What is the evidence that sound travels as a6vfaz0. f1,fl 9ucddw wave?

What is the evidence t3o fth a.hnb78hat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a str (:m2uws1m u2ded3dd/n s b0pring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard as:(udd/p 2 0mdn dbwmes31r2u t 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 expec),egs;n j8 b.nm8gob)fv n0r18 dzngz t the frequency or wavel)v)mn1b.j,gf s8z8 b ;goze dn8gn0r nength to change?

What evidence can you give that the speed of sound in air does no t2m0bwj(d 6hyt depend significantly on frequency2wdh06(t jymb ?

The voice of a person who has inhaled helium sounds very high-pitched. Wh )i/ci 0ir;eyzy?

How will the air temperature in a room affect the ppdchw,/xo+6 b,ql 7 reitch of organ pipes?

Explain how a tube might be used as a filter to reduc.3sgp4ec7p n ge the amplitude of sounds in various frequency ranges.pn3s gg pe4c.7 (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up 8+is43dxjwihdu 2;av the fingerboard toward the hxj28ds vii+d;3ua4w bridge?

A noisy truck approaches you from behind a buil qz; x zvi5+hjqf zmkp(8/e7u0itw6c ;ding. Initially you hear it but can; pci5 8 e6m wfuzxjz/khv;q 7ti0+(qznot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to c;7t+y ifw:yd6wa6 awbe due to “interference in space,” whereas beats can be said to be due t;iyad7w 6wwt 6a+f y:co “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouls6zq 5;afre 3 vv6hc7gd the points D and C (where destructive and constructive interference occur) move fa63;cher 5v 76ag svfzqrther apart or closer together?

Traditional methods of protecting the hearing of people wh(2 :nuhbwzr5ab4 gie:u*x :2ap b3u+w shdq+lo 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 heabs: u*r4+u 2bnzwguwhh::( blax 2eiap5qd+ 3 dphones 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 ofjif w0 5g4gxv) as a superposition of two sound waves with slightly different frequencies, as in Fig)vj54iwg0 xfg. 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 same direc ho/-c /nnhvr,tion, with the same verh,coh nvn//- locity? Explain.

If a wind is blowing, will this alter the frequency of the k bbcrph7x br/.9q4t8 o4et1msound heard by a person at rest with respect to the source? Is the wavelength or velocity changbx mb ptq.b97thr4o8ek /c41red?

Figure 12–32 shows various positions of a chiuj09v;cv2r q 1nyngy-d p5c f6ld in motion on a swing. A monitor is blowing a whistle in front of the child on the yn02j5 yuqr1; gcd f69pc-n vvground. 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 of her swh8*2joc2(zu2+uq q2o e3 .lhrrol hs hout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengthzjrlhuc+ h2qq(22 8r3 h*2wo.oso lue of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ec-zk)gqlb/t9y (bfuo7 hoby)lt 7ou /q( -9gfzbk of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of 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 20 9 a754qpx wuqjv,2al v$^{\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 abo)4d8td7vo a.gfz1q 1/ku exkqve a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km 1 zt kadek8q41o) /fdquv7g.xaway (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 c3,/(utdl cfgrjt-j)p liff. The splash it makes when striking the water below is (p ud ),g 3jtf-c/lrjtheard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the groun6/h6wtk9u tva cz9/qh d, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.w 9actqhk9t hv6 6z//u1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percen crkugt,nt: *r dn3zf2 2pfojf/)n 03lt error made over one mile of distance by the “5-second rule” for estimating the distance from a lightntn njfzr3 fn),*cg/ rf3d0po2:2k t uling strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of e(mt:65)ir/8eedwmflwz 0u h a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inten eqv7fo -h;y.csity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d3q- fyjs sit(.B when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,sf yj(q-s3it. not dB’s.]    dB

