What is the evidence that:0 ebhix8f8n gx3by,so8 bi0w sound travels as a wave?

What is the evidence that sound is a bk 2(4wdd kx5-srjky8s8yzz/ form of energy?

Children sometimes play with a homemade “teroaq r(;+ e3re8u +ptulephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cupr 3u;oupr 8r(+te +eaq, 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 into water, do you expect the frequencrty)21 l i yy-r5gs/5l 1uqxkuy or wavelength to changryiy qyl)u2s/u x11 55-kr gtle?

What evidence can you give that the speed ogzq6-nh4 du 7png88 mvf sound in air does not depend significantly on frnduqv4 z p7hmg-8g n86equency?

The voice of a person wdjr8 )nco9l+ lreg7f59ra h 0who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect tu3e09ho z*xg ohe pitch of organ pipes?

Explain how a tube might be used as a filter t4x 9u-nvzdd6 y.pg+fms :c)sdo reduce the amplitude of sounds in various frequency )x-dc dy9sgs.6+:z up fvmnd4 ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced ci)9 9bsavqu 8floser together as you move up the fingerboard toward the8bsu9va)q 9 if bridge?

A noisy truck approaches you from behixrp fa o+. *8ujb3miv+nd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequen3 px*j+8mfura o .biv+cy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sthz56n4-8q uik (xyfqaid to be due to “interference in space,” whereas beats can be said to be due to “interference in timzxhu6iqnyq4k( -8tf5 e.” Explain.

In Fig. 12–16, if the frequencywx v ld1+i bd1cj6+v-h7 6vgcy of the speakers were lowered, would the points D and C (where destr-1jc+i1xvy7h b vdv+66wgd lcuctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectingj)/rqra; 0hw+gf nx 6m the 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 do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the 0x +mn)ga/qj6f wr rh;sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave zxbs 3ryece f0cs+k*4w9 0g:vcan be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) orz9 0bx3 fcsswr+04gyek e:*vc (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move ifumwh*4 4,v0p; lgl psn the same direction, with the same velocity? p l g4p*0,su4vlfw ;mhExplain.

If a wind is blowing, will this alter the c1b 47is/o) mhk2gyns frequency of the sound heard by a person at rest with respect to the sourceb7ncsg oi2)mskh 4/1 y? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motio4sjd ll+7d u53ele xt1n 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 whistle? Explain your reajs3ludd 4e +7e15l ltxsoning.

  A hiker determines the length of a lake by listening for the echo of flvx6*hh6 ,drgii*g;o e8 ns3her shout reflected by a cliff at the far end of the lake. She , e;rs 6odh nh*6xv8 g*gilfi3hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jgm.x6f5t. vv aust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below5v t.v.6gafxm 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 wavelengthp e)2ebk73, xq+m ynfky djp2ik 7,jl(s 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 k adxvp h p2i(h;4c);mdrifting just above a school of tuna on a foggy day. Without warning dcmp4pa;; )h2 ikx(vh, 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. The splash it makes when eeye,6c r-0lqmnqu,1 striking the water below is hee lm-q 0,u, 16ceqyenrard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike thei x)ium0l(7 zu concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur?ux0 (lu)7izmi See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ov enqwz:3 7)ano9 nhlk5er one mile of distance by the “5-second rule” for )q5z l7kneo h3n9wa:nestimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dBcdkw.auj 8qhll b,361?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leveltsth p/+, b9uj of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneou . j4n+vdme,dg6onm0ja(v xu -sly at a certain place, what will be the sound level if only one is explodednm,v m4(nxvgd.j0+j- udo 6 ea? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane withdms4ktc (:* lud(clx8 four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. l*: 8 m tldc4c(sdxk(uWhat 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-o9xyahad)vuo4f ,* lozaki ;/5ro .u3noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the soo5lhxf*)k d.z4r o9 au; ivu/ay3o,aignal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakinl y 5e67r /* bqj l,hc)6 r;twevqwbx0*bd(jjlg in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformlyq/ecj6j7 0ejl bd bv6rl (h x)b*tw *ylrq,;5w 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 strikew*5:d p6gtqv 0jkhv9 odit+ k9s an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest am.qxi41ldr*v)g;l1d2jfh o ys plifier B is rated at 40 W h2ld4 fi*voxs)11;q .rdljyg. (a) Estimate the sound level in decibels you would 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 dB meter registered 130 dB when placed 2.8 m in front of v7h i.ttp*8bhz9a8hsa5gy 4 1c3vgsn a loudspeaker o pi8*h5ct .8ahygat9 3 szvg71hn4s vbn 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 differd,q4kio)l v 5lence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds wh,llv k4)io 5qdose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wb yc.)ghl;w ss/1 i2ps zf0w7ghat factor will the intensity increase? Igf y)cbsw/i g .z 2plhs07;sw1ncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hac /*xlabex5 i1;l f9nb, obhm(s twice the frequency of the other. What is the ratio of their intensin(bexfh9*xmb, a i lcol1 ;5b/ties?   

