What is the evidence that sound travelz2mzndu x4or+*c+va /s as a wave?

What is the evidence that sound is a formqn,hei.yu 8r, of energy?

Children sometimes play with a homemade “-zh) hbb.e;bp 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 from one cup to thh)z.b;bpe -bhe other.

When a sound wave passes from air into water, do you g.ut0tmmkdijy:4md *e0f j9yt nx9 , ;expect the frequency or wavm.9;0yjd * mt y,e udn:94ittj0 gfxkmelength to change?

What evidence can you give spq2 0z -d/-ovznw;*jm5n kbxthat the speed of sound in air does not depend significantl-jdz5 v;z nqnb/o2 xsmw- 0*kpy on frequency?

The voice of a person who has ib0hqh04 lt 1jdnhaled helium sounds very high-pitched. Why?

How will the air temperature-f2 ybtgq6 /3k bflpn2 in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to e 5jsl9r6gy)3vi bjn, reduce the amplitude of sounds in various fnb3 l ,jjirve9 )56gysrequency ranges. (An example is a car muffler.)

Why are the frets on a g+i /tte)ci-cdq1x9gvthx *o kk)pb9/uitar (Fig. 12–30) spaced closer together as you move up the fingerboard 9cg/h)e ) ktt*xo+xbc /p19kvqd-iit toward the bridge?

A noisy truck approaches you from behind a building. Inff agpvj*w8 j,8gd u52itially 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 11–12w 8*5pguv gfdfj a,j85 on diffraction.]

Standing waves can be said to be due to “interference in s yxa - q(7lls:1(fikmapace,” whereas beats can be said to be s-qailk1 (y x7a f(l:mdue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wezz.uyo* )itq 1re lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer o q1 *z.iyzu)ttogether?

Traditional methods of protecting th ; g;8tjwhueyx+)mc j0e hearing 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 doh8;w0+ cxeg tjm;) uyj not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fiq:2d5tpgwud4 i5i um(g. 12–31. Each wave can be thought of as a superposition of two sound waves witu dtq2p(g4iwi :d u55mh slightly 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 taak*jjv; .y 9the source and observer move in the same direction, with the same velocity? Explai*. ;9aakvyj tjn.

If a wind is blowing, will this alter the frequency of the sound heard b 6 /bf+r(ir4ev /7bb(kr5 dafqsd yw,by a person at rest with respect to the source? Is the wavelength or v(abs+qr/bi / f r ky,56 f(bvwrde4bd7elocity changed?

Figure 12–32 shows various positions of a chil1m39-o zntpezjl1ux 9d in motion on a swing. A monitor i e1zt9j -z9onl3up xm1s 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 whistle? Explain your reasoning.

