What is the evidence that sound - 2xx6-qr.cvm cl eg:jtilxkz1+4u;rtravels as a wave?

What is the evidence that sound i5ypm j +(gx 7s,jnf0 j7ptcg,cs a form of energy?

Children sometimes play wyl h4lj (+wv+1o..nf8uii hkud v,,lbq7sn f3ith a homemade “telephone” by attaching a string to 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. 12–29). Explain clearly how the sound wave travels fromv7w.huykfvu.n i,1lo sjib83+d, l+ (4fn qlh one cup to the other.

When a sound wave passes from air inqifn1 e8/:f(bp v2h dato water, do you expect the frequency or wavele(h 1vde:b/q 8ifp2 nafngth to change?

What evidence can you give that the speed of sound in air does not depejz+lo, 2mz(zpl; g1 xrhd bjmf.km1*;nd significan. pmgb z*hlrod11 lxj,;zm+j2k f;(zmtly on frequency?

The voice of a person who has inhaled helium sounds v,bj7a8 *)hac ysftqg0ery high-pitched. Why?

How will the air temperature in a room aff; gdr:qspe7p/pyq of4 ksr,,*ect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplcgkz m.,o+gn)itude of sounds in various frequency ranges. (An g.,gk zc+o)nm example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clow dd.pt0kklbz/d) gj h-(m( nr 3tg5i/ser together as you move up the fingerboard towark)ttp g (dmw hd-(d/r53z.lnjk0g/bi d the bridge?

A noisy truck approaches you from behind a building. Initially you heasf yz15zp-3egr it but cannot see it. Wyp1g 53zesz-f hen 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 be due to “interference in spaceaktzc8( 45k iw,” whereas beats can be said to be due to “interference in time.” Exp( 8cazw5kk4i tlain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the po: b i )zg 99zvgfljsqw;sip281ints D and C (whg vl1psgzsq9 z8;j iw 92:f)ibere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas withm(cqj.*zt9 bmjfsjx wy (20xv.ag t.. very high noise levels have consisted mainly t b2xf* .t.vy sm(jj9gwqzjm.a.x0( cof efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of aw b4s(lr: .akzs a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compons:(z4wa.lr bkent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same o7 asfd*ig* p0direction, with the same vof*ds ip*0a7g elocity? Explain.

If a wind is blowing, will this alter the frequency of the soz7j)vs5,r g 2k vzuof4und heard by a person at rest with respej zo g) ur,zk7vs542vfct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mrpl5zc(136l9 j auu xq0 halw(onitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explalj5ualu r63l9(p0waqcz x1 ( hin your reasoning.

  A hiker determines the length of a lal y 8qz.6sb zuc:a05vfke by listening for the echo of her shout reflected bb:av.f6 05uy l8qz sczy a cliff 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 hearn10g m1fdh gqu 8gh 1v;1vyul)s the echo of the sound reflected from the ocean floor directly below 2.5 s later. How 1h gv;v n)u80u1 qgmygl1hdf1 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 q 9l7mpuww9(n a0sw;d in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just ab 7t9jf hsf4+ hyv1yty7ove a school of tuna on a foggy day. Without warning, an engine backfire occurs on anoth f7yh91st4 fhtyj+vy7 er boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it make+w (x2vchv/s 1kd9efls when striking the water below is heard 3.5 s lw c2vex 9hl+d1 sk(/fvater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cocfom /xsv9;8cq a hit(952xzsncrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the t 8i/ om9zcac;vsx(s92q5h xf 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 madovk+o p2 -1cane over one mile of distance by the “5-second rule” for estimatina k-o2v+ c1nopg the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at ty) lo-; gwwj.dhe 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 intensityeerb*rfzhq+ 3lhtbr8; - an), is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soun- yfusm2( 3zknd level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, no-2 k(s mfzyun3t dB’s.]    dB

  A person standing a certain distance from an airplane w,uw.kwln 1ybi,p5 dc8nhc ;l1ith four equally noisy jet engines is experiencing a so8ud b,wn. 1h ,lcky;n 1li5wcpund level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rafks;jaqu0v:bd 0jt;7g 5/5t a lj1ioy tio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sign7t 5kyj/idgjs:fj v t;ul0b;qaa10 o5al and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frv/6bv lp k4ns-aoav 17om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughls-7vpak/v b 4nvl 16oay 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 7qndqgrtn 3(*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 modeet2 5arofa9p y.pvo75n o+ cj2st amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected .tfpeoac+a27 jov5952pyrno 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 regist4ng.6ygv40nubcgr p8 )fr5euered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. fgn gpygv50r8 b46u r)un4.ce
(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 lejhkmx1 u *u*,hl1)g mmvel of 2.0 dB. What is the ratio of the ampl *mmjl u1mhk1) guh,x*itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,b ui7tk+kz ,-i (a) by what factor will the intensitykiz +7,utbik- increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dg xuvog ;1biv:/4j1p xd4nni- isplacement amplitudes, but one has twice the frequency of tixbj1o:1/gn xn pu4dv ig -v4;he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wa5k7s-tqqehe3jgi-jl+qxxg n 3 7z p72ve in air that corresponds to a displacement amplitude of vibrating air molecules of 0.173 l2qe 5g37sjx+je7ptk-hqgqzx n -i3 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem1vp mqh+5 r8d 25r,k22rgx1x yyq tivc as loud as a 100-Hz tone that has a 50-dB sound levelrmvh5 t 2 x2,ri2vkgqdyqc 8 5ryx+p11? (See Fig. 12–6.)    dB

