What is the evidence that khrj5ssbi8(uy gie*b n (x: 9)sound travels as a wave?

What is the evidenceum(o(m s;n sf+p:lp:r that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to the;j:h zx.)gm(b.oykno(r nw g 2 bottoms of two paper cups. When the string is s(n r;hw..obokx(jyz 2gmg ): ntretched 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 expect the fr;wdz f5 sws0h12;wedhequency or wavelewwe;z h0d2s w1df5 ;shngth to change?

What evidence can you give that the speed of sound in air does nou7rka oz15jo4 b.-djxt depend significantly .bko5xu-4 a1 rdj7ozjon frequency?

The voice of a person whnrd6ads - 3afu9. t*nro has inhaled helium sounds very high-pitched. Why?

How will the air temperature iny9 0d6(wrivju+kztwnx )y-n, a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of2hl51 n zez(pm sounds in various frequency ranges. (An e m15(h2zlnezp xample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) . ;lmf .rlwz9)g7yejk. v rpw-spaced closer together as you move up the fingerb9rmle g.ljv7py)k..w zrfw; -oard toward the bridge?

A noisy truck approaches yo- y5rej8z oqi*3r;of zu from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffractioroyr* 8 - 5;qeofizjz3n.]

Standing waves can be said to be due to “interference x. f4m 1qw3o o6dkh9n5sn-jutin space,” whereas beats can be said to be due to “ioqjnhdu 59t3mfn1x kw-s6o. 4nterference in time.” Explain.

In Fig. 12–16, if the frequency of the+dp i 1d os(6y)ua+sqe speakers were lowered, would the points D and C (where destructivepi( +yus6do1aq +ed s) and constructive interference occur) move farther apart or closer together?

Traditional methods of protectingq8lg ou4cy*y2z ;z;zg the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relati q4c;zz 8ygyz o*l;2guvely 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 thou8)i3 ah/azsjc:nc; fcght of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, :3s;c/jza )fnc 8ahic(a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourc(gy;:g2dy8em4u6im qr un) afe and observer move in the same direction, with the same f8 iu: ;ym ad62n4uygr)( qmgevelocity? Explain.

If a wind is blowing, will this alter the frequency n*i ; zl,w kyub,(j0mzof the sound heard by a person at rest wiz in ,z(kwbmly;u,0j*th respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in my(7-i zguv7 cbotion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whisty 7vc(uzg7 i-ble? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout3 gl)rvq(wk 3.p-wkz p reflected by a cliff- .w(q rkz 3g3wlppv)k 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 hears thlj/n6x9 7gz urir: 7ixajc;/w e echo 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 seawate6z/ug7 :l i; 9njwarxxr/j7icr is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wah.)5au4 qa19mqv he dlvelengths 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 above a school of tuna on a foggy day. Wixbju 9hlnj60v/(l t4 lthout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) 4 (l0lltuj9 jvbnxh6/by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff.-pf8kei) zixfr4j1k4 The splash it makes when striking the water below is heard 3.5 s later. How high is the cli1j)r i-ifkk4xe4 pz8fff?    m

