What is the evidence that sound travels a/b78lh;q9f ae,pyn kps a wave?

What is the evidence that sound is a form of 5zblij i3 mjlrbw+5om q*7 v:82u bp3denergy?

Children sometimes play with a homemade “tele , sfa*0aocvkzc .v5fn1v.xr.r 4wxn(phone” 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 t0 nvco.an v4zrv k.(x a5f. c*x,s1rwfravels from one cup to the other.

When a sound wave passes from air into water, do you expect the fri1o,g-veof h 1jy45tqequency or wavele-qo tv 1gjh1y4,oi f5ength to change?

What evidence can you give that the speed of sound in air does hrl w2y8le. byi+6 dfrve k rgl;81(uj*p:h 3xnot depend significantly on fepbvh3wlx :y1gk2h68ijer( llr fu*y+d r8;.requency?

The voice of a person who has inhaled helium sopd 3if jn1:gz6unds very high-pitched. Why?

How will the air temperature in a roox pnky: hlale4+a7 o4suk(-2dm affect the pitch of organ pipes?

Explain how a tube might bebs:zfi d071 2xf gyz4p used as a filter to reduce the amplitude of sounds in various frequency rag xzbf:2fy14zpd s7i0 nges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethy- *t4n9;lbc 5mnjcbper as you move up the finge; lc*nbnb95- t4jypmc rboard toward the bridge?

A noisy truck approaches you from behind a building. Initia itl7n(+ld2p1hz:dfk lly you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brightzpnd2+ t7lk(fh :idl1er” — 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 “interference3dyw ad1w7 n*u in space,” whereas beats can be uw3yw7* ndd1a said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would tkeu-em7(x d udc(z/npixc)a01n1+ hm6dc 7i whe points D and C (where destructive and const7)udmxc6 an ec im/01cip(+wn(d x17k zeh u-dructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wi k,op y,uiqudhz8 1r;mj6, y5dth very high noise levels have consisted mainly of efforts to block o rdd,jo56;18 khuuy, zi pq,myr 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. s9xjcn;.e9oi 12–31. Each wave can be thought of as a superposition of two sound waves with slightly diff9.ei9oj x ;ncserent 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 shito;h;rh jlvr 5*t-8 bg *kc+dgft if the source and observer move in the same direction, w jb k*t-h *rtvo+58lchgdr;;gith the same velocity? Explain.

If a wind is blowing, will this alter the f1*y azx vb6*c:hrxbst. nh4 5lrequency of the sound heard by a pers4vtb cl r. *baszxh6x1n:5y*hon at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A m .bnxaj n;137dp 4pwhyonitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear yd47npjx1haw;p .bn 3the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by l l px1ep:caq++istening for the echo of her shout reflected by a cliff at the far end of the lake.p+a1+qec lx p: 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 thopx)8a*xy)ap ns5k*jwbz9z d wl).npq( 6v -se waterline. He hears the 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 seawater is wpaqp-8x9b5pz.)v *o( nwssz j6nyld) xak )*1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthq m*gp f7/0j/d x*nn 5/4tsuphny+iebs 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 aoouyxi ,.r* 7,fwd20dq3ggfy6i4+t f. butnz school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33)rxy,g+yqog,7.20 udiwf d.ftf t* ib6o3un4z. 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 sp1ytr8u wlnvi yt*n g)/f 1i(-llash it makes when striking the n)gtln*irv-(f8/1 wyuy1 l ti water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hunakmh dv 1ugul;i07d (f /h).lge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and thedi/ ) h au;h17gml.0(ldvknfu 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 milufhflwb0 z rn8.+ 0lr554xc)k/qmz txe of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a)x/uq r5zm 85l.z+ fk0x0 cfth 4rnlb)w 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofe:fsey apk 5**ps-xa / a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intenr7u*gq8 tgdb iwi9.b( sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultan zvnutom8s.* q- r+(dbeously at a certain place, what will be the sound level if only one is exploded? [Hint: Adms rqo8.z+u(v* tn-dbd intensities, not dB’s.]    dB

  A person standing a certain distance fr ydufzi27c1g7f70 v 58hnuoem om an airplane with four equally noisy jet engines is experiencing a sound level border 58fv0gf 1hm cidu727eouyn7zing 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 sai tjrub/n o6uyd 27fv7.wvpl5 )d to have a signal-to-noise ratio of 58 dB, whereas for a CD player it/)vwb6 tvfu upnr2 .old7y7j5 is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conv46 ggh(uok 9zmersation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphku6m(oz94 g hgere 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 i:zm4wk,cn7 e2*d )tob psrn9.ka ci 6zs $5 \times10^{ -5} m^2$ (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, whileyaw2l p3,2tci the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in dep awc,l ity322cibels 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 registered 130 d9 disno: (fi(jB when placed 2.8 m in front of a loudspeaker on the stao 9d i((jsifn:ge.
(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 le 1ak70 t1x-xrbnct9smg xn o:, j8eg-dvel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Se ag:gj x08ns- 1tcbxnxom-9rd 7, e1ktction 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (ar+tn.t db t6fp)*itw yc)gj1:) by what factor will the intensity inc 1j ).f*+btiwtr6cgp:td) n tyrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amp 9/b0zhdvf fxk5x; l5dlitudes, but one has twice the frequency of the other. What is thekfhdxf5zxv0b/5 d ;l9 ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponk0l :yaa:4 jpfds to a displacem:jkfla4p :a y0ent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sewh(dj : :;jxyyq htj+ -xp/mp3em as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 1t(pj+wh3qm-p jdj ::xhy xy /;2–6.)    dB

