What is the evidence ti a.s*)4jkinh5nss 4b:09qnpi3 lqqlhat sound travels as a wave?

What is the evidence that sound is ) 5 okx4glat0za form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to 1an nq(d- x70aihzx9w05 wfaq 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. xq0 a-95ni07ahfn 1x qwwdz(a12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes frdg w.ly ;eo 7),htzyp9om air into water, do you expect the frequency or wavelength to change,97)g;lp wyd ho.tyez ?

What evidence can you give that the speed of sound in air drgup+ m.v5al; 3x/siioes not depend significantly on frequency?r.3i vl5ps;g u axi/m+

The voice of a person who has inhaled helium sounds very high-pitched. Waz 5a,,ise b;pu4ysy3 hy?

How will the air temperature in a room affect the pitch ofdlsox ;n3h(a ;ct8 k3n organ pipes?

Explain how a tube might be(g ,far e.lus1twq02m used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufrm 01uqa2elg , (wts.ffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov2mr.z k nkimi/;q7vc ,e up the fingerboard toward the mn,;ckz kqv7.imri2 / bridge?

A noisy truck approaches you from behind a building. Initially you he mc293/g9 jtv e:yg1b)bj ndp1upkxe4ar 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 1tgkd3 exbp u 9nyg9m pvb)e4j/:12jc noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said tz92jj ) in,*xcn,hxcbo)2zv f o be due to “interference in space,” whereas beats can be said to be due to “interfer,v cb)cz9,jn*foji2x)zhx n 2ence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were 9l)lg3a54esi l9nzw+l h( j halowered, would the points D and C (where destructive and constructiv s we)jla95h+ hz493ilalgln (e interference occur) move farther apart or closer together?

Traditional methods of protecting the kyot -kq,dy+mu(7kv9hearing 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 kvdy9k7+,mq - tykou(headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of v ec:fc6. 01qpff;in xas a superposition of two sound waves with sliv.x;ife cfc06pnqf 1:ghtly 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 observer move in the samv2r ;n9 h;ly*3rc./r twzsbd2 ) pgsfb0k( cwve direction, wicvsr frr)zw w;2v n3kp*9 bdh;2s.y(lg/0tcbth the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a persa af:qti -hxqoqms,:*bp 627son at rest with respect to the source x :pb7sto*-q,sfh2 aqq:6ima ? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child i ,fyuw c*hn /lbwsl5o43;wh7a n motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the so* u/s7yabw;wfn4 h hcwl3,lo5und of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her *lz;9 w 3oswl-nre2m(g rn+gzxc e0y;shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 r(lmle+cws9;yo3xgg* zrw 2z0 n- e;ns after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlin .plcmxb*-l)ye. He hears the echo of the sound reflected fropl y*-bxl)m c.m 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 wavelengths in air at 201 miq m+u3cv 8jgwy zrm..2u yj2;g)vl $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna ztprl,;bx8glfgyk e ; :-8b4 yon a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Ho lerg;bf 4lt8byz;x-g y,: 8pkw 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 strikuo+wg0f41:x s0y 3cx zhiuli .ing the water below is heard 3g.40uz o+0fulcsxy1 wixh i3: .5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike1bd7yncpr ;k/*ds ha9 the concrete pavement. A moment later two sounds are*1badysdkc;9pn7r h/ 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? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dists ,do, ae 5cu/hvqe9y2ance by the “5-second rule” for estimating the distance from a li9,y/co2u a5ehsqe,vd ghtning 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 o;h d:vcygjplp 3/ 0t5xf 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 intensity 2ze.d 6(ovn hois $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fir- dr7tm snv i+(o ety9189ceqred simultaneously at a certain place, what will be it79-e 19m qds8yv +e(nrr otcthe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanjlx89u jt:ogmd 9/ de+ce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but onu8ldxjjgo9/ :td9 +e me engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas ;gs(8 r j cv5+y)vfjaqfor a CD player it is 95 dB. What is a)y58vfq j cj;g+ srv(the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powq98up 9 s)i5n4 ljv .kuhj/vljer output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o5 /4 8lsjipn ukvjuh q9ljv.9)n 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 eardyg1kloh7fkdyzm 1:-3(m6 haprum 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 amplifiermhq 3qri ,t:r.7le 3o7srg.m n B is rated at 40 W. (a) Estimater r7mg,sirh eln3q:q3 . .7omt 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, amn(nwohj/r k:d7c uc //1xk9t dB meter registered 130 dB when placed 2.8 m in front of a lotrm: j /h//ukkwd n1(xc 7on9cudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whahv .v (x pj;y qvf0:,jwtd+*vft is the ratio of the amplitudesp w;dv ,vvf0xy(v.fhj *+t:jq of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) a4tx izb1z;g( by what factor will the intensity increase? Increase 4 i;1 g(zzxbatby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hqk3f kif3l p.7r 2,raql:j:ltas twice the frequency of the other. What is the ratio of their inl7 a tjf.,plrf:i l 3q32kqrk:tensities?   