  A person, with his ear to the ground, sees acvfm qy..-x+t huge stone strike the concrete pavement. A moment later two sounds are hea+xqtcy f.v m.-rd from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one qxzh(*uq+) hbmile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (+ hz*)ubxhqq( a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sou* b1uvflecg10/ g vf(vnd 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 sn3r-d4 7k9vaiz-adzsound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro jj)of+h7/e3ieh7gc t duce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only on)/+fhi3 e7 7teo cjjghe is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain 0qj 2agfn1n(d distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captai(f qn10ajng2dn shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a c)4d o y9vl eouv2j7;hsignal-to-noise ratio of 58 dB, whereas for a CD plalhov;y u472 c9 evd)ojyer 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 powauv)y3o ) jlsa8e d3-q u8:oar 5wequ,er output of sound from a person speaking in normal conversation. Use Table 12–2. Assume th8uur oswoa)j5 a33v:,dl8e-qeq a) yue 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 stuq xuy:qm 21trat:q*p+f*s y4rikes 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 ratl a0c+.xr 7:ppfwyaa o r4-s/ted at 250 W, while the more modest 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 connexp7.o arty / sr0c4alpw-f+ :acted in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whe.x h(ew ( 9hricnmq;r5n placed 2.8 m in front of a louds5;e.h(w rnr9 (hcqxmipeaker 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 typeb; ui :c gsym4tsf l*;d;,*zvically detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levf,*y z;dvu: lmgi *s4sbc;et;els differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilh8 xi1:o c;mslz3xa7vl the intensity increase? Incre;a o: ci xzl8s7hxvm13ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but bd:rfa./ 0-utz nam r1t11lyyone has twice the frequency of the other. What is the ratio of theyr0a: f-malz 1rn.dtb11ut / yir intensities?   

  What would be the sound level (in dB) of a sou b-k f)lswfwv.go2pe,b1g+ t,nd wave in air that corresponds to .kfg,g slwt-bf2o+e1bw v,)pa displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wbzx4bcug k,n/ la,1,rhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See/zgcnk url, 4bxa1, ,b Fig. 12–6.)    dB

