What is the evidence that sound travels as a wave?y 5jkmhc6pp/ bg,2ihu+ 0az63 g;yngy

What is the evidence that 4 ;rczx7pyq sk( iw:(esound is a form of energy?

Children sometimes play with a homemade “telephone” by a6ff5c8n+u l )ix ;2 32uz5kr sspmcem;xjnv9xttaching 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 soucn2l;5snujrmc;xp 9 m2sf8 3 zf i+xk6xv5e)und wave travels from one cup to the other.

When a sound wave pas.lq pl0)l5oh jses from air into water, do you expect the frequency or wavl05o jl.lq) hpelength to change?

What evidence can youm vjk43:x;xqg give that the speed of sound in air does not depend significantly on frequ;4g x m3jk:vqxency?

The voice of a person (l lxxyx4tzc-.9-e dkv0s 2ufwho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a ro9 tvyq;bv;.hj7rdam b 1 xt29lom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reducjrw(q9 36mlwb )upu )xe the amplitude of sounds in various frequency ranges.ul w xjpm(qu6) 9)br3w (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spzmf p4i)wfy8pe+(r 5gths/0naced closer together as you move up the fingerboard towar5 8 0mz f4pstf(reng)y/p+h iwd the bridge?

A noisy truck approaches you from behind a building. Initially you hear 3 oj vgfc;t6 l0o(*oidwj-6y pit but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — youj 6y-covd03(*tpo f ilg wo;j6 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 space,” whereas beats c5 ;i0wu6mhzm ran be said to be due to “interf5mriu6m zh0;w erence in time.” Explain.

In Fig. 12–16, if the frequency of thclm.qnj 9w1:me speakers were lowered, would the points D and C (where destructive and constructive interference occurmcqj1l: 9nmw.) move farther apart or closer together?

Traditional methods of protecti oqvp1b6;thf* ng 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 relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it elec fqoh v61tb;*ptronically, 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 Fipkb3hi bv -mv3 ri.9l)g. 12–31. Each wave can be thought of as 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 component frequencies farther apart? Explv 3vibmpb-i .3r)k 9lhain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direkuvwq+pff xf: zq; -;9ction, with the same velocitqw+f qvk ;f-p:fzu9x;y? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bl/x/f 4aj ze4by a person at rest wex4az /b/4f jlith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swiw*)j/i+ . sthg/op5zllalzs* z9 kop8ng. A monitor is blowing a whistle in front of the child on lpjizl**a psw)glst8 /hz z./o5 9 +kothe ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenivyeta;s 9v y *es.7/khng for the echo of her shout reflected by a cliff at the far end of the lake. She hey.tk ysv79e;shv a*/ ears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his sh37mp 2pd / 5vvzfd n;vofz9bo;z sz,w/ip just below the waterline. He hears the echo of the sound refv /2zvmo 3z/z5z9pnov d;f pfd,ws7;blected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a 9vhupd(ov:p9 mu,e( bt 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.)is;wv5a/ vh d Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–dh v ;iw5)sav/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 h i*ir t;ca*vbw.kkwnt )4lkr.u,a)8 the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the c),.4ktlitv* . w*urkk a)hb w icra;8nliff?    m