  What would be the sound l4 vd/z 0vk 8m+kojudzcb2z(4wevel (in dB) of a sound wave in air that corresponds to a dis dmv d8ok4w/4kz(+ 0zvzcj u2bplacement 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 loud as a 100-Hz yq54n pr bi28xtone that has a 50-dB sound level? (See Fig. 12–6.) nr 2qb4px5 iy8   dB

What are the lowest and highest frequencies that ane c0v )tgryg,0(uclp,l8r; m5yap, xx ear can detect when the sounc rtl0p, ,xr)yl,yup5(xg 8ca0 gmev;d level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of xja psvsaz4yf 67k3,1sound levels. What is the ratio of highest to lowestpxjazyva ,k3f47 6 1ss intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin a qkywq+6:mj 7has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed? 7w y+aq 6mjqk:   N

  An organ pipe is 112 cm long. What are the f,+h+hcsiiiqyn- k35gq 0 a 4lvundamental and first three audible over+0sqk5hyqn3h+l ,i-cii4g avtones 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 fr 0ilxbnx; z)hnhymftgz(9-4* om blowing across the top of an empty soda bottle that is 18 cm deep, if you a)hi n9g4yh0;x(x-*tn zbmlzfssumed 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-tube0a6 5nz9a;.a qho8:jq rvdevf pipes spanning the range of human hearing (2vhd:zqrnaea. 6j8o9q 5fa v;00 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 Hz as its third harmoni sa8mga-rn 5(pc. What will be its fundamenta8 -a m(5gpnsral frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strm bgbm6,5ytkv9q,ctucqo27ra6p4gb s4h; 5 qing is 0.73 m long and is tuned to play E above middle Cv4 qtbb ;6amsuo5y926k7 cmqp t,4 rqb 5cg,gh (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middlr31ar8e v k6zv22icyce C (262 Hz) when the temperatuzre1ryac viv 36822kc re 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 xpy u;d2sp e;6k.y2s; 8bi0us6it jmlat 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 Exampl) .d(mt kvc); oaojzd:e 12–10 should the hole be that must be uncovered to play D above middle C at 294.v :o)t;cj zm)dko(ad Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but n0jj czayad9 s +2u5qd9ot at any other frequ9zsa0j j+a25d uqyc9dencies 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 mja*deo-h( k;d long is open at both ends. It resonates at two successive harmonics of frequ-*ka(hddej;o encies 275 Hz and 330 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 *k:ch (q hct3l$^{\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 2e2+xpnz ;x9wf4+ ob az.14-m-long organ pipe9fbaz +w 4nxz 2;+poex at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is app- +y ilt5n.abwzc2xy; roximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in ;taicyb y-2 nlxw.z5+the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one )bqt1uq)b y*cof which is sounding 440 Hz. How far1ut q)b )yc*bq off in frequency is the other string? ±    Hz

  What is the beat frequency if midjab7:e kz *abcd yjl6vn jv1 j05i4/,cdle 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 aykstnioc7osf r,wx .9b.66 l1 t 23.5 kHz, while another (brand X) operates at an unknow6or fs.7x6lto.91 i bwskcyn,n 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, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35u1pfu30r ft vy4s7wf80-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationa4y0wsr 8uf 3tu fv7fp1l frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2qa 7 e2pyhpv9994 Hz. The tension in one string is t9v9app2e7hqy hen decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard ig uz memz98s8g5-mk(qf two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C andg(z es98m ug 8q-mmkz5 the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4c -5zym7vff v)41 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 Hfc- zv5fm 7)yvz. 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 m from one speakv qquk)mrt. ldq):09 aer and 3.50 m from thqmtk .a)u qqrvd):l90e 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 suppu(g firz, 8s6hosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played toget i8u s6frhz(g,her. (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 air. How many beats pmt.v0,cro2k6 bj 4 knqer second will be heard? (A , mq4jrb0kc.ov6nkt2ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fi-0w jle.tbqrh 97tfy8 re engine’s siren is 1550 Hz when at rest. What frequency do you detec0qb98ly trtf7 -h je.wt if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engrd w4 ww+gat*8go +v. :sjdj0sine whose siren emits at 1550 Hz moves swj+t8dv gjgs4waor+*d 0.w:at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you -1dq2crm:xe t at 15 e d-:qcm txr21m/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 equis/uxwvr 9;bj5gzh,,mkid i-+sgw 3k6pped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emgi- ,kbw963u+gx/ sr ih;wmzdvks, 5 jit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultra wee- a6q9ktl83shb 0csonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the rt893bce0lwa he6sk-q eceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, p -; ak- axv2e2w3duynthe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the r-uw ea3y2p-2;anx dkveflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments,/vbh ) 1w:u rk9*eiqhy a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the r * 9q1kvy:b)h er/huiwailway 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 wavesn,7sosdj) (( vsszz;z 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 bsnz,zjs s vs7;z()(do eat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraky7 bv- ;iltz)88qbfaf -pqz9sonic waves 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 djl q( 1j:av((rr5f1ls o o1dtsound of frequency 570 Hz. When the wind velocity is 12 m/s from the nor:lfts51a j1d drq j(voo(1lr (th, 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 moving on la5zwvag q,u8dno. 3 9wynd 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) Wcacof : 79+8am3cvpeahat is the angle the shock wavm7fp a+oa e8:cc9ca3ve makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of aibe;8: ytpa +(p 8rbuq planet where the speed of sound is only about 35 mepbbq(r +8; iu yp8a:t/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/sgt wc0uo n*.cgl3*jk/ strikes the ocean. Determine the shock wave angle ig c3l/c*n0t. *jwougkt produces
(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 *7thmb0 azl0jhe)9ie $/theta$ 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 ground fl12h2z)d i ciggvzuo51 ying faster than the speed of sound. By the time you hear the sonic boom, the pla)ii 2 g2gv11hzc uz5odne has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz n2oy 9l2l1w8betw9gm sound pulses downward from the bottom of the bol9tw ny92wol 1be2m8gat, 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 sbwdf +d*s12 nare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympjpfi9sh 0mk) 7hony. It consists of many plastic pipes of variousip0kf 97s)jmh 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 sounduvb/d y);wt+kq pq1p04go6n d close to the threshold of human hearing (0 dB). What will be the sound g1 n ydpuqtpwvo;0k+/bq )4d6level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and utjr c -xk+(.fan 87-dB sound are heard simt(+.cr jfukx- ultaneously?    dB