  A hiker determines the length of ax7wyk )qbg 6qh6gy2v vw c8,/l 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 s after shout6hw /vgw cb2xykv l)qqg87 ,6ying. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ecb2v+fpnj1 byzhxf obi+9 7+1v ho o1 x7pf y9+oib+vbjhz b+n21v ff 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the waveg g*xppiba 8f96l b)6,lqeb3xlengths 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(0q 1g- t+mnxk pxtq 7jrc6g*r a school of tuna on a foggy day. Without rgjqtk7(nprt +1*c6x qmx- 0g warning, an engine 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. The5 6u9cui*mov p1bp( bh splash it makes when striking the water below is hearim c5hu v1op(9b6 b*pud 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, see0eo 2kk5,xxk ls 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. How f2xk50 o,keklxar away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over oe1a 4 l;7iavdtne mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is lv 7ai1;at 4ed(a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lev2)jwy km rnyg5)5bz1uel 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 qpm3bb; f0xzaf 0kd *u6mu 7dcj(x18h whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneoxzg q63wf/1f qts9p pllez 088usly at a certain place, what will be the sound level if only one is exploded? [Hint: Add inte8l8lpqt/ s6w z xzpfq1 9g0ef3nsities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisrlekc 8z4r xiu8*ch*7*y xgop*nz4m: y jet enginr*lzy47 *pxig8n :kx*4r8euoc zc*hmes 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, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whey13jd ux b 1lk ,0/gp.jgdwm/breas for a CD player it is 95 dB. Whxd/ g0 b k1umgldb31jy.,p j/wat is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conve0ht0b)(s odo( hv xu7ersation. Use Table 12–2. ev)( xd 0b0u(oo7shht 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 whoseyc 3n;se8s ui+ 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 8gd x9.djfp 3ev 97oejrated 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 e9dvgxj. f9pj7e3d8o each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front oz padg m4;26kkf a loudspeaker on the stazk2gdk4m; 6ap ge.
(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 detw3 a+m gnp/t;iect a difference in sound level of 2.0 dB. What is the ratio of the ampl/i3gmnt pa;w+itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wav.nrl* 0 gmiqi*k 2gt7me is tripled, (a) by what factor will the intensity increa.mt r* mq0 k7iing2l*gse? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqp 5hj7h hooj p0 mq+x4gr(u(y7ual displacement amplitudes, but one has twice the frequency of theh7h+j7j ohgym 0( q 4xr(opup5 other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a j /s m+wanq)i)q* gyugmw1+d.sound wave in air that corresponds to a displacemeiwdy/1awjg +*+sm.g)n quq )mnt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see-4qeensl.+26d2mwy +c iyjdem as loud as a 100-Hz tone that has a 50- ysdqcjd l.- wnee2iy6me+24 +dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequenciem.dxn4s gu0k l .181gegj*vabpt2: dq s that an ear can detect when the sound l8lb1mqsdg.v.:1g et20 dakpujx * ng4evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rez/qqg38ll,c qxk s 5)ange of sound levels. What is the ratio of 3zle/8 lc)qksx,g5 qqhighest 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 vi-ehk,b vj6 dzi fz;)q,olin 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 tenb6-je,k,fzvd; )q zihsion must the string be placed?    N