  A person standing a certain distance from an airplane a vomu44a6ag/lfj29*/u exh cwith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound lm9uhxegcu/4 ao6a /2jlv* fa4evel 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-wqv:c q:qq b:fc y9,,znoise ratio of 58 dB, whereas for a CD playw, qc:qbyqv:qz,9:f cer it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a(pbepz3*6/iilis:o o person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered:p(ip bo3is*eo6liz/ 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 strikesw t6mvqpgt 64;;mty4 yt2)plh 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 amplifier a s wf)haz; i /ma-x2 pi/2c)jmpg+mt:B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a lzmmsmtf /) 2)apcxh:ia jwp i/;-+ga2oudspeaker 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 c-l95ua9etay twc3* txz6*fn meter registered 130 dB when placed 2.8 m in front of a loudspeake wnczttt yc9x5fl9- 3a *6uea*r 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+e4sn j. gh;kq detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: Seen4he;gq +s.jk Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will t rbhw 27*m4ce ewq1)olhe intensity increase? Increase by a factorq hblcew47 1e)mow 2*r of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the iu,.k lk/wga/iwc 1-w frequency of the other. Wh 1wawi - ck,ukw/l/.giat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tz/:hzfom 3 z:jo a displacehz/m:zoz3f: jment 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 t5lp: xdzll.h h2:bj8yone that has a 50-dB soundhp l :l.l8j2:dbzh5x y level? (See Fig. 12–6.)    dB

What are the lowest and :u86ni bobt- qhighest frequencies that an ear can detect when the sound level is 30 dB? 8-bib:q uno6t(See Fig. 12–6.)

  Your auditory system can accommodate a huge range ofcckd2;ag(bf0 +cj:w v sound levels. What is the ratio of highest to lowest intensity at 2f+;(0dcgjvbk:ccw a
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a f+paxipmo; ,hr *eh :s6undamental 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 muhs*:o; ripph m +xe6a,st the string be placed?    N

  An organ pipe is 112 cm long. What are the f*kw /4tk)2mz of:vrd) ire axq+h-5ziundamental and first three audible overtones if t4iiw)ed2 / hvrfa+m5* rkzqxt:ok-z)he 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 wo0, y)fms0jawn4.wlq iuld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assum.n q 4)amlf,wj0w0 isyed 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 opes/ fe1s8 o2lxu::oc nkn-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengthu/ :s2cnlxs kf 18:ooes 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 hahv fzzs1c +kpxi6r(2* rmonic. What willhp sf+ k(1c 6x*vzirz2 be its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plnky.xyw+i+ -1yp.r/sxm 4( fy+ r taqkay E above middle C (3y irmp+xk-y s+1(ny4q.+ wafkx ytr/.30 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 middle C (262 Hz) lz75 mf ob4wj3vc.z8 5regi7wwhen the 7g43zv5l5bmcz7w 8rwief oj. 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 ato m l 6.ti4l+no5aiu; bule8w1 qx-1iw 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 12–10 should:f6h,ki/cq7cefd 1*tvi ( .n/wp glcglxt ;d 6 the hole be that must be uncovered to play Dp cce6/ 1hg/ii7*( wxd gl ,c tfq;:nvlftk.d6 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 resonat i e-2lag*:az9)e x,sfulip j4e at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wh *u2eif s gxla4z-)pia,:l9je y this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is i xfp29:wj3ut open at both ends. It resonates at two successive harmonics of frequt: f2px wui9j3encies 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 uuwa8j;h7g 5 p$^{\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 fv 34-f ,wlwxl-r q5qfc.z;/rqcr tjo) or a 2.14-m-long organ pipe atwf/,q.q;c v3o)zt 45fjc-w rrr-qlxl 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 iu wey:9*2-a( kxde p8r*ewrd open to the outside and is closed at thew2*wp-i*dye:9e( eka ur d8rx 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 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 bvn8(,)z d jbkof which is sounding 440 Hz. How far off in frequency is the other stringv ( d8zn)kbj,b? ±    Hz

