What is the evidence that sound - 5ztp1wo vier(fqg(3travels as a wave?

What is the evidence that6 4fwn9wxhq i(8nz2nr sound is a form of energy?

Children sometimes play with a homemade “telephone” by attacd l+,)xutaxh +hing a string to the uxtah xl+d)+, bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you exf*iv t:*v vv)r*wef x/pect the frequency or wavelength to i/te*x) :v**vrffv wvchange?

What evidence can yousmoh6g3 (r/ + ns( 7qkmlv/kiu give that the speed of sound in air does not depend significantly on freque(lu//m+v s hr7s6 i kq3knm(ogncy?

The voice of a person who has inhaf;) gnma m7yq.led helium sounds very high-pitched. Why?

How will the air temperature in a room affectki.;gc8muyfw( 8( vdt the pitch of organ pipes?

Explain how a tube might be used as a filter to reducedzg e+crumcl4 6s (qzhv;5mg, -bs/x8 the amplitude of sounds in v8svh 6r54/,czz-msxgcdm;guqebl (+ arious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo)i1 gji:t pz m/-wis9lser together as you move up the fingerboard toward the bpwsi:jt z)1 /lm9-iigridge?

A noisy truck approaches you from behind a building. Initially you hear zwo8co s936 kj o8-m*uc,opql3n4lml it but cannot see it. When it emerges and you do see it, its sound is sudde 9pklocol38-zmjo ,38*w mln q6cs o4unly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “insj :l ngufibh js4 gr,d 1zg7q.dq)280terference in space,” whereas beats can be said to be due to “interfefblz: q)ud1sj gg74.jq8 nrh,s dg0 2irence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lodjr-t5xbu3 ; gb z*5ez,m6 m*5iqnqnuwered, would the points D an 6,5b xe-zznnrgmd uu*qbt j 53*iq5m;d C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with vok;w fee+pe+ z(1xfy1 ery 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, in1yzkoe +;1p exf(+wef verts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. E:;r cqx1llga,ach wave can be thought of as a superpos:cl xa; l,1qrgition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if th9u:kb8nw8z/dio- w;kn t y( vd/m xqo.e source and observer move in the same direction, withtz odd/um;/. -y(8i vxk:bwnqn9ko8w the same velocity? Explain.

If a wind is blowing, will this alter the frequev2lrf iv8 ,scs k3 xsk2/yse7h,8av6p ncy of the sound heard by a person at rest with respect to the source? Is the wavelength 87,s ,hiv6 f3r e 2ly/sv2s xkpkc8vsaor velocity changed?

Figure 12–32 shows various positions of a child in motion apap x(.i/;vl on a swing. A monitor is blowing a whisp v/.;aipl(xatle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lena*/ uzbs ly/,4h:rxlz l 2 ,yfau((dvq(od: xtgth of a lake by listening for the echo of her shout reflected by a c(4a *lu:fy(du t :d(,yzh asqx// o2zlxr vl,bliff at the far end of the lake. She hears 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 just below the waterline. He hejn8mc,w: s1v /lw;xs yars the echo of the sound reflected from the ocean floor s;sl :8ywnj,v1w/mcx 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 wave+dg7ykz5 h4i7, bhngglengths 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 pryu ;)zfj/5u02ui1 oyc4 nw sis drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anothero4cy ;f2/njp0s 1r ) wi5uzuuy 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 if7 s43 6glqfjrwcuo:*t makes when striking the water below is heard 3.5 s lateg64fs wl7f :ju *rc3qor. How high is the cliff?    m

  A person, with his ear to the ground, sg.2 onz4uh9 pqees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one tn2.9 4hzoguqpravels 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 b5o tr4 6zvwi1mile of distance by the “5-second rule” for estimating the distance from a i6zrwv4b to51 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 levelgk 6 f ;;w(hprhq:lry6 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 intl;4h, c7uu gdmensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired siq 2vqmx0ck g90s2- c /or-funwmultaneously at a certain place, what will be the sound level if only one is exploded? 2s qcgkofqcmw--9un0vx2 0 /r [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally ) y2xqk,3xh a gqb5;pic6*s benoisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add inteq b;i6,* pq5sacyg xkb)23hexnsities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wherea+-(f+9xnx rvk g,vn rxs for a CD player it is 95 dB. What is the ratio of inte-xg v9rfk++n,(xr xvnnsities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output ohtgw6p j*)5 j l7wq)ohf sound from a person speaking in normal conversation. Use Table 12–2. Assume 6w j)pq*jh7 )lotg5whthe sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is huoa 5+2x*n+ tsb1nfg$5 \times10^{ -5} m^2$ (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 ampl 6n0vl-g( nu aiywz0s6ifier B is ra azn6(u 0gwi-vynsl60 ted at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to 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 regis d2t6) a-ghqwdtered 130 dB when placed 2.8 m in front of a loudspeat aghd2wq- d6)ker 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 ln 8undy65roqmkyn.u x pa p 5*q8,p98bevel of 2.0 dB. What is the ratio of the amplitudes of twon ,n9 dxqpuy6kon ry a.mp8u8pq*85b 5 sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fax- ) ps8pge;wa4 znrr vj3d9p.ctor will the intensity increase? Increase by a factoxp. )-szn3a;wp 4r dv pg89jrer of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampoq6n q vc9x0)9*ftw , qyxss4plitudes, but one has twice the frequency of they9xq6fx s0cw 4o ,sqp q*9)tvn other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds/tld:lpo-, zf qjmj 07 to a displacement ampli ,mldt: j0ol /pz-qf7jtude 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 ( jg4tu/rdn .nas a 100-Hz tone that has a 50-dB sound level? (See Fig. 1.jnut/ ( rnd4g2–6.)    dB