  A person, with his ear to the ground, sees a++;mjo2p)g(j/b df/jfb asny y4 6uag huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far amj;/nbb o gs6 + /+d2)pfay(fgyjjua4way did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error ch3d* g+akz; lcrg+x2made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the tempeh+k2+gr g3zdc a* xc;lrature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sols;0 r vmg-llu.h jw7.fvy:2iund 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 intens44,g jwfc7 5o*-oipe)g illikity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produ-jtla0 ky4/yz ce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sok 0t-lz/ayy4j und level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an+3vwvm sk-- 6 /jyuggn airplane with four equally noisy jet engines is experiencing a sound level bordering onw-+ y3m/n-g vjsvu6k g 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-tk1 2(wnu qnjv8o-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each de21 n n(jv8uqwkvice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal converwbovyo +03 p1+mukxx4y /dmp :sationxb+kmx/ +v m3p1: yy04odoupw. Use Table 12–2. Assume the 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 ss,kbuy q3 -zf(trikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W0/bw (zstd2s66 dcz cd, while the more modest amplifier B is rated at 40 z ts0w2zb6d/s( 6cdc dW. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frongan,1 +w,u ,tf-t xeegt of a loudspeaker on the stagt+wf1e, ntu,,-aegg xe.
(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 level of 20igom p1 ho ka,u, *dy,b2wts4.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section otp s4*y,m adw g0kh2,,i1o bu11–9.]$\approx$   

  If the amplitude of a sound waysd-9mdb9 q(nk/ ppt)c:vc 1y ve is tripled, (a) by what factor will the intensity increase? Increa k9tpynd)m-( y dp:9b1/qvcs cse by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudx* l;;z 7aokuces, but one has twice the frequency of the other. What is the ratio of their inten;7ok *zaxc u;lsities?   

  What would be the souzg y l;11keuubj.m*-qnd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of viby ;gz. b1leu-mu1k* qjrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what86l6sy*sk hig l5d; qnxx2i*(o 0haxd sound level to seem as loud as a 100-Hz tone that has6yhld sd lioh2ixgq5kn **6axs ;8 0(x a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest a +,xz;v9 nutv4a foq,hc yul/(nd highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 9ah,,/tvu4 +fyo v(lcn; uxqz12–6.)

  Your auditory system can accommodate a huge range of e9qoqwp g( rbs+-n0,jsound levels. What is the ratio of highest tow +josb-9p, gq(0 qren 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 hae,oo qg0l+sw)xt 66w;1 l rxkms-b g*is a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensionxtim0 so 6rkx,wewoqlg +g*1l-) s6;b must the string be placed?    N

  An organ pipe is 112 cm lonc3zb4 bw xz a9cend5+4g. What are the fundamental and first three audible overtoneex4n9 bz4cd+acw5b 3z s if 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 from blowing across the ton y95-q m *6thxo9m8v:qyd jitp of an empty soda bottle that is 18 cm deep, if you assumed ittydnmq 659jhxom-t y9i q v*:8 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 openzee7hv*8 d fsy)8 pgb49na9ss-tube pipes spanning the range of human hearing (20 hy9a8fnp se )7*se84 bd s9gzvHz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What wille/5,7h9x 2eqg ubzwf;g9b xoo5 + o)e*mquzdy be its fundamental frequency if it is fingered at a length of only 60% of itsb +zzguef9do gxo52m 7oew9q e)5h *q/;, bxyu original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abov;kq/k1 q689+uhufad buu x3wv e middle C (330 Hz).v/kf u ad6k1;qhuu98uw q3b +x
(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 alrmb u5 r,j9k2n open organ pipe that emits middle C (262 Hz) when thmrr5ub,l 9 jk2e temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at b 1ghj1lw l)iw;/gkc-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 shouldoua(py fzg* ,d+p1s0q0mc6 x n the hole be that must be uncoverscyu a,gfdo+ pn1 0xpmq6 z0(*ed 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 hbbj)pg2ws8 *w4+ ofc resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thip)24jwb h gb+*o s8fcws 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 b g. a6tu x9yl q9y2sipfn6)b*1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies*gf 69ba)pbqs6 9ny l .u2tiyx 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 /x lt;i0(c/nmy abpk)$^{\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 audihg4,kxr7 6oul ble range for a 2.14-m-long organ pipeol4, 6r xg7hku at 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 tev xd* jm-xlayqyyw*0 q )y.2e;gt.8mhe 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. What is the relationship of your answer jem ymqa.lqywd - exv8g)yy;x**.t 20 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 az q+5vpuvj)qn10d nm.djust two strings, one of which is sounding 440 Hz. How far off in fr qjzu0nv)p1 md. +v5nqequency is the other string? ±    Hz