  What would be the sound level (1t*h 0 9rpeg-o5sww)r tfax du-*mr/ b*k:ziuin dB) of a sound wave in air that corresponds to a displacementeh:*rs* r )bapm0fu195ixoug-t-w*r z/ tw kd amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudv9*gf svi.ep2 as a 100-Hz tone that has a 50-dB sound level? (Seee.fi2 v9 *svpg Fig. 12–6.)    dB

What are the lowest and highest frequencies3 vbm2b k7(oem that an ear can detect when the sound3m7bk2bv e( om level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the21w 7ypv(j ndnkr.u5w ratio of hid(rw .271v jnwy5ukp nghest 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 440 Hz. The length of thndbr.)d- 2h 5ctkgz4+ air*z(x.cz poe vibrating portixtro4. zgnr zbhid2kp5.(azc )*+c-d on is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firkwedv 33 ofp(g .))mrast three audible overtones ifow3fm(e3).r agv k pd) 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 59u7av6 l gzxbfrom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed l65g xz9avu7b 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 open-tube pipes spanning the range of humpan-r a5js2kcn3v j k6o )ju+3an hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes reo2kks-naj3np)3 6a r+ jucj5vquired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string 3- to5yo d-iflhas a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a let-dl y5oof3-ingth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mid +hrdzz g)i.ie/xv.h3dle C (330 rh+zhzi / 3ve.dg)i.xHz).
(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 pq a jeca96.q3open organ pipe that emits middle C (262 Hz) when tha pj3 ac6qqe9.e 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 /1uoqe4z vm3h(( tynmzle-,e 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiectv1 euma, b2z*h:g,hdt.ct, ne of the flute in Example 12–10 should the hole be that must be u,hcb: vtthg,* zm, udta2 .1enncovered 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 05iqx.v7 nipe ;bf8 2pe/tvbg Hz, but not at any other frequencies in between. (a) Show why this is an open ort8.x;eib5 0iv7ne2gp p/ fv qb 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 rjb,x-mxdtj d)do 96 u7 ib0ixwo(+8c fesonates at two successive harmonics of frequencies 275 Hz and 3ijfx8 6-twc+9i 0 djmb o(d,x7b)dou x30 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 j laz3;kt.6h h$^{\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-+ (g7xriktlk4long organ pipe at 20 4rlgxk+7 (t ki$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cmvi4r yx;yg2(z 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 relatiyv;gr4iyx2 z (onship 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 ev8u*0axg,meh y-58le1wxbbyr x j9.uj ery 2.0 s when trying to adjust two strings, one of hu.jgjer 8m* ybbu,lx 5xe8y w-1ax90which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mi8f,k u( eltud4ddle 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 (bn2y:uuf ld 335vpbcjx6nr, w,rand 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 plf v luyn6bc,j2,xrnpd3 w3: 5uayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning ;(i9jvb5 bxpg fork and 9 beats/s when sounded xib( 5j 9;vgpbwith 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 f t ( n/t(4bjbqm2rfk/9ijki0xrequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strt/k40bxfmqrj t( / ib2i(jnk 9ings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identi8c t,*mpcn y-fcal flutes each try to play middle C (262 Hz), but one is at 5.0t,pm8c-ycfn * °C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fregw (jcy- 7p2aos1/)bomiak s6quency 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 frequeok2/py (1)am c asjg7s-w 6bioncies 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.g /jp*daf v(4 m*h,b0k pknt +gs+aim000 m from one speaker and 3.50 m from the pjg,( ta *kvbism/00 ha4*+ mdf+ kpgnother.
(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 atm51vt9b fm am9oa1a6t 132 Hz, but a piano tuner hears three beat1mv9b oa61m9 taf5tmas every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   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 invxh;j,wu j:7*nj b) jqg x1/y3gjt+da air. How many beats per second will)x xv:/judjqw 3 h*njg71tb;,aj+yjg be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenb1vtyl ( jo)a6 hxz7t5cy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you mtbt (y 5z jhavlox671)ove 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,dt 0ykqbyv 3mag* /t5bzby* 9 engine whose siren emits aqkyt,vyy95/b* mgza t 3bb0*dt 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fr6jrguh4k4 f*;wcz vk) equency if a 2000-Hz source is moving toward you at 15 m/s versuszvurk4*6jc g4hw;f k) 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 the same single frequenf0n1f0foj.;y i.db s.nsa .ez cy horn. When one is at rest and the other is moving towarfonn0e. ..f y0j i1fs. zasb;dd 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 acjau-7:t ek,* a dshq(t 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What -kca7ae,st:d* u(hqj is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s Asg yv)) urwit1p,n ;vok/pn:n( -1wvmx it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecmk -1 n gi nr:w)(nw,v p/vyuop1)vx;tted wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playede s28i7(na23/epv (fhclh- y 1jfm nxc on a moving flat train car at a frequency of 75 Hz, ann3mix7nh1h/e2(ffc2asv 8cey-l(p j d 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 ulo7on i*q u7uhl 4xj67qs;p. irtrasound 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 so7i7hq lsnq;oir7p* 6u j.ux4ound source?   Hz