What are the lowest and highest frequencies that an ea8 . 3kecl wh /2/kz7pb*quwhipr can detect when the sound level is 30 dB? (See Fig./.c*8i7hw plz bwe huq/3k2kp 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What ihnbcm)-b4z5* h+ parss the ratio of highest to lowest intens+-p4nh)ar sbm chz*b5ity 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 fi.5em1kgkwjr*sl4 j8 a 0msf4undamental frequency of 440 Hz. The length of the vigk0jk.m8sma rs *ej4 i5w14flbrating portion 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 fundamenta- epw bpix,j51l and first three audible overtones if the pipexpw1 bpj-,e5 i 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 fro 3ecx4 c+1qbymm blowing across the top of an empty soda bottle that ieymcb413xqc +s 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spm h51yk3v c7jcanning the range of humyv h 7cjk15cm3an hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third hai fx -emsu/3h,rmonic. What will be its fundamental frequency if f-,si xu3mh/e it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and do7s/5a z-wh9 3hwuwm is tuned to play E above middle C (330 Hz)7ou 5w/ w9 3as-hwzdmh.
(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)b-x5z xs wg:y 4oks7;i when the t7box:sk5s -4 wx;gziyemperature 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 20 5wcppg7*n pg5(l l 2rh6p+*i4kcyvwy $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampzx b7y nz09 foaxieb7+(z0 r(wle 12–10 should the hole be that must be uncovered to play D i(x7b bxn+ae0 (oy7fw9zz 0rzabove 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 Hz, burb1bv4the 5yw-pr,go )b9fa)t not at any other frequencies in between. (a) Show why this is anay9bptwgr)hbob1e r5) f 4v-, open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two suckycsmwe2 ;5fidc-e ;.cessive harmon; f ;dmc.5iye2s-wkc eics of frequencies 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 clzs+qpi +2 hklv1s8f5d+ )pr $^{\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 audible6omu o*n1c3yf range for a 2.14-m-long organ pipe am 6fo c13y*nuot 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside av/; w;tywgvm/nd 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 relationsh y/wv;mgv/tw ;ip 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 2m1 r3hz xz-7qz.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in freqmh1 zxz7r- z3quency is the other string? ±    Hz

  What is the beat frequency if middle C (2621xz3gh7supa 0 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates av;dq c;.p 1 nzw*k(j titxm8b*t an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequem*8*1( zi.jwq tb;cp kx;d ntvncy 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s w9 qbz47ly2d4 2x ncg s+l+upcdhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequencp us++7cnqbx2ly49 2gld4c zdy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29x 1rn/z )biqs34 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toges/ ibxz1 )3nqrther? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes sltb1pqxg4c(p(a,;a each try to play middle C (262 Hz), but one ( ,(lp;xg1 cq4atspbais at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning wy o6pivgxe* 4y py413forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sou4gypyp 63x wyeo14*iv nded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands t + t;lw/arf:/le fx(a3.00 m from one speaker and 3.50 m from the other. r /+a(:tfx /efwlt; al
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, b2a c*r;wglh y6ut a piano tuner hears three beats every 2.0 s when they are played together. (a) If cw;y2arl6g * hone 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 andyk-e g5 1/9z+f d j8ucvovi+ow 2.76 m in air. How many beats per second will be heard? (A 5c8j-+e+ dv 1ow/ifky9z vugossume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sl my.dy u, iz1/vf7fjfv+11av iren is 1550 Hz when at rest. What frequency do yov mufyza+ i/7,f j11f v1dylv.u 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 frequency do you detect if a fire engine wh uj /ww6mht0w2cmoe3.ose siren emits at 1550 Hz moves aoww3 c w6th0/2mmu. ejt a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 200.0tyngqf /u.ix 9tqgx 0t-ee( 0-Hz source is moving toward you at 15 m/s 9/xt efiy.q. -e x0nt(t0guqgversus 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 frequency horn. Whe*/cb ztagqa8 .q eb93tmnup31n one is at rest and the other is moving toward the fc n*bta ug/q9e .1qb38mt3azp irst 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 soz 5uycq;+h97ivlulq .und waves at 50.0 kHz and receives them returned from an object moving directly awa+l9;lhy izcq5 v uqu7.y from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m//4t vqg2k.dom s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Whattm ok.4d /2vgq frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a),ks mnmnyq jcw09c (. tuba was played on a moving flat train car at a frequency of 75 Hz, and a second idw.0n(ksm,cn j cy9)m qentical 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 b4a est eem7x47lood-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 bxeeea4 7st7m4 lood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequenyu*svlk(q7 fbd.3 5a; dkdsr*cy $2.25 \times10^{ 6}$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 wi f;9p *fx2u 39,2dweejpoadpx1y,t q+gd hco0nd velocity is 12 m/s from the o9fe h,0+jqgppyxdup 12d ex fc*3;o d92wta,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 moving o , -xgki:waytdy4e n(qb79o4fn 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 /lwry.0pb0 ldzc b4z*t8 x(s jat Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with tty l0rxjs.cl*(4 b p 0/zbw8dzhe 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 a planet where the speed of/ h0ds9oj..;cx9tews j ay l3h sound is o0.lh3t/xjh. ys w9cjd9oe ;a snly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wa6p(wohioi/-4kb9xb5t(bz4eavudk 8 ve angle it45iikkuw4z e advxh-bbo6t(8(/b9o p 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 /v)vrn s9a)yorf1 /s o$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above th8prkyn l 1, ld(6ppz ajj,rp9p .m5h,he ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has mpnl5l,h.6(p8ppyda ,p rrj9kh ,z1jtraveled 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 snhr / zu7.;nspja)7ooound pulses downward from the bottom of the boat, and then detectzh o )no/ua7p.7rj ;nss echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human auja 6rwzznrzp3b44a6m02 h + fsdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symp6n qv1;inr4:pf5 hfllhony. It consists of many plas14 fllrv5 fn iph:;nq6tic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makep9gcgn k(h/y *yd5lh4+d l wr,s a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosrwnh *yd lypc4 d,/5lkh9gg(+quitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound g8r 76.+t/yom9 ql ezwn6lrpoare heard simultaneo6le /n6rytg8qo79 mozl+.rpw usly?    dB

