What is the evidence that soww.pc9r 9bdw6t1ik5vm jv3 ,fund travels as a wave?

What is the evidence ku-j ,vp5ad6v diblwwnc5) rh) .(x3jthat sound is a form of energy?

Children sometimes play with a hfs6wixusrx 42 6o *jn y*j+vw8omemade “telephone” by attaching a string to the bottoms of two paper cupsixxuvs4*6w r 2j +f*n6wsyoj8 . 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 the other.

When a sound wave passes from air intbh1sm*.* h0 *sncduj wo water, do you expect the frequency or wavelength d n*0h*ujbs.wsm *1hcto change?

What evidence can you give that the speed of sound in air does not dei1:dbqcbchmq) )1 p21ljdp ;apend significantly ona; qp 1dc1mbjb:h)12idp)ql c frequency?

The voice of a person who has inhaled helium sounds very highntkh,z6;-;5cc-xxr nbs hxr 0l 7bf4q-pitched. Why?

How will the air temperature in a room affect the pitch oz 6fxr *vvuo)*s1.k24 r jyrvif organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of souv ,ciq8h;gs.g nds in various frequc, g ig;vhsq8.ency ranges. (An example is a car muffler.)

Why are the frets on cc;mh,ib(g8o22a lsom, 0 igr a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard0 ( 8mccgsob,moraihl; i2g,2 toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it bu.7m vyea :qse;s :l3pjt cannot see it. When it emerges and you do see it, its sound is suddenly “bright .:7msep e:l3y vsaqj;er” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spxv , hjpw 6/d; 1o bspey*1l/us3wp3sqace,” whereas beats cao; 1suewl,xpd /p*h6vbjqsp3ws /31y n be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointobb-*1ept wkt*x c:*ev 7y9rd fmc92 ss D and C (where destructi e*s ykpv cwt*1*bm9:9e2t c-7odbrf xve and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas witt5d y.h5w axy7q2m en374jspi h 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 electronically, then fe.ei qx23s77p 5jh4yadnwmy5teds 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. 12–3bwb(z gtu p*/01. Each wave can be thought of as a superposition of tg0z( *u pb/bwtwo sound waves with 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 the source and obser vudkiqi babpz(:f j ;3,,bn1(ver move in the same direction, with the same velocab: zfk3jb( u(iq,1,v dpnb;iity? Explain.

If a wind is blowing, will this alter tnki:+ f8oib) fd)g k0hhe frequency of the sound heard by a person at rest with respect to the source? Is the waven+80 :i)fikhfok)bg dlength or velocity changed?

Figure 12–32 shows various positions of a child sv2-f c50dt qein motion on a swing. A monitor is blowing a whistle in front of the child 0fc2tq sve5d- on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo ofa,;z /zpsn gne unf(/: her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lenfnsg (zzu//n:; pa, negth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the oe 4r.q sy+n-(/*qg lzx8igclecho of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume t e y*q/ .qnll4i+-(xrcogsg z8he 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 wavelengths in air p*.zn8h v:ew*x)yqt w 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(4cuq s ajm 1nn m g6197e84vrnxcp/ta above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the back76m1q n8ncn/ta4u (e ajrgv9x4sp 1m cfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from thl1s6vitz, rp1rjkwtz e 2u,96e top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. Howe,6i1jzt 1 ptwl vu9 2,r6kzrs high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concre* eur w8yw4+azejq7.,rrc+ rt te pavement. A moment later two sounds are heard from the impact: one travels in the air 7,yqtu+e ce4z j8*+arrr. r wwand the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dista- o- ary en/3.htwrlh3nce by the “5-second rule” for estimating the distance fro.rtle 3hh 3w--orya/n m a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of i e)yn(hgfpc 1-8nxm 3a 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 level of a sound whose intenyqxrn l(rsb -b 0*v w.)luj/(ssity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelqtpsni/x 6sxho. 0kn-p 63b 7u of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one it n/0q-xpk. b6ouhs 6npix7 s3s exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eqikjhp5g q v6 r6g j//3m7okv5jually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [ /vqk3hj 6p55o kmgiv7jr jg6/Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, where+h3yj7erhh nrqys ( q ;3z)c(zas for a CD player it is 95 dB. What is the ratqrr+ hsyz 3(q) n(jy7hhzc;e 3io 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 conversl e:vb r7g+;;izuv18:xme hyh 7j ph7ration. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered rh hjh87m 1:v+ v;b7e7xzeyriu g:lp;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 j m m59t7o, xdcn: pxvbk*du3:5lnef3 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 morepf +k(zz7ps7 *edyhv8 modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wopfeyds hk 7zv(z78 *p+uld expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dBo(y syb:p 3(i0om gq7z meter registered 130 dB when placed 2.8 m in front of a loudspeaker oo(p3y( :sybi7g zqo0mn the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference(pplshv3 pm nt7:s1n 3 in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ byv mh 1 t(7l:psnn3pp3s this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wh j71( ts qldyi72*tnpvat factor will the intensity increase? Inci(tvs1 7ylqjt7 pn*2d rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eq 5(pbr dzos+a8ual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intenbrda 5 8+spo(zsities?   