  What is the beat frequencigl 6imd/ 0v:v4*g3 vfcf1 reky if 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 anothe67u,8 io )qdgn4hiby tr (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine thn7doi6 8,gq4b y)uiof 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 wi.27tgzm*dyq es yop c48ty9x9 th a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What t97zs .2*qyodcpy egtx9y4m8 is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensi1w4v(ruha ol b8x8 ic;on in one string is then decreased by 2.0%. What will be the beat frequency heard when the two s hcaiuvx48 l(b;8wor1 trings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heards5vjie o81x7u if two identical flutes each try to play middle C (262 Hz), bu58 i1o s7juvxet 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. F67ss j)+o pzl34ucg*t pn w.toork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequencyl7j ooc.4u+ ttg z6sw3*p )psn of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.k:h lgg50iv4cpvsp70s /h fi ;80 m apart. A person stands 3.00 m from one speaker and 3.50 m fr;pfshs0phv ig/7 i4 0klg:5vc om the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be yawci gbi 5xbx3t;k:h09x z,, vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequenik:t, ixczb g;x5w 9hb3a0,yxcy 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 beat tzdki 7a(b;t-s per second will be heard? (Assk;bi a- ztd(7tume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequen*w)0ji0w zl o-zk+fzucy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency+* kwlo00fuzw i) jz-z do you detect 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 freque-ccps k/q7/z/ l/kwbz0)edeency do you detect if a fire engine whose sirebc keeq/l e/p 7/zs0z-ck )wd/n emits at 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 if a 2000-Hz source i4a9f,gqb,4i iuc4 yc ms moving toward you at 15 m/s versus cci 4,9q 4fg yu4ib,amyou 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 frequency horn. Wh3pgbtpkv0.b5b 78;r +wmiq bev+e n1 nen 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 1e+kb 5b8vg p p;q3 i0mw+t.rnbvbne 7is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic s7jw,efc9pni: b8i ;nr r z564uuzz0bzound waves at 50.0 kHz and receives them returned from an object moving direc, ujn:9i wep85zznzfrb6z 0ircu7b 4;tly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w1n-kgd*s6h ppall at a speed of 5 m/s As it flies, the bat emits an ultrhgd-6s1p*kpn asonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played onx78 2u4zz fexu : :xktbxuxldt4f8k ,0 a moving flat train car at a frequency of 75 Hz, and a sk2fl:f 4tx8 ,7ud u8e:x xb4xzx0 utzkecond identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spfl5mt)dp ,aucs 9:;zjeeds. 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 artep9u, ja5ct;m sdz:)f lries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of rkjet+u ny)e c842v2qfrequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocito 5bry ck/17qm hq;)cdy is 12 m/s from the north, what frequency will observers hear who are loc7) ; /c1dkc ybqo5rmqhated, 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-f t1e7;uigz(cvq9z oc ;ww: a $^{\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 Mace-g1)4 kfvro.p an7x mh 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directione).1xp4 gf -kmv7ora n of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soujh3s1 rdti k(z1z4 osoqu1xc:zc ; :*qnd is only abozoz:i;r:h 1*qzq1j d 3oux t1sscc4(kut 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 8n gvcv( 8 fa-)y,4x m3oo lw;*dlvi5gl500 m/s strikes the ocean. Determine the shock wave angle imvnly5d*) v (i38c4vll; -xawofg ,ogt 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 o4me s(wbh3 ;a;qqnke6/l17ia+tdkr $/theta$ 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 da44zm1xhe1dv6v r 9o -bb, huabove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a hom1- avdevhz6 44d o1,hubrxb9rizontal 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 sjm- fc4r gji210iy 4vuu u2k9aound pulses downward from the boaj iuk2c 0jrivfu 4g4-91 2muyttom of the 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 tw7*3tqu+w ,rdrts tv+v ; mwk-here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe u2fmcl5exwz :k 1:m8 q(isri*symphony. It consists of many plastic pipes of various lengths, which are open on k w58x miq*f2 (ru :i1c:mlzesboth 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 makessvdu1ab ,fi y7o2pm37 a sound close to the threshold of human hearing (0 dB). What will be the sound level of 10vi7ob,d3y sa2p uf m1700 such mosquitoes?    dB