  The sound level 12.0 m from a loudspeaker, plac4y w.cw/ x:wbe afl;i0ed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directionwcya /fwi:;.we x4lb0 s?    W

  A stereo amplifier is rat11epjlshxxvle v* r/wz)y ,8cq 2yt53ed at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 153csh *y2/1 j8r plxvx q1lw5ve) e,tyz kHz?    dB

  Workers around jet aircraft typically wear protectb ko1el +1dwm+ive 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 humm+1o dk1wl b+ean ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gair zsa(0(+cz ojn, $\beta$ 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 tow jt*n+,cbg(d+6qp ir a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with uce: +i930extbqf(mf*y ( ivca fundamental frequency of 440 Hz and a mass pcieb *m x+(0iuyfe( tvc :9fq3er 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 w-+:m - g,aqbyxznzcw ;ith water (Fig. 12–35). Th:xyngb+-,c a mz ;-zqwe 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. 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 opennsd.mh7+2c qpgvt ;z 2 at one end and also 75 cm long. How much tension shozh.tm c72qnp ;sg2d+vuld 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 observed to resonate as o+i3o3ty)h,en : r x5uobcehxw750 nqbne 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 500–10gl;0lx.5 fb fw00-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To def0. wlb 5f;glxtermine 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 whisyxdc.opszzyu1ec:11c9js,0 tles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the zecox,1z cucy1yssd .p9 :0 1jmoving train?   m/s

  The frequency of a steam train whistle as it appl(piy1f j 28xsg0a9uib kmw b-)+9djiroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume congiiuj+9dp0fsm( 1k bli-2)9y8j awxbstant velocity)?    m/s

  At a race track, you can estimate the speed of qvc 9-c;5nv3v1si4vp , mcsnmcars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the str9mv- 1s;n3vn ivscp,54 vccmq aightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. u9gum :q7 jrn)The shr7mu q9 njug):orter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it eb7/+q:v k;z cxzvxb 9moves 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 observer when (a) he listens from the position A, in front of the car, (b) he is betweenez7 k:9cvxx /bzbq+v; the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.3 2b2jxa,nx-uq. *(n kvsw2 sqh2 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and r2, vaq2xhk x -2sw*njb nq(us.eflected 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 lmv qn29v5zt mqc7 +agb5,,m gthe bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wh ,g c9b52v qnq+mvmla t5mzg,7at is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of higiiq,) jke7ty n71r r50 nlgf6fh frequency 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 tr ejg,q5ty6 n7l knff170iri)hat the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals fro.fhvzlfym2e-1 -0zbnw1cz8idu i0 v1m one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns weredlc20.ze1wz vmf y0b-hnizvif18 -1u used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the p7apzf: 05 c;w3ps.plhvn +t.gr gjn h4resence 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 2sfht+g:w npgc0 7p35.nv .;rz a4 phjl.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 vlrya*0l g5zo nn1 4( lwbgx.-rods,” involves a long, slender aluminum rod held in t.xzl1 v(nbgrgo-5 lwa0l *n4y he 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. 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 tqcv 0ib34v ip7a,okk4 hreshold of hearing for the human ear at a frequency of about4i k kc 3b,0viva7o4pq 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the grog5*dqmu - t12tieq m(zund hears the sonic boom 1.5 min aqdm*e (-mqzig 52t 1tufter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i3e j*1sf1 i/5ybmcjkvs 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h