What are the lowest and highest frequencies that78 pk;z c9joy ;ul5lxksx ,u5 8tc8qiu an ear can detect when the sound level is 30 dB? (See o, 88ujk7;uzt58xipk9;l y xqc5ucsl Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whalzg)4;hdfs51th (ca 4pw(vru t is the ratio of highest to lowest intensit(w;zv 4s r1cf(u45l pgth )dahy 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 lengh1gp ;3i5fauws od1 fk(yee5 6th of the vibrating portion is 32 cm, and ewe3gf 1;pdak5(1h5suifoy6 it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three dr nk y0iyyjf. ra;i1v/jb)5i*uvg :; audible overtones if theyb gv ujdr.)5j;*/fi kyvy0niri ;1a: 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 freey5omx+(o 9rk quency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube?+ormyk 59oe(x    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ withf03 wsc.rz nw5 open-tube pipes spanning the range of humn 3. r0zcww5fsan 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 thinuq 2i yqfj(p1 v(j.*wny5sb.rd harmonic. What will be its fundamental frequency if it is fingered ap (.ysq yjnn2(q1f*bu .5 wijvt a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 mik2r/**uo rw m long and is tuned to play E above middle C (330 Hz). / or*i r2uwk*m
(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 emi6njla4 4)f pvif9l7q yts middle C (262 Hz) when the temperature 9l)qa7l4v4pyjn6 iff 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 2ls z2+pp :86vrui q*dz0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of tkp:+g* pp6ut lz4atu*he flute in Example 12–10 should the hole be that must be g l z*apppt6 u*tu:4+kuncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can rejth.) de/3gqvirhf214d hwe6:c zw -s :,okxusonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies cw2.xd164e i:3 hoh-uswe q/v:hrj ),tgz kfdin 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 resoqzrlp0u9zj 0 v /hd1t5t2 *pmznates at two successive harmonics of frequencies 275 Hz an1rt90p2z/ l5dpz0mzuvtj hq* d 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 yddv5t 2:q b+g1dogw -$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-l16 s.kghh o*ok* f te+sm(eizjax4.l,ong organ pipe athx1 ,k+a.je l* 64oozk*m(s.ehstigf 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 and 4qki 1 z9*tzmfp58vpj0-vj jhis closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to th 0 1zfzj8 jv45ikthj-mpvq9p*e information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every0 (ee52w(b4bsilnn hl 2.0 s when trying to adjust two strings, one of which isil0e (b2(ne wbh5s4l n sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequfu9 yccgw/wz05o 2mq 1ency 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 ate 5gspq955 occ;z1fpwtan q.3 23.5 kHz, while another (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, estimq1pfw 3cc t 5n e.a9gzsq5o5;pate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sound:k- ( dtw7 hvgpn9/er xkd(d4sed with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What -dvn s(dg h(/r w97:4ptdxkkeis the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one ss3:2 mi rt7msstring is then decreased by 2.0%. What will be the beat frequency heard when :ssm7s3 imtr2the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if tryp)gcd+gg b9z-)kqkg x;s:h, 17myqwo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othezyg,)hqc-mkg;k)gpgx: by 9 1q dr +7sr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fr fduh8n s+;a.2jpt)nx0i hfs+equency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencieshsns t n;+j+d2 h.u8fiafx)0 p 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 :y (u4br fyez,e fwp3 +z+ymh7apart. A person stands 3.00 m from one speaker and 3.50 m from the othzm3ry,wf(eyyf7+ z up:hb4 e+er.
(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 vibrat 8h )tbrwoi8+*0qlxuxing 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 frequenchtb8ouwx8* lx+rq)0 iy 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 nemmgaw, /ts cef1h;5n/)pw(of wavelengths 2.64 m and 2.76 m in air. How many beats per sec, wm cs/f5h)1nwnegm/a (tp e;ond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque mztk:;xno,(. 2gm cnyncy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detecc:tx2 k;goynm .z, m(nt 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 y9/mxlda x)(9 bf w-m0rbgyo(i 1 wf+tyou detect if a fire engine whose siren emits at 1550) tx9g/ yylwb 0-w1f ((d+bxrom9a mif Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frem): slojf +0rbquency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two +rsb o m:j0)flfrequencies 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 hofs7 tf5ww5x q*rn. When one is at rest and the otherwq fs5wx5 *t7f 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound 9cc2r :cbuf5 ewaves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the r2c:ur e59bfcceceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits :nbb p1+em 8v 2czr:xpvu2ac m10c*ysan ultrasonic sound wave with frequency 30.0 kHz. What frequency21v+8cbny0pv s c2zr :ma:e x*1pcbmu does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expern-pj4dj 5 9x3 jijv2bhadq*-liments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat freqa x32 jjd- hj vjnbdq9li-5*p4uency 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 speeds. Supposm5uz( o v3d 9uga++0kb d.eakue the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s za mdu5oda.3 kge9 0+ukv(bu+What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using uiwu-vju f 72.nltrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits souzwk6 gf15hhwd8 1cej 0nd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, 1kj 6 8weh0gfh5cwd1z what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if jr kv 2(k;1s,zeeacm)m7 1ocwits speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed ze 0 pt5m2-ndh303 5xoi vdnrsrh n:a*of sound is 310 m/s (a) What is to3:nmv25ix0p- z 3har hsn*e0 d5d nrthe angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the tj-ko3w 2pmi3p cc) 4bxhin atmosphere of a planet where the speed of sound is only abouip-cmjb2kp) o34x3 cw t 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 8500tmygz g:,a+7 tr,dj .lv 0p:opmv2aq.aa(fd / m/s strikes the ocean. Determine the shock wave angle it producesdmv grtva.m7az ay:j 2d p,lg/:t0 .qp,+ofa(
(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 o4 kzfyf7vt12$/theta$ 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 1xdm h u2,nnmg vje3p8vara8 y-9: mr9 tat./*s.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the srnr3eg jmu8a: ma,/t 2xd9.9natvp* m8y hv-plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar defx3g9k+gh zaxlh9pkfttvy f)1/ q:. f m+jp( 3vice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is tlvh9kj3f pgykx(fpf)f9+tq hz3/g.a:txm 1 + he minimum time between pulses (in fresh water)?    s