  What is the resultant sound level when an 8k3n.vo0wkzpns 5 w:c ,p4 .1z 3kpwklo2-dB sound and an 87-dB sound are heard simultaneouslkkz wpp s 0vw.:kkn,lo3 n5 4.zop1w3cy?    dB

  The sound level 12.0 m from a loudspe izd-)ljucvt-f;rtkhm64 6,b q 8esh/aker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker,u6/jh me tsi-hk8 f z4l)qb6d,rt; -vc assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. /ix)lq7uf3 lvThe power output drops by 10 dB at 15 kHz. What is the power output in watts atx /)f7lqi vu3l 15 kHz?    dB

  Workers around jet aircraft typically wear protectinrbofo x-vtwn79.+5ive 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 intercepted by an unprotected ear at a distance of 30 m from a jet airpla o 5x r9onw.+nb7tivf-ne engine?    W

  In audio and communications system34+ zjgl5pz cmu**y pzs, 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 fr/hv rogshgj(f :w:da0(a l;4 requency 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 p;(yqpix4x0g4.cspe xju* 7szoints with a fundamental frequency of 440 Hz and a mass pe; xg7*(j i0zx pqys cux.44sper unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wiw *gzqo*d.bs+th 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 tuning fork when the distance from .+*qz ogs dbw*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 onec59xzu e+.l 3gomvcjmz-:w4z end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in uommz5-cvzg c: 4.z+exj9lw3 its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observedh+qo .iw/3hvj 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-Hz range coming from two sourcedn jnq/jjc+09 g6t4 rps. The sound is loudest at points equidistant from the two sources. To dej0d9 nj/ptnqgj c r6+4termine 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 other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductork2 7fb r6wb ,av 2(f(4ijk pf-mh6iswd on the stationary 4 p2(7dw ,b6 abmf6f(sif hji-w kvrk2train 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 approaches you is 538 Hz. Afteat .4n 3as-avlr it passes you, its freque3tl asva-a.n4ncy 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 caqaw1;y99bejn l++e3vek6 i ,7eaw vk rrs just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound ,rn1ilk 9vj +kww396e eay7eva+b;qeof a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a bl2( v npp) 3dp51w trcwpj6m1beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othepj 2tn63(dwlrbp511pvp mc w)r?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past n t/ap e)q o,rspq*6-pa stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they h/)rsppqt*pn ,aoq6e-ave passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s whal:bqd 4/h n 5qmxd;r4gt beat frdhqxl4qr;/4m 5 bg nd:equency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth :rgyj4o //sp iat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after thagp/r o 4/s:ijyt wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Tnpr6h +s. nnak77r5 qkhe pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next pnr7k+q7 kr 56ns a.nhchirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villaox-) m96 uuk,lcwacj*e8o7cr hw1: uo ge to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep soun xk8celucr) ,o-u7wo uwc9: 1moa h*6jds. 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 liste-mb ,nm-us:68 /vprpiby acf(ning can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this ro,im8usv6rbp amc-y(fn/ p b -:om.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumin1*kefoa (;,x v 0 wettjglie35um rod held in the h3* xvw;ak,lft15gj0 ot ee( ieand 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. 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 fre*q o1wwnj1xy o 60guz)8us9 brquency of about 1000 Hz is uswzy*ju16n qobg9wo1 ) r08x $I_0$ = $1 \times10^{12 } W / m^2$ 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. /dpu76n.irq m0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s anmr7.p/u6 d iqltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1*hkr0sh8y pqm zd+:i( 5 $^{\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