  What is the beat frequq*1xoa,,hdtl)uydi) ency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brasjitg - 8pb/y2.onqg1 nd 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 simulta8ntq1i.p 2 -o/sgbyj gneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wittvar /8lg 3xsc25s 0fnh a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is thvscfagltx 53n r/s028e vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tu4 8u; m6kqkuus sx8j+gned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0xkmug8+ u 8q;s4jusk6 %. What will be the 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 th+ryi ;iax 7,oo lut7)o play middle C (262 Hz), but one is7x,a li7hoi yru+)t; o at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks0 c3+/vmp pvxd4;xovq, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are t/ qo vvc3 x0p4md+;vpxhe 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 nfup0*44vxv dhri/(gk yy+t1 erson stands 3.00 m from one speaker and 3.50gr d+np1y4k *yh/vxi4tuv( f 0 m from 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 vibratingw lwc6gq* f*;r04.iu*pk byhh at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (ayihk flbw0* . p;rwcqu*6*h g4) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats pe omj0id, g-7uw2s*mhar second wiiomu dm -w27hgs0*a,jll be heard? (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 when at e1hqkc(gdy, * rest. What frequency do you detect if you move with a speed of 30 m/s ( 1cq,he gky*d
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wt,3k9;s*avc8 m qze 7l8dji lfj(3rq rhat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s c,j83 rr kd(9l mq3s;zqae ti j87v*fl
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-ux *)v/eqo/jcj +w;poHz source is moving toward you at 15 m/s versus you moving t q xv cjo/pu*;+ew)/ojoward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequencymtx61er;s sp. 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 horn ;mssetr6.1p xs emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives th 533 yt6kdfuqae ,/klbl*c9w ri sk,2bd;bh)qem returned from an object moving directly away from it at 25 mlf2 )etbksq b3b*,hu;wy3d,k ia/clq95 rk6d/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 flies, the bat emitsu l4d0bi1ka: y an ultrasonic sound wave with frequ: 41ia0duklyb ency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler e;95y 1g wtsfkfxperiments, 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 frequency was heardyf k f95;1swtg if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasounw+kt ( x,szx1nd 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 in large leg arteries at 2 cm/s directlyz s+1xk,nt( xw away from the sound source?   Hz

  The Doppler effect usin 8rg9*tx kv,jxg ultrasonic 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 emit3o 0tsa 9fgsf4s sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rfsa9o3g4 0stf est,
(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 i:.+8h2s-a;n o;popc ju x3glleu d0fif 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 tseg;w, ovr 5)i;9cjo jhe speed of sound is 310 m/s (a) What is the angle the se,;oj)viswrg j 5o;9chock 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 thiwbqfq2 .8f/n j/pa+bklcge0we)z4q nt5k; a( n atmosphere of a planet where the speed of sound is kkg4z 8/p.;/0+e2tq) j wbq ebafnfqnaw 5c(l only 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//sfr hy24ej : m6lrzc0s strikes the ocean. Determine the shock wave angle it produle6r 4:m0hz yr /cfsj2ces
(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 0,. :bh*oanju fw wrk+$/theta$ 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 exry 4m i) olyu28r9wj .am/us-zey2ss7 actly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane ha)ry 8s- iua2r.9o4s 27 mmeszluwy jy/s 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 devicenzj2* yz z4wr6 that sends 20,000-Hz sound pulses downward from the bottom of the boat n4z*6rz w2zyj, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible radahsfjp7x81v6g.gy h2 v1q j4nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer piy/rq.,h s pk:nt8twp 1pe symphony. It consists of many plastic pipes of vyp1/ nksq8w:h .,ttp rarious lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thre0sr+4cnd u 0 pyk 2 mqz060ut4g;hoy i+/zqyabshold of human hearing (0 dB). What will be the souqp4thd q/4s;ygb0muo 2+yrzuz 0+y0an0 6 kicnd level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound em e+w ly8qby 1r8 glnd(,g3.land an 87-dB sound are heard simultanegd8.bg,re el+nlq8l1w3ym y (ously?    dB