  Approximately how many octaves arthvs 6 fa*7yojw3;q+ 2sol n(ge there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewerk dbvp e:177 7z33jxmedx c8wz pipe symphony. It consists of many plastic pipes of various lengths, which are open on bd7:e1 d8vpeb z3wjk 7mxz7cx3oth 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 ) 1ifesy7-j4(t jix1pigu cg*the threshold of human hearing (0 dB). icsxjig17p t-i * )gf4eu (1jyWhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sop v(20kzk6bjflof ,rc,-ot- rund and an 87-dB sound are heard simultaneously? l k 2(o jkr,c -6b,r-of0vftpz   dB

  The sound level 12.0 m from a liedz/rd6b ot h g5 qswmq3k1uz5 a/(+1oudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions? s5qw/h/z+r13da(5 1ugm zt 6bkioedq    W

  A stereo amplifier is rateepph1t 8+8id os-s )rmd at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in w18r)homp sts ei8+pd- atts at 15 kHz?    dB

  Workers around jet aircraft typically wear pro(oc,hd eq n)3wtective 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 i noc (h)d,eqw3ntercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communication)sw6 alji ubhgva )6-lb/ qr5rj,4r5zs systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is t*c -,dnwx sjc,uned to 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 poi1o 6j g4xpnha 3zg-zq 1*:jrp/:mafi pnts with a fundamental frequency of 440 Hz and a -gha p f1:*z4zjp1ir mnpq3 joga/x:6mass per 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 o pzn2 b5g39vlkx 5g3t(leq qabb+ g87tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air ib 3l8gq27gx epo+kvn5lbg5(zb9at 3qn 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 tu h;lurm) fbm)dc+u7 (gbe that is open at one end and also 75 cm long. How much tension should be(+ubrmcd gml)u7)h f ; 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 wa etsnez81lf/ 1s observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz rang tmjyk:nob, pn+)qs-u* u -j;f -ug.zbe coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a pk+ zgnyu,jbnq-uoj.f;* : m- u-p b)stoint 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 tra,u ty.ab8:v dnin is stationary. The conductor on the stationary trai tu8:ydv,.nb an 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.oi js8p atfa0cqacia 3.1.8t( After it passes you, its frequency is measured as 486 Hz. How fast was thea cto 1q3s.ijfc. a(ai8pt8a0 train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeniv (j.2xn lb8elng to the difference lvnxj.2e 8( blin 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 straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency z3 uo so855fl cgen-gvv(.he8 of 11 Hz. The shorter one is 35e osug (5 h lz88vnefcvo.-g2.40 m long. How long is the other?    m

Two loudspeakers are at-.hemx9u 0h7q b.tjrt opposite ends of 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 is between the speakers, at B, and (c) he hears the speaker 7mxt br9.q-.e hjuth0s after they have passed him, at C?

  If the velocity of blood flow in thy,)6 kd2 ib2/lo9-h3ts xc8lors rpf re aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directlo2 soc2rdf hs),8 xt3/r6lipyb k-9red along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whi.*odnsazna 4m57wsw vi. z(vo56ee/ cle the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 5n/a .*deswiweo.zz7 565n4 caos(vvm 1.35 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 ut 023 jio ,:ydzcgin9.zrd6rof high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 msud9z3j :2r. i 0c6ntgodz,yir apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) waapu5,bl 1f+n .sh,g ias once used to send signals from one Alpine village to another. Since lower frequency sounds are less gus+51, f na ih,p.lbasusceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereotbwa7b ) p++c*:b lmal listening can be compromised by the presence of standing waves, which can cause acoustic “dead spot c+7*aml pb+)wl:tbabs” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slevi9;y:io yi:i 2t axd2nder aluminum rod held in the hand near the rod’s midpv i:a9 idi 2yi2tyo;x:oint. 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 frequency o)m/m z.u.tzp af about 10ma u .mt/)z.zp00 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. Anv7r*hn6 rpr 1c observer on the ground hears the sonic boom 1.5 min after the plane passes directlyr1hnr7 *rc6pv overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb0i ry +htds:jjlv1(6j w83qv jfahsi6q7*c6p oat is 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