  An organ pipe is 112 cm long. Whatnumu6, ;1qkkk545c*:ym(zu xyhnru x are the fundamental and first three audible overn;xu1zh,cn mu5 krkky mx654*( u yu:qtones 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 blow,lh 8g*t e.w9 vttg 8dzl)+xeoing across the top of an empty soda bottle that is 18 c*e8gex 9t8wtv. tg+) o,lzhldm 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 4el,, tmc(0 0bb ztqj-pjr*pxwith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be t e(* pq,t00czxbt4,jmpjb -rlhe 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 wilel ojo-t9 t.mzut63(n l be its fundamental frequency if it is fingerz.m3ouotej 96-ltn (t ed at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned c:aikyk8 li 2,zb g6ke8a8q3ato play E above middle C (33za2ke kl86g 8y8: ki3a a,bcqi0 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 o3xsy xtby( 7)+y)h go:pk.tykf an open organ pipe that emits middle C (262 Hz) when tho 3yybtyksty)x+7p.x: h(k ) ge 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 20tkx r2n4q-1e kzep9l 6 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thfybz cq:0- e6pyw55x7r n*upre flute in Example 12–10 should the hole be thatuqeywb50- np*:rz fc 6x 7p5yr 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, an*eq s, waa8k(gd 616 Hz, but not at any other frequencies(ag aesw,8 q*k 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. Ityk(3k-tg.l7l fex h+ c resonates at two successive harmonics of frequencies 275 Hz and 330 Hzg ye+ 3cht.7lk-x(f kl. 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 sft ,0hb 9)uhpqkdwuo, sr9/. $^{\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 fads2s+ f248unu(qv nkor a 2.14-m-long organ pipe aqu2k n2s 4nuf(d 8v+sat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 ranx 66n nme308 a/fdjcm 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 ear canal. What is the relationship of your answer to the information i68n xr6fj/n3a dme 0ann 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 tryi woz riuvjt+3: 2v,1tlng to adjust two strings, one of2 or3i,tv1:jvt+ul w z which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) sdgb.iu3i5 1j 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 anoths; hc()wfhrj2f fa4 v0er (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, estimatfv2wj4fh0hs;) (ac r fe the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning for9 cvrud.*6 thck and 9 beats/s when s cvhdur6*t. c9ounded 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, 29..hn5l 95jd)5(pqlv6 miwxoz1 s kram4 Hz. The tension in one string is then decreased by 2.0%. Wh 5 (q6oldv9a zjl)swkhp5rxn.51i.m mat will be the beat 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 play middle1p,ufd+u 8kblgwm xn nn,,9ck)us h(* C (262 Hz), but onu 1ld +p*,sc,x,hw u8 bunn)nkm 9gkf(e is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A:y.*7n3taas ft:m gsvwqmk5/6 zl cb ., B, and C. Fork B has a frequency of 441 Hz; when A aa :y.3tw csk g / 6ztm.7*vnf5saqbl:mnd 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 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 9uz gqc:29w1s f(boscm from one speaker and 3.5fcoc9(sbqz w gs1u9 2:0 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 suppos08ah/zc stpi8 ed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) Izc/ hpa 8tsi80f 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 ad vnjt-j4gmmu /(1(udmsk 3s5nd 2.76 m in air. How many beats per second will be heard? (Asssumjnvj -/gst mk1(( 45u3ddmume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a 0 *2fsyy3;.z3hy,lpcuaompq certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if ys y;0m. 3uycpzyh23 pql *o,faou 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 engine w9fjm .,, htplnjvvp/0bjw2 *ghose siren emits at 1550 Hz moves at a speed jh0vg n.m29 twb/jf,*,lp vpjof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequnk)bp 71sj1+ylsb;rq9 3z 9psu+chcbency if a 2000-Hz source is moving toward you at 15 mqyjzh+lb+71b scsk1b;3 99u cnr) s pp/s versus you moving toward 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 44hxuho .y5f*/* r5wni o yj zthzn6l1the same single frequency horn. When one is at rest and y5y/h *x nzorh16u*zl4htn.o f j4w5ithe 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz a sxpf6+ w)vso41gt-t bnd receives them returned from an o4tsx1f b)6gov + -wpstbject moving directly 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 fliyw s+a75bn i:ies, the bat emits an ultras :ai75y +nsbwionic 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 e2a*xqts0 p:ewmz ,ta+4sm su 4xperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a sesz4m :2ms+wte*t0 u 4q p,xsaacond identical tuba played 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 mm.jk2 g2xv8 vg;22t ycq;mao leasure 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 ivjmg2.y8mv22l ; toqck; 2gxa f blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency25+j)w fvmsnn- 3lj ec $2.25 \times10^{ 6}$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 emiiy -hu)bs)i2-f sks llxkj8 6,ts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what fr- x6ui2yk f,)isl-hs)k jsb8 lequency 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 mo )ci;orwh6x4q*jgx u: ving 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 sound is 310 m/s (a) Wha2eshnoz39 qlb eeo r- *cx*81ft is the angle the shock wave makes with the direction of the ai9 8eqr 3onh2lsc e*eb*f-xzo1rplane’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 pla x3+s z/akc ze,pd*nbcp7 e+y +7hlj.knet where the speed of sound is o3*n. lxe7ja+p7e+ z hc c+p, szk/bdyknly 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 v+-y e;5,vd2tvw2 poebpp xr1wave angle it pr5teyov xd 2rbe-pp+; 2vwp,v1 oduces
(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 ukl fb*e22r: o$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grr*,yllz+sf 1a;q kvo. xmu; z7ound flying faster than the speed of sound. By the time you hear the sonic boom, the pxulvq zf*zo 71 m;srlk .y,;a+lane 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 as;p djd;q-k4 k sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and the4pdj-k; skdq; n 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 xw7eg)/oo*h ;upgf;(uhfk 7do+cz/ qbx u65ain the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe pc aez3o./dj(sd9a 5msymphony. It consists of many plastic pipes of various lengths, which are open on b co3j.ps(9d m/zada5e oth 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 sounzh( o4hqvp n*/wv r4ya 1urmt86 ieu.;d close to the threshold of human hearing (0 dB). What will be the sound lman.u y hz( vih*8/1pqv rrwtu4 6eo4;evel of 1000 such mosquitoes?    dB