  What would be the sound level (in dB) of a sound wave in99 8epgey9rvs air that corresponds to a displacement aysrv8g e9 e99pmplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud asq1w( +0r thhdc a 100-Hz tone that has a 50-dB sound le+ rwcdhh tq(01vel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can deteru/wnrmz;.j14ukryt2jkz55e hl 0 +uct when the sound level is 30 dB? (Se50 r+tjy uwlj5z1; u4hknk/u 2e m.zrre Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.k6 f g3ftpt,n/ What is the ratio of hig6 tf t3pgf,k/nhest 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 fundafbl.a4tc2 9trv l9qy0 mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has r9atv94qb20 t f ll.cya mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the funcmmkq8u w* adu:cu7lp bt* s(4)d +g*zdamental and first three audible overtones if luqgpt*dm +)47s8*uz ckb uawdc(* :mthe pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top q0v3( xgxvg ;d)mmmt5 of an empty soda bottle that is 18m5v0mxgqxd t)g3v(m ; cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with lnzc6um7e55n, - p 1joulg;lzopen-tube pipes spanning the range of hump6uoj75u mnzc1e lg-5l z nl;,an hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 H3j+h+volu c rd)7u9jbz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of onhbdvoluj3++9 cu )j7rly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long y auss: 0mz63:n o/d9p(zb9 qykt56 cnq. gkwuand is tuned to play E above middle C (330 Hz).59.(qzn9nmo3s 6cz ayuwu:kbq:0/ dyk6gspt
(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 orgw*7b *kiv7ywb an pipe that emits middle C (262 Hz) when the temperature i vbw* w7*7kbyis 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 e/s-bx 6su 9gwat 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 Example ) apxu-+obe,i ffut-(12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz? +x)pbe(fi -a-o t u,fu   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 cangw8p1hptl 1 z- resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is apwzhp t181l -gn 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 jvy o/u8e+6:x:s0xk )psx dwsends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. owkux/8 +px:e60j :s dss) vxyWhat 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 u(k f.cn)n m+z$^{\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 ae8awt)iu 20hsv g,;q-av z kughy9j: /re present within the audible range for a 2.14-m-long organ pip8/)uh,ve hq:k -wgsu j0 ;vazitg29ya e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside anf bq/a3n(+xicc 0r(ba d is closed at the otq3(bi0a ( bccfa/xr n+her 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 in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears o)v a ofjfj82o;ne beat every 2.0 s when trying to adjust two strings, one of which is soundingfov); 8oj2fja 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency i)gtx2zp i) g70 k:qby7hva 8uff middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) opeuc.quoj 9g)-e5)t n,k ut 2bqorates 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 bqkou.tnj9c2) ot ,)-guue q5 are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with pi36-ole h zx4uqpa /3:dy4qea 350-Hz tuning fork and 9 beats/s when sounded withppz4e64aiy d-lq3xo3u /eq h: a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 2d+oo, tusuqam) 9l z/Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playu,o)al/o9mzqdt2+u sed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flfor.d*b zi5k :utes each try to play middle C ( kzo*dr5. b:fi262 Hz), 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 frequ. k15japnfr; a :qh-wfp8b4id ency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C;.8aarnd b-hq f5wp:14i fjpk are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from onp bn):zecfsap s:x448e speaker and 3.50 m from the other cn xpe4:fa s:p8b4z)s.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, bu;j .cxu5qg6znt a piano tuner hears three beats every 2.0 s when they are played togethnz6j. uc5g;qx er. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in f p(ea*2n-9+)/uc buin+s3kp6 z tkalz va.pnair. How many beats per second will be23evkbnpta- u. ( ip psaa/zuk)+6 nc+z*n9f l heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cehcdf6+04an sxrs/t 4ertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you s+4 0h46e/tsfarxcn dmove 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 ir6ppiwe:2*y af a fire engine whose siren emits i*a 2:r p6ypweat 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency 6i prfcaenck5 qafgu: 6f)ms1-c +p5+if a 2000-Hz source is moving toward you at 15 mfcp5 g pckiumaaf++ 6qnsf 6 ):e1c-r5/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 yqqdns(ur - 6op5* 0bothe same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the d50bqq *don(-us6or pyriver 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 j0gv *mezt4 ov s64ha*0wl4c:6rmsum 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound freq4e4vs* aztm glouwsr6:6 0jh4 vc0*mm uency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall a,2g bc +eiv92mdprhj,t a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Wheg2 h,b i d,2+m9pvjrcat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wa go6 ytm .q8qs7aw:7dzs played on a moving flat train car at a frequency of m w7o8 g tsz7y:aq6.qd75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound m32y exuhyc1 .kxty8;p t92ju waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound mey uyy9x x;pc2h ku1t8j.23tsource?   Hz