  The sound level 12.0 m from a 3+;o0gzoo zmi 4gkyy;1t/n,ax y4fc vloudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radi kta0zyx3 fcgg ;/4i+;y, noo14omvyzates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dr7(rb gv-s apvr9:b 4ruops by 10 dB at 15 kHz. What is the powea: srg 4vvb(rp97br-ur output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivesc.m 3gj4n4tord ss. 4 rwr00b devices over their ears. Assume that the sound level of a jet airplane engiomcsg4n dr04sw.s .3 r4r0tbjne, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systp v26b9nsjs yzt5;f6ysv:9o mems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to(dpm1ytbbx+zbd-3g mr 2 vd:2 a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wpurpo 4sm .g sc) /l.vk 0ks(x6m8el9xith a fundamental fsupvemk0xcls x8m.sr6ok9(g4l /.p )requency of 440 Hz and a mass 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 vertvo6 ot wm:-p2tical 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 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 tunin pott2- w6:vmog fork?   Hz

  A 75-cm-long guitar string of mass 2.9n oo yp-xv6 4d*,ufte.6e)gv zrbs/y 10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (iyysv9d re6x )4 ,tv6/ bno.z*p-ugofen its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was zjq-kjuw,e5,y, l 9 qiobserved 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 5hem ;x,y0qf8vws59 jvs1o b-r00–1000-Hz range coming from two sources. The sound is loudwo;jq81v fhe0 xr 9,m-ss vy5best 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 point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statv 5v0 nfx+. ws,mmq4uqq ..gdqionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What q+,fs g4. wqmxu .0.dvqvmqn5 is the speed of the moving train?   m/s

  The frequency of a steam train-c:1gp f mux qw(zleixa*b5/ 3 whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume lz-*ebgixf1 5cx:w(/ qp u3ma constant velocity)?    m/s

  At a race track, you can estimate the speebms7i3e 2kqt,;ai -scyz- 1ktd 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 straightaway. H q73ct- i-,a yb2;simek1zskt ow fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. u cfi r7eu,(3tn7f1yjy,kwbl1 k h7v/ The shorter one is 2.40 m long. How lou(cyuihfb3 nft1r7vk ,l /1w ke,7jy 7ng is the other?    m

Two loudspeakers are at op, t eglitiqi,rva7 dx4 p)0b4+posite 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 li ,i dp4i)lt0teagvi xbr,+q 74stens 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 in the aorta is nol9ndg. :rxgrocu-a h 4y02m9p0dn ed.rmally about 0.32 m/s what beat freque dr4 2pgm- e9n0 0lg.uy:dnd xr9oa.chncy would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 9 wstzi(a z:g wy7vwh, )vr+1s6.5 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 wave reflects ofwt) yvg(w,7zs: vs+w1 z hair9f the moth?    kHz

  A bat emits a series-* hl;hu9,(m xnnb sid of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth b-(;nmx*h,dlshi un9 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 Alpine vimq5 cctkv8d a;2;9db illage 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 overtqc ictvba;d m2589;dkones 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 listoiac9- y8ql: iening can be compromised by the presence of standinq8i9 i c:-olayg waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called -afxox/ wi oe/ v3(nv)xv f(r7 ,3cebk“singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s mvx3nwce)x( 7vvfo- fx(// aei 3kr, obidpoint. 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 f)szo* c ugu5b*or the human ear at a frequency of about gbsuu* )5z*co1000 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 z8f n+( mm0zc(eb gjf42.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s e(fm4 (zmn8 bgcz0jf+altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 78+i e/ exfl9.a mqh .csb5lok$^{\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