  The sound level 12.0 m from a louchsh76v;5c307f koxp wekrc: dspeaker, placed in the open, is 105 dB. What is thh07 p57fck 63x rhec:svkw;c oe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powei1c5wj 9;tqe wr output drops by 10 dB at 15 kHz. What is the po5 j9t1wqe;icw wer output in watts at 15 kHz?    dB

  Workers around jet aircraftvnir l5e(q: zup/4ay/ typically 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 has an effective radius of 2.0 cm. What would be theuv(yprn/a /ei 4q5zl : power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communich . pnp (/--j am,nq+avb9fmfqmk 9v.z f9rm3eations 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 tuned to a frequency 1ltve/r;p1 d felme,5rl - 0x 2nhwce6,$\frac{1}{2}$ 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 bakx.i6( h zv1cetween fixed points with a fundamental frequency of 440 Hz and a mass per unit lenv 1iza .c6xk(hgth 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 filled with watjww ac90m-x g+er (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 tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. Waj wc-mw90 xg+hat is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar s12 pa gf7v0kx3.oatiqtring of 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 string if it is to produce resonance (in itkv 3g10o.qt paif 72xas fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t os:mf/ j2ac)yo 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 tl 1x-* v8 r3xy9jteazthe 500–1000-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 th- 8v*j931 zlxxte aryte sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statil)+7sj1zs:xx5fa dgq ,x +ip ionary. The conductor on the statixi:5if) asj xql d,s7 pxg+z1+onary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approache-u2uhr1yq )+i6s 6 zkpsy7 so(ehbap1s you is 538 Hz. After it pasu pq- 7py yhu(6b2 1esh16s+s)akoizrses 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 b ( n6)k6pplevixvs (6-ggyug7 y 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 pvip(u6nv-k )76y6eg (slxgg halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toqg 9+yst/i ddfb(fy( mu/xq2,gether, produce a beat frequency of 11 Hz. The s ff+dsx/d ut m ,qy(/(ygi29qbhorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves c 5;lcpy 9sv+epast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequenciese;pvc cs+y 5l9 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 -.ppu(nikx 4b normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along t4kpx u-pinb(. he 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 flying toward th6irph4oi7n,r6 fo + u;bb pqh/e bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected b;qf+hr unp4 ,boi p6/rih7b 6oy the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freque,(kbhbx7cg1*g4 ( x ltkigxkm 2 ;0qozncy sound pulses as it approaches a moth. The pulses are approximately 70.b1b(x7, q2(hl4 kgcoixm ;k0gkxz tg*0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was onic 7tobq3 e-pix1ka 1/ce 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. 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 q1t1x/i3kp 7i -be acohorn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised b 07cbw 0 w/,1l2cymspvic kb0ty the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Cob 2pyk70,mclwcvb1ti 0/0w sc nsider 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 alum)i kb*el6h(-5cv ucu oinum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little prv6i* -o hl)c(uc 5uebkactice, 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 hearing for the human ear at a frequenyj)f0sb f+,dhw(+;/d g *hh rm evgdv2cy of about 1000 Hz is ;hmw 0/es*jf+gf,d)vd2yhv( h +brd g$I_0$ = $1 \times10^{12 } W / m^2$ 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 1u hwflsyc(df)iy ftkj5 .x61vu;/:rsonic boom 1.5 min after thev 5wfyk fih(u1/djt;s ulr.)y:1 f x6c plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15x1y6kv ;:sl 3thjp /i6o15u bz+srqha $^{\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