What are the lowest and highest frequencies that an ear ca icl- g)cc n+eyv k4;yr4k)l+hn detect when the sound level is 30 dB? (See Fig. 12–6.)ch;ckgi)llev )-+ y 4cr kyn+4

  Your auditory system can accommodate a huge range of sound levels. What i5 i.kym.mwi 3qs the ratio of highest mk.qiy . 3mi5wto lowest intensity 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 (jf0ikt,v k a:of the vibrating portion is ft:va,0jkk( i 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 lon cltv+k-+i4g4 vx2pm ng. What are the fundamental and first three audible overtones im xt lvp+4gki+-n24c vf the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from4 k qjcych42g8 blowing across the top of an empty soda bottle that is 18 cm deep, if kycqhcj428 4gyou 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 spanning the r:cnt, /zfx;bh .r:y l -g3nizrange of human hearing (20 Hz t 3ncb ;:tr z.hnfz-,/il :rxgyo 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 strin.tbls;p2 mzg2g has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it2 b2m g;t.pzsl is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above0xh0nla6r x -k-2iteu middle C en6a-k00 r2-xlh uxti (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middl 3 dqvm)q*hjo((koc/ ue C (262 Hz) when the temperature iod(ov(c)u*qmj /qh k3s 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 20tw8c+ red g: /cv3ej:a $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examde:d/o dk1y/aei248l.e1uif dtv- t dple 12–10 should the hole be that must be unot.add -y:u/vt/k1 4 di1l de2eefdi8covered 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 pih8oqc dc*g17n pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenciesc*h7ncdq 1 8go 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 botho cy/gqic;75h d8e;o4 qzd, hm ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What 57;qg4mddz,;h/y cie qch8oo 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 oj9k1aq 5tits* 244dhkmi tn k+h /q,n$^{\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 for4qkqu:i( 15 .k*msryobrpaw 4 a 2.14-m-long organ pipe akaq1kqw5:u sb4y* ( p.r ri4omt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is ap c drd4vwh+*d./hfjc) proximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. Wh/c w4jd*c.r)+vdf hd hat 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 ever f+:wgcm-,17edpko ozy 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string?kwd-me7zop :c+gf1o, ±    Hz

  What is the beat frequency if middle C (26 ftag c.hm+py85 y1j-n2 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 operat gk8yqu ai(jj mtj ,9c4nm6/7ses at 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 nk 9ytjmu ,gs/6ji7(aj8qc 4m they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produ,0 im+ w6rqku,/pdoarpei+ -r ces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explai+wik e6 puq/rd r, i-oa+0mp,rn your reasoning.    Hz

  Two violin strings are tuned to the g-d tq k:lbgmg2/xz/y l/50znsame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playegdb lg2 l0/zmy5q/ znt:/-xk gd together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mfoyy1y6r3dkznha l3c1xv5;cj )+1r ziddle C (262 Hz), but one is at 5.0°C and the othcf1 r6v oanxr13hz1;5yj zk +)3ydcyl er at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; wh 0 ywcn0 c2wnjzybdg(wz)2;6m*agof)y*x7uien 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 wdg6nw jmz*)0if*yb0 (;72a yuy czw oxgc)2 nHz. 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 apahbj 6stc0 /b s2hcu.-yrt. A person stands 3.00 m from one speaker and 3.50 m ht2ccbs 6-0 ubh y/.sjfrom 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 suppo 3fp:k+7k o2 ui7u3k::ndnhjc.p hwy qsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what muspn3hh:+di3o:q : 2.nkkju7 cwypk7fu t be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. ,vm gfz,gf-u 6How many beats per second will be hea6fv -gzfg,m,u rd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz e;3q j mdwqglr+sk62) when at rest. What frequency do jmwe; 3)2+sd qrgl6kqyou 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 ifle,27wdca n* d a fire engine whose siren emits at2,ceal 7wndd* 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towar+g nagovebkk;l ;t73e 7)u,jh d you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sam7, gelovu)j ke;kt 3a7g+bh n;e? 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 frequenm (y2)5xy(ooxdjs:fw cy 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 hy(()xf m d:oysx5wjo2orns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sx7ahvv)m4 r8 w q+ri6sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 rirh m4aq8svv+6w7x)m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5mgz21o;gzy 8q4 u) y-zagf6og m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in th oz16 z8y)gyg -4ou;af qgz2gme reflected wave?    $ \times10^{4}$ Hz

