What is the evidence that sou ,r 2r)o40mh foslg:ytnd travels as a wave?

What is the evidence that so57gikt.w) w igund is a form of energy?

Children sometimes play with apmo4rjsd 7i v*+mt9i0 homemade “telephone” by attaching a string to the bottoms of two paper cups. When the strii4*7jr+mp 0o md9sitv ng is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into96h1ve t5(ithdsw )f g water, do you expect the frequency or wavelength to c6 hgd 1vwte9 ifsh()t5hange?

What evidence can you give that the speed of sound in air does not depend -,h,p-j6 p5bbu rshacsignificantlp-r b,hab6p,-s c u5jhy on frequency?

The voice of a person who has inhaled helium sounds very.3p*k es,a/ zjccqahj1n2+h z high-pitched. Why?

How will the air temperatu 0u+1xmt lacc rgo21a4re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce au*mlrn)ym6i( x09zk the amplitude of sounds in various frequency ranges. (An example is a car u9 x)inl6ym*0k (mzra muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yo4fbv ju/ay9d7n 8i4bxu move up the fingerboard i djxauyvb4b794f 8/ntoward the bridge?

A noisy truck approaches you from behind a building. Initially9s ltofcoy-iis n3bs * -*k-m/ 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 Seci**k-smo9i l3y o-csnbfts/-tion 11–15 on diffraction.]

Standing waves can be said to be due to yud4n57premvv ,x1e, “interference in space,” whereas beats can be said to be due to “interferevr,1d, mu4 xy7epnve5nce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were .dn2ua0d *ep c jn7klgvehl25nk1g .4lowered, would the points D and C (where desd7 nnehl4e1u j5lknv0 2 ap.k*g2.d cgtructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting xn1( gfz1 k:vnthe 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 i( zkgn nv11x:ft 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 sdf f -*)uvzl2mhown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. fd 2f-zl )u*mv12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift in ey; pg we4w/a(k/3ztf the source and observer move in the same direction, with the samyn k ze(tg3pwa4ew;/ /e velocity? Explain.

If a wind is blowingq1 ,euvo 68dq mis,h2to(de4o , will this alter the frequency of the sound heard by a person at rest with respect to th oh(e4o sedq ,816vum2o,iqdt e source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions ofchm eys4;foe w0-n.q t, l)*3kntdgh-k/7 jse a child in motion on a swing. A monitor is blowing a whistle in front of the child on the gj 3nf7,s0kkdeme -otl*t wh;.h4 /sn)yge-qc round. 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 listening for the echo ggogy8pbt 996mo0,i) q gyx-tof her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the ,g8yo9 6gp9t0 )iog- tmygb qxlength of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship justi4jk2 1m; ymea below the 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 1560 m/s (Table 12–1) and does not vary signif24im1 j ayme;kicantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aiy ,4dfm1nzyo16nu x, lr 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 b ,;tus1i 6oeqdrifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is 1qo e;uit sb,6heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cyat)vbf n292ynxx 47g liff. The splash it makes when striking the water below is hearynaf2b) 7t4x g2nv9xyd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a b1iu nnjzyk1 ;k ,r,2thuge 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. Hon,y;u jb nkktrz 112,iw far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-seci yzfea1ghm9o3g /s87ond rule” for estimating the distance from a lightning strgs3e a1hz ym/g o89i7fike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1dui p9kr8ppp 2;9t k9: mw0kye20 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 inu/a wejff+uz46;s b5 mtensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of ibj r;sdp)a6;95 dB when fired simultaneously at a certain place, what will be the sound level if 6i)sjdbp ;r; aonly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eqbuzp+px5zh;o/ 9xp2 y ually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience izuhxp 9x;+oypb/ 52zpf the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas f fpq0/sodm v6m-11sq lor a CD player it is 95 dB. What is the ratio of intensities of the sigsq1 1m0fl v/osm-dp6 qnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outputyux*t xoq:*, jzx( t4p of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over xuyt j(:qxx*zopt *,4 a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose am,5bev) s50zma lde6 drea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more m n- gx855jbeqgmw /*nkodest amplifier B is rated at 8nwmqgb-5/je*5g xn k 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, adic*mr-+ (yrgpjh h7 2 dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stag yrdchp (g2*rhij-7m+e.
(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 differe (5q tp(ndb(fknce in sound level of 2.0 dB. What is the ratio of the ampldkq( ((tbnpf5itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave iso; w)xvd,i k1j8ic4mh tripled, (a) by what factor will the intensity increase? Increase by a facto,x4vmio;k 1jw id8)chr of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the *bijntvqz ytb nf 369u 58e0mk6x65s yfrequency of the other. What is the ratio of their intensiin beju83xys9znq f*56 v656by0kt mtties?   

  What would be the sound level -j 2+c+cfgdoz75x 5uivd) gmr(in dB) of a sound wave in air that corresponds to a d 75vrd2-uix + g oz5j)gdc+fmcisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone th,+kn9 c5 g( z84nkjwyxr bodc2at has a 50-dB sound level?,nz8cxb4 kg k9 j n5od(y2rwc+ (See Fig. 12–6.)    dB

What are the lowest and ng /;a m:th,rkhighest frequencies that an ear can detect when the sound level is 30ga;:rthkm /n, dB? (See Fig. 12–6.)

  Your auditory system can accommodate aby7ods mp8,b7 huge range of sound levels. What is the ratio o8d7pmsybo ,7bf highest to 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 vxog bti cch*uv4jq57:498m slength of the vibrating portion is 32 cm5gmvuo 84x7c9 th4v bisq*:cj, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundvp(x0jgl)t (cg: kmf 4amental and first three audible ov:m(p4gtv (0kl )jc fxgertones 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 acro8u/ hd .s,vcbyss the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube/,.y hcdsv b8u?    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 fo2fce/79mb0b co5k fpipes spanning the range of human hearing (20 Hz to 20 kHz), what woulde7cc/9o 5 om0ffkfb2b be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hi xga2-d:,s6q(yiha8z z z5rnhn .ig4as a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of i(xn4ns aq2 5 digh.zyz ,g6r azi-8:hits original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middzc ijxpk8x e d .t/o5h38:dsr-le C (330dphsxe .8cojzx8r k3/i-:td 5 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 organsmj66i a/n am1q/pzx; pipe that emits middle C (262 Hz) when the temperaturxp/m i6n/a1 zj ;saqm6e 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 2 7*5berlth2dn0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampjj(*vxqa6 ge*wzs u1;n6r /c ele 12–10 should the hole be that must be uncover;*gucq x6v6e e nzs/a*r1w jj(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 resonatenl6:l,*)gl5 5lgfzv tuk+,bw ml .vgb at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a ,6lgkbwvfl*:gb+ l vn5l.g