 zsu ,wjave angle it producexj*90zlvw,s us
(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 )(kp1yil,bt5jn;n f w$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactl4 xpofdx 4z)ajxnx9 q/l9g+(ay 1.5 km above the ground flying faster than the speed of sound. By theq() /dz no flpxx+ aj94xag94x time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20(r;mm69r fojq,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depf9(mjr r om;6qth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaq o,a9 eodimljrbl5+ wtt-mz 3*/l /k:ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipelrho h v,1q;k4tw7,al 0cojy. symphony. It consists of many pla4qh trv.,0;l kwo 7jy1clh,o astic pipes 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 from a person makes a sound 4s cm 9:wfmk62 uzhd49b,kmqv close to the threshold of human hearing (0 dB). What will be the sound level of 1v:m 9ud,wb442mkshm9qfzkc 6 000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound an6wge65v bc z3rd an 87-dB sound are heard sevr6c z3 6b5wgimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, pa8hy5c p.i yb;laced in the open, is 105 dB. What is the acoustic power output (W) of the spyy 8c;p.ab hi5eaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outputi j .2-a z+mu8th:tdqnl4. gkt at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts ij g+ kunzdqtlta84 ..-2t :mhat 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theirk* bvaxbv ;qo6d+h* wxs7+ pizy7z8*q 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 unpr** svp7vik+qzb zaw+yd h 7q86 xb*x;ootected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sys wgkwk;r8ywo x-rw*9 1tems, 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 to a freque , psr v bk)uq51zxm:ts9 j -u++qi5x.oar;smvncy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixedxi. w.buu1*a y r)7pkk points with a fundamental frequ ik7.xk up.ru*) bway1ency of 440 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 in:3 j8/cuvb) pj 67m z)zfxpio)4e9ar1nskhwqto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tafb18q) z9o:rs4)67 wc/n3 zjpje)hvuip k xmube 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 tha uv 3k ybhn+m)*uzfr79t is open at one end and also 75 cm long. How mu f y)u+nh37m*uk9z bvrch tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obse4l2 g/dnqx px5rved 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 8 exspm-ozx8bk 2kg:2500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency issp82gk oebmx-8 k:x2 z, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train iskal. x/o ;xrfy50yr5 l stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency r;yo/5fx ylk0al5 x.rwhen the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz.cw;ss2tl))z k j oe/.w After it p skw)) s zto2.lje;cw/asses 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 estimatfe 6mg t*bq-m8e the speed of cars just by listening to the difference in pitch of the engine noise between approaching and r -m efbtg6q8m*eceding 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 yj/e nhoo*uifps1w3dy(- g del/lf 8 f6i-)3itogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lon/fef iy) -w38yfl/ 1o6 uijde ndpo( *slhig-3g. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves paj+yckctx/v5 :jn 3.5tsg txk ,st 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 .nt3v :ts/ cxj,yxcjgt5k +k5is 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 norma:80 3,bjsfzwun,pm i clly about 0.32 m/s what beat frequency would you 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,f3m,n0 ipz:su b wcj8 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 toward the bkz+z wi)tdf*o ((mm d(at at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What dz i(m(+tz)mof*wdk( 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 fr p )8u)rs:jjnvmjc(d t (a,9fhequency 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 echo from one chirp returns before the next chirp is emittenc9shujf,8r: )m)jpva j(t(dd?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from oa/.df iaq9 n/bne 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 the fundamental frequency of this horn, and which overtone is close to Fq9ib/na./da f sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromjkawq;m9dciod y20n29 rt +m 6ised by the presence of standing waves, which can dt9 riyak6cwq+mo dm 0j2n;29cause 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 “singing rolini1fj9,:q5v,(r 3wx d eu 4 p2yin8ydcv)kods,” 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 “sw5r8c:(2ix9n ,y1dd fujqnyp l ok,v 4)iive3 ing,” 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 thr.-yuo0 xs f0a rx,aq6 x*8thuceshold of hearing for the human ear at a frequency of abo t*6qaxxsh0,uxc u-fa8 o.yr 0ut 1000 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 2.rrd47h2uw6 fh omfqz42r zi.ir8 )krvaf j6-,0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plaq )arrhfizzw 4,r m62f8 4oi27j6fud h.-kvrrne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ip)lq2dhh wn)v2wq ) t5el i,c.s 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