What are the lowest and highes,7uw ;2yr5ao 2p(qh/ukj rpp+gb jf(pt frequencies that an ear can detect when the sound levelp,w5y2g p;/fu rbpj (r(ojh q 7kau+p2 is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What j)x pi fua(i6wu))h, wis the ratio of highest to lowest intepiwuu ijh ,( 6f)a)wx)nsity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of gm;x2tt 0qh- c *g7oarthe vibrating portion is 32 cm, and it has a mass of 0.35 g. U7g-* 0 qaox htg2rtc;mnder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What a .bsk um,qic m4k)(rs4re the fundamental and first three audible overtones if the pipe i4.)ic mkksbu(4 ,msrqs
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an e be5+e (4ianpp9 jjf49 dmzx2qmpty soda bottle that is 18 cm deep, if you assumed it was a closed tuj4d94pfze+jbn e5m 9ia2pq (xbe?    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 p3zm+ek l4.esripes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of p+lr4 se.3 kmzeipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmont)e1e2vg2 p uoic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original le2vuo p tg2)e1ength?   Hz

  An unfingered guitar string is 0.73 m 4pc1kn:+0 n fohcy2dllong and is tuned to play E above middle C (3y ohkf0nn: c 4plc+2d130 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 emir*s 2egkq36 qgts middle C (262 Hz) when the temperature e3 grkq26g s*qis 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 atvw+ xu:g5v-dx 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 szk 5kf)oph4 x.pe6.wg hould the hole be that must be uncovered to play D ahwk. zp. e4x)o5 p6kgfbove 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, but mv).l9z(9 k6k( ea k znvbouh1j f8mgwg:g*r+not at any og6oe( vklwgmf19n)a (* huk.+g89 zvjz k r:bmther frequencies 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 m long is open at both ends. It resonates/8b7qfb fp l-c at two successive p8 flb/7 b-cqfharmonics 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 ixs1fhso13 o .$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14/ mcfy97o.ek)lqxmdb ax)1l( -m-long organ pipe ak my9)oc)1qef.7ml/bx( adx lt 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 tob srb(r(9of9h the outside and is closed at the other end by the eardrum. Estimatebb9 (orrf9hs( 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, oneufbor0um pht5q20)r ;6yt3)5hdhkg 9v avg 8 p of which is sounding 440 Hz. How far off in frequency is the other5k) 6; rvdvhhp) ah05uq ymo 0gtug39bf2tr8p string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anj,,4 vh(o xdj zxrr2a9d $C^＃$ (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 kq-d+n l2,lhw (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimn lldk+hw,q- 2ate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whenc;96kv ,b j2z lo7v3usl q)rnw sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frelwkl vrjz,3b9q 726csvno;)u quency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensiq29cj+wcf 7ys2t 3t rzon in one string is then decreased by 2.0%. What will be the w3+ 9rys22jztctcq7 f beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middlusli,k o t/+3cmbk:5yg;l;mop ,wdx7 e C (26oitu:73lx/kocmg+m ly ,w; d 5sp,kb; 2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; elp 7jvu4e-f-when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequel-v4fu p -7jeency 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 p:l2e*g sz ve60iwh5p derson stands 3.00 m from one speaker and 3.50 m from : v0i6phws le25zg ed*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 vibratic(d3 oaglgle4b9mn. 4x-qql (ng 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 frequency ofgd q q. gex-m4oln(c9al4b 3l( 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 vj/877hb h1ku(rvvkyio- dqn 6s: g+ebeats per second will be heard?1 + kh8nvu7yk/idr6g- hvqvb7o (ej:s (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ctg nc* 14zthe0ertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect4*nc 0tezhgt1 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 ekpby ,cu(e;0fire engine whose siren emits at 1550 Hz moves at a b(kee0yu, cp; 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 towar/xjoqtz ac42 2( jrm-gd you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly go/(a-2 cxj tjz 2qmr4the 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 si0puyk96 8 vn cfp3w6nbngle 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 emit? Assum3f w8 0 ykuc6ppnnv6b9e T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at2x 4qeug0; jtw 50.0 kHz and receives them returned from an object moving directly ;ju20egwq4 t xaway 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/s As it 2lg spzecx4,i )w2h 8o9p7smq flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz.)292lo cm hep8wz,qsgi 4s p7x What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a ufk-wdpi; *i(t q-whv g4c* i8e ;l8hemoving flat train car at a frequency of 75 Hz, and a second identich vuph8d8 ;g-tk 4e-e iiwql(i*c;*wfal 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 speed1erd*d;7dz).5lvptki su9ez1zw8gy jdr7 g9s. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directy ded zwd;1sz8 5g .i) et9kvdglz7rj79p*ur1ly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequddjf 1**i1 l.sb l)zidency $2.25 \times10^{ 6}$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 frequensq 5izmw( ndu,g0ijb0)h ) h6-fyad/qcy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are0dsq ,hn0hdqy /b6m)(5-iz iu aw)fgj 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;78du/jtilk+tv1w hflxc y7: moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speaq9r*,6i-c lyjnh 3sded of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’ 3n ajcs69-rhy,dqi*ls 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 speji7 fg82hnr buw8:1dred of sound is only aboufh j2:nrri dw8b u1g87t 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 svmex z3g4; v-:ca4sw ktrikes the ocean. Determine the shock wave angle it pr-x4a:;vgwzv4cmsk e3 oduces
(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 xa6jqlcck y*(ad0-;k $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and seea+ef2w) +x oe;zo1pi*m9,af 9qsocfw a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dista e+feax wo 2c1 f+oi9,zmaofs;p)wq *9nce 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 sendurzfa dq4u.kflq :+xl mjm )0p+;3;d qs 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is q+ufau3p x +k.q f;dz0l :qr;lm4 )dmjdesigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are therpu yi*,w u./ct xtqs7s)a6h 1oe in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calledjsp3s3m5y(cud 3rw* 02tx hm:7 wzgsn a sewer pipe symphony. It consists of many plastic pipes of various le3hg2j y 3xc5w7pwm3 sms0dzu(sn:r* tngths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold ewryk9wtx.1*x8 xf .w.qoyi r 1;(hacof human hearing (0 dB). Whaif(.rywt;ew1y o.c*xwq.x9h x 18krat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soo h9c1lga1 ;clnurjv/* 7 7upuund and an 87-dB sound are heard simult*un1o 7lg h97;lrucpauv j1/c aneously?    dB