  In one of the originaa.ttjvq+8k21h +z tmkl Doppler experiments, 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 freque8zkt 2q +1mtj+at v.khncy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ult 85ptnc-t+qtjwkrd je/a:. /f rasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing i: n. tc8wk/-5rptjdajt/qe +fn large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ult57wcvhl;brn v h5*)w jrasonic 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 sound of frequency 570 Hz. When the84u)dk n ut. 08qjfqq4oqtv 9y wind velocity is 12 m/s from the north, what frequency will observers hear who are locatedt 4)ojun0ykqfu vt9d 8q8q 4q., at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speeh9emu* :qdd-q.c o. e8iwv5 /7r b;hnmw0erur d at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of:hr*0q. ewfkv sound is 310 m/s (a) What is the angle ev qf0kw*r.:hthe 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 thin atmosphere of a planet wzr p kg ; *ee3v:qf*ghxc+eh:)here the speed of sound is ocr e*hg; z3kg:f:phe * e+)vqxnly 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 oc i3dkp syp-/b7ean. Determine the shock wave angle it produces3p k y7pisbd-/
(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 bxu:l0p;x ;t/b,aa 5gwwws /f$/theta$ 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 kg.-c w5lv xj2lm above the ground flying faster than the speed of sound. By thejx5 g2 lv.wlc- time you hear the sonic boom, the 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 device that sends 20,000-Hz sound pu lpj-zh /meufoo.pm5kdkio4f gx:5* :v16:e jlses downward from the bottom of toege4mlx-h / .56z1f:m oj:i* kdk:fup jovp5he boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves aru(xx ( x1xv+ftod )ux0e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It co392ly2zc(l (bgof6ole .hoxw nsists of many px.lzo2b2 o l6 39eol((gwyhcf lastic 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./wen2yv6,u-j jls(obmw 2,q x0 m from a person makes a sound close to the threshold of human,yojj6x (u-w,q l em2n2 bv/sw hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB n 0ivnvkj(3n0 1nv8toomtq+ 6sound are heartnqtmo 8v n+vv(0nj1 603inokd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What x8;io ukdu8f ;is the acoustic power; ud ifoku88x; output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropb08o1 e,erbe cs by 10 dB at 15 kHz.81obrc 0 bee,e What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.q t9 )*qbs(h d3b) jrkpgsv)1b Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dbb stgbp 9h kq)1)j(sqv3*rd)B, 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, th 1aw4:(fwhge me gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fu *12w (.b wteqlk/xjdzi o0,jrequency 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 betwn:6wxhr kvs,7 een fixed points with a fundamental frequency of 440 Hz and a mass per unit le h,r:7kxsn6wv ngth 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 verticallj* 82uq(;ae rp0azjok ,3gqe open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning a8p a gj(kquz e,r3j0o*q;l e2fork 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 open at one eozdhtw/yg,m t vg ,092nd and also 75 cm long. How much tension should be in the string if it is to produce resonance z,,tt9hvg/d0 gwym o2(in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obser 5/ b5hyaunah51.ba ayved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sbv(.0n8j :u hfd sbdy)ources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about an:d(j f8 dsvyn)h b0ub.d 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 whis w)i rm0)u,xyq 0l,ppvtles. One train is stationary. The conductor on the stationary tral)0 pxpv,i0u, ymrqw) in 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 whist:7 :acus jx;zile as it approaches you is 538 Hz. After it passes you, its frequxsci:;j :a uz7ency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimaoti; -, 6h8c,j w ofxqj3s; vwxiw*d+jte 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 the straighox q ww,fd,jj +* ;v;i-wcs 68ito3jhxtaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, o q 99n6h/cn)x /wguap xqmm7oeg*.4f produce a beat frequency of 11 Hz. The shorter one is 2.40 m lfen.ha 9)4mo gmno9c/6q x7/w*xpqguong. How long is the other?    m

Two loudspeakers are at opposite ends of osp7qix x 7tw4f/ 5kt iy*k:x(a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identicxkx p :iowki47xq* /s5(t7f ytal sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow iinmxh4 *0dwf2nxba : 6n 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 reflected2xh n afmwn:6 4xbd0i* 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 moth3uy-x-gv6 liw at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wa- 6v 3w-xyguilve reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth.t6l7o.p*ry cf The pulses are approximately 70.0 ms ap7p6 lfct o.yr*art, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpingu:cw. o 6dysu6aty7 m7c,s3fe village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is.yaousmct :6 7udyf , ws673gc 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 gd 9bd-,omdo- the presence of standing waves, which can cause acoustic “dead spots” at the locations of g9oo-dmb d,d -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, v;hokt4 jpc 4k -l*vd8ej8azr*sx8p/called “singing rods,” involves a long, slender aluminum rod held in the hand nealaesck4todv 84-/vpk r pzj* 8jx8 *;hr the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for th 8uv0n3o)y i9it*h/m ykxp -j8qeh;sbe human ear at a frequency of about s /yt)mqp-hexvh 8jbo98n *k yuii 03;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 2.0nfinipl;a:2 z;;ov w1 . An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitudfan2o ;1ipln;vw i; z:e?    $ \times10^{4 }$ m

  The wake of a speedboat5x7c u (m*u gfa,-rwkr 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