  The Doppler effect using ultrasonic waves ofpt2n z bw/ f2qv,z*:b+aj qw xl29kf4f 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 2yjnmoxv, 0qikc ,0tw, s7sg3j:vc)ksound of frequency 570 Hz. When the wind velocity is 12 m/s from the,vk0y72xqmn 0,kv3)i cwsotg c:,sjj north, what frequency 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 mov uiceo;7qcyosa1/ 34z7gh7 tcing 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 ofnd xtq fy6o8o e )1eabo1/nh;8 sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion? n ebx;nh)t8o 1dq/y e8a f6oo1   $^{\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 jw skh+,g(4jj(zrdw /speed of sound is onljj(w k/g 4 (s+rz,dhjwy 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. Determineffz,84c 7jpqz iem2c, the shock wave angle it produ fcq84mzzp,f c7eij2,ces
(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 +b: x6c:kv2jddjh/ug$/theta$ 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 abovd4guowx0sp ; 9i0/uh ce the ground flying faster t00g;p xdwc/ uoih 9u4shan the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 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)ukfpck. (m(qv5iphx2 q 01hd sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth fhiqc.u) kp2(x 1 0dhqm pvk5(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 human audiblevepb fptfzoru0km;0t 498+j 4 range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display oeiq*h5 /tfa5called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open a5 e5qo hif*/ton both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to thex*l yr+ b/+kj 9y+fvcw threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquc x+/9*kf +lrwyb+vjy itoes?    dB

  What is the resultant sozqr.7kc f k:vz48pl 1hlbs;m* und level when an 82-dB sound and an 87-dB sound are heard simultaneouslyr c*pkl;1hvmfqbz8z47 ls:.k?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What bkbwo wtmh.wo:2 86d) j m-7cm0b fio4is the acoustic power output (W) of the speaker, assuming it wk6djcmwm o08:o t)bm -fio7b2bh .w4radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 tc hnqu/ i,+pd 4du,7vHz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15d,7hq+i/ntu4, pdcv u kHz?    dB

  Workers around jet aircraft v.7- k2xaa l4 l1eqdk/pcv;hmtypically wear protective 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 ha2lkvp/ k a4dve m 1.-xcq7ha;ls 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 communications systr*k56vqe oep )hvps604 oqm4 uems, 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 freqmj3pbju f8 82 x6;,pgfn2s uayuency 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 poio:ps0 h/85/gv nkjm40jp h(/iopstk.si :y aznts with a fundamental frequency of 440 Hz and a mass per uns zp8 tmji. p 5/jopvh0 ik/sgy/no40h(::ska it length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibr,/ +oupscch mt5k1,qoation 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 is heard to resonate with the tunin,ccs/o u1q h5tp+o,kmg 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 tubeuv7ja g ijkvb :q2qr-bb8;7 2y that is open at one end and also 75 cm long. How much tension shoul-2 k8;y :a2bbbvju7jqgq7 vr id 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 w/)(fm-mm3sin kh k1g observed 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 500–1000-Hzfh d )0isn9um1 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 thdu91h nfim)0s e other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The co 0:ap3 vto7g(jhlo5rq nductor on the stationary train hears a 3.0-Hz beat frequencl3jvg: (t a7h 0oo5qpry when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it app )2j4mg(g cepjroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity))4(pjmj g2 gec?    m/s

  At a race track, you can estimate the spemhr3 gxn5bevtt3 ,p/ 6ed of cars 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 h b/mvt5rpt6,ng3e 3x 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 tog j bah;uoe)f-./gw3iy ether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?jh3)a -.f eb iugyw/;o    m

Two loudspeakers are at opposite ends of a railroad car a v)rks3t /1xix.ci apjh 5v9d4s it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the 5v9ixsh1 3 kadjicp rv.4t)x/ 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 normcp br :(z 07vf;wt0shqally about 0.32 m/s what beat frequency woulds;0: w0b(vrf7tqc hzp 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 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 flyjt () sl*tn1xiing toward the bat at speed 5 lttn* xi)j1s(m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high ff 3 90xem,2uza 6-xnjx w,ktcqrequency 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 nex6q -2fx3anc m 0x,txjzku9 ew,t chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sigukunm d, zq)bzgg6 3 osxiu.-f*zx51*nals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F*uqg 51 d sxkzmb3*fzxngz.) -uu,6oi 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 o gg 45 8 9by*;n9ldzodre9rd3yp:qwklistening can be compromised by the presence of standing waves, which can cause acoustic “dead 9r d9 rwd*;geqgb9p dl5 oz:yn3yk84ospots” 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, c.t*uc a; wpyu/alled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. yup;./t*cuw a 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 hearing foq ias gy+,u 6fdxvx569r the human ear at a frequency of about 1000 Hz iqx59 6f+ax6udg,y s vis $I_0$ = $1 \times10^{12 } W / m^2$ 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 observkz.wtnq 3qw) 6zy83iper on the ground hears the sonic boom 1.5 min after the plan tiw yz qzwpk3n.)36q8e passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is wq z/2s-d8t; lmtr ;ub15 $^{\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