  The sound level 12.0 m from a loudspeaker, ptx 2w(b stk,le +:egt6laced in the open, is 105 dB. What is the acoustic power outputwtl2k6 xs(+e:,ettgb (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rat+pok 1r:dk 5kued at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whatukd5 :pkko 1r+ is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eckeks6(mrov5 6 pj)g* ars. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140*j(os m56) r6ke vcpgk 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 airplane engine?    W

  In audio and communications systems, the gain, a5rl67c3v mo fj xbi//5h mtj)$\beta$ 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 t;z+ vp4z5 5;vukvqeb eo 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 l bi 283lirsby.ong between fixed points with a fundamental frequency of 440 Hz and a mass per unit iy8rl3 .ibb2 slength 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 with2chd)1+fsuszs(d2a+g0 ct hr water (Fig. 12–35). The water level is als a+ )dh 1sd2(rcgt u0+2sfhczlowed 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 tubexi+ gkh.orbyfu4 3,p p;90i ee that is open at one end and ali9o ugfkyp4 ib+peh ,.;30x erso 75 cm long. How much tension should 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 oneapd 2g71 rm+sm 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 i zos ;8,0nyh lpff;o5f *jzp)kn the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the to;fsofnkz y*;p)0 ,p8zj5 flhwo sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistlxtep 0ssnnj 71 ii,p;,w95 khges. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What x7,1 w n0j;9pi k5tn,isheg psis the speed of the moving train?   m/s

  The frequency of a steam train whistle as itn8d)/ ot5fcl6 ttd)6eln -pyw approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz.6n- ptl )8e dydwt5)o6ntl f/c How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can esoy z)yiil h9prb 3q-+/34sju -,hap motimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the3 ,) h pbjaop493+-mi-/lhyyiu r qszo straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency oia11gc1;g :vhhl at h6f 11 Hz. The shorter one is 2.40 m long. How longhv;i6 a1 a 1ctgh:1ghl is the other?    m

Two loudspeakers are at opposite ends of jm 67h6y46qtd*iaarcg7l q. o a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he i hg cqlt j.6y7d6a7m4*qaori6s between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow l0l+ih)d9k;f. oe/ 3f+v f tdieu .blhin the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Ass9b+0/ )3 h +ih;fkl.tv o.ldilf eefduume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth k5lyjxpz:95o6;weiz at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The ba5x pol;z kezw96jy:i5 t emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approae9n+*q itx ql,ches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away canel q+x*n,t9qi 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) wash z+:(8ptyxc0w jpcl9qp+k8n once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns wln wcc+q j x+8tzp:p0k 8p9h(yere 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 combm ett);p :rh6promised 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 freq t; )b6hertm:puencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration,wxote4h6* cn-c0bcrr5lh * 6s called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound.br*-t wcc45e0rlh *h6s6 c oxn 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 of6 m;ro(osx wi5 o3vz9wlaz3wmvhx4;-4el )i t hearing for the human ear at a frequency of about 1000 Hz v346mosz r3olazmx)how9ix w4i;-5w ( lvte; 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 f)arxw sxvj 97q q+5h1at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes dire)rxfq+savq 9wh17x 5jctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1,8n.:l8ayfmmm2uw eg u) s z2k78bzwx5 $^{\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