  What is the resultant sound5ybt l1t:sq nae7a5y 7 level when an 82-dB sound and an 87-dB sound are hea t5y:b7a1qsn5 eal ty7rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed07jr;v kop q9jtv7p s ua )ltsv1:-w8j in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equal 0 jvts: r -vpj p7k)w;791s8avluqtojly in all directions?    W

  A stereo amplifier is rated at 150 W output 3mb z.jut +;mpy):fqb at 1000 Hz. The power output drops by 10 + mj 3t;q:yb fpzb.m)udB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices p0j 1f omf4eh5over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 d o5mff 0hpj4e1B, and that the average human ear has an effective radius of 2.0 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 communicatth4vb1/a7ncmb xvms7q q k 744ions systems, 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 tunedeuxp 3ab-h.(s,racc/ to 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 between fixed points with a fundafe6rt *h w5q 3jispr3zruvp)ag:.2a4mental frequency of 440zp33vhrr a ag.ef5wtj2su):i 4r 6q*p 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 ipnko3.3f3;xgufoc:gw x8k .q g( vbo *nto 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 tube above the water level f :3;.g *u.kwx(8 g3foqcgpov bkn3xo 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 of7(ewhrp5jvo k ( 866ujqn qj4s mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the str (pshjnj5ro6q6u(k 8 v7je4qwing if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as bsymwqf 1. u(6one 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 sources. Th2gi uk ja.kp(-/jt 29wizs y-se 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 oth2 -2kitsk-w.syu pj/(9 ziajger. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is dy- owy76gcn +stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approw67 no-gyc+d yaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftc:2)sx6f znnfph0 i4e er it pass c0efhnxpn2):6 if z4ses 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 speed of cars just by listenind v2 6jhwrboget +6,x1g 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 straight+d2t 6w ebx6r,g1jhovaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, v,g:x ))7 nehtmd4lac/g/lfu produce a beat frequency of 11 Hz. The shorter one is 2.40 m long.al dhmg )nf g/ct:le,47xu)/v How long is the other?    m

Two loudspeakers are at opposite ends of a rail3uk j15 rm 9ku07hk: 4nchpwklroad car as it moves past a stationary o4:h 5lhwpnc7j krk9u1 3k 0mukbserver 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, 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 w n 7aeypm8 j(p.nempy-bvf qf3 (so.73hat 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 pf (o-naye7fyv3bjm. ppnq8m( s3 7e.of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at h e 0jrx mzu4 0nnwpen7uzw r180g02j3speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat em e2ww 8zmj7ez0rjurp0gn4uhx 00 13nn its 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 frequency sound pulses as it approaches a mozqds04g.:r r/v v ab/85y8g awi4eznsth. 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 the8a5 4nbzer/a/:8s0vg di.ys w 4qz gvr echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38c9otq/k6 e a0;k1xo xj) was once used to send 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./xk0xc eoaq6; 1 otj9k 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 ca se ;t:d7u7 i-yl6w wuvqgk)b)n be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living ugw) 6;)d7 sui:ev l7wqyt-kbroom 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 demonstratiov d)lqm)/q f8tn, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod8) mv/fqd qt)l’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 hear5i;i dh pb2vx nez5d;qj*f /*fing for the human ear at a frequency of aboutfjdxe5 z/dip*nb5i;v h2; *qf 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 2.0. An observer on the ground hears thoen i+/yit e3( y:n9nwe sonic boom 1.5 min after winn3y +n/t:i(9eey othe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa/xepm jq5uiu )m40 kdwkr;.x (t 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