  The Doppler effect using ultrasonic wem3 eh xy6hh9 umr430daves 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 fr:14je bsb zhyi68l 8 7vfu6cuxequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are 8l4yhjubs :c1 7f6 xzubev6i8 located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20 yo2s( pzd/;bt $^{\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)b 2+(1lpou q1uwjhrf m/s (a) What is the angle the shock wave makes with the direction of the airpllw 2)fjoh(u1+ ruqp1 bane’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 planj 9 dyvdniflj: j-61w 0f70tqlyait)wc08 yy( et where the speed of sound isjj i0:t- 7 ycyyf 9(ndf0lv 0tiw8l61w)adjy q only 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 tiu ns 7bab2uzb ;as3mb /zqw871 n9ax:he ocean. Determine the shock wave angle it prod2 :; uwsza qbm n3sba bz9b/axnu781i7uces
(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 t.ib o91fo;:m m*r-p kp0mhwh$/theta$ 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 abf0 r-(lvr8g1luvjp+6b7 ws pzove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizvujf+g6wsp zrlbv7 1 r(8pl0-ontal 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 20,000-Hz sound pul5irerj6q -/tyses downward from the bottom of e/ 6 rr-tiq5yjthe boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humaqdrnajuu* b4pk)fgbe7 *)r 2*n audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewek qhx;r-qq 1t,r pipe symphony. It consists of many plastic pipe,k; qhq-r1x qts 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 aj .lar1g0x2d close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such 2.1a0jd lgxar mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are h svfg1fc3b **peard simultab1*fpcg3fvs * neously?    dB

  The sound level 12.0 m from(m.mo h -flq/ upyf twkfg;k,+t+ uq/uy8+ys( a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all df+wy/( utkl;/ p y.u+om-yhqu,fkmgtqs f 8(+irections?    W

  A stereo amplifier is rated at 150 W output at 1000 H*;,vqxen1qrqj b ;k+ pz. The power output drops by 10 dB at 15 kHz. What is the power output jq,1q*xnqp;+eb v;krin watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prj 2 b9 9rsdrqsfx58h+tsdx6-rotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power i+s h 9rbrx- q5fs2ts8d69xdjr ntercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communibu,j lg t9,9 c+6rociications 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 vio937haqw6e aul lin is tuned 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 lo)v yv;xwh5 f8al sr:myt +0q1hng between fixed points with a fundamental frequency of 440 Hz and a mass per unit lenh)m5; hya f1rv:8 ls txw0y+vqgth 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 open tube fillek6*pe+/ rn9 4yktba4f f2ixyrj9/cj wd with water (Fig. 12–35). The water level is allowed to dro42 f9wtf jyc/y+reibakpr469/ * nkxjp 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 that is open at *a/x3x q+lrx gone 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 hxq*x3lxg+ar /armonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate asajud- 73ll no1 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 v(aj/i1 0yndteyqpy*v:-p (,cjub f3500–1000-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 point 0.34 m farther from one source than the otviy0e3/(ypn1( ujv y ,qcb-tp f*jd:aher. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistlw(-f ee3eb5b:nsq2f ses. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequenc: eb 5 e3(sswnfq2feb-y when 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.6 qzke( f8qm.x After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant ve6qqz. fe8mk x(locity)?    m/s

  At a race track, you can estimate the speed of cp0 bvxr3lwq123+d:djg m,bl hars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it gx+rg3q , :b0wmbdl2l h 1pjv3doing?    m/s

  Two open organ pipes, sounding together, produce a beat frequency k ri 0yzwr ayg/er z/i*5r p86aj07ey:of 11 Hz. The shz :7*ryi8e z/ 50j6rry rpg0i/aya kweorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends ouv m h31;vnao2 l0+p.jnknli.f a railroad car as it moves past a stationlj..u2pom+l3viv1n h k0 ;an nary 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, 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 abouy,yl-:s itnld8) 8 ogot 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directe:8n l -l)i,ydg8yotsod along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the motxcibf/ vrtkp09n su0l*w ( *w xw4y1/lh is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequew*9*xc4ulkv 0f0yit(/sr1wl n p/w b xncy 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 moth. Thedrgac s06tv,8c 9 ucv25,mk zj pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be 52umzcvd,90 c,v86 trg csajkdetected 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 signals from one Alpine vietd .r/ *kbaq*vu/bc sv:4y 4qllage to another. /s. /baqydk b:4qcr4v e*utv* 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 F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromivxm v 2fk16,qqsed by the presence of standing waves, which can cause acoustic “dead spots” at the locatiov2 1xvk mf6qq,ns 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 rods,” involves a long, slender alumifyr3+q u :nra g2-ks(cnum rod held in the hand near the rod’s midpoint. The rod is sg2u+:r k -3qayfc(nsr troked 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 o63:bj o9tk3cwy jm,r threshold of hearing for the human ear at a frequency of about 100kto9jy3mb:r jwo 3,c60 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 the sonic b9ci*qd8-x tntg rh,ykr z-v3)v3jpo,oom 1.5 min after the plane passes directly overhead. What is the plane’s altitud-krr3jd t 89hon x,g i 3zt*v-vypc)q,e?    $ \times10^{4 }$ m

  The wake of a speedbf7q+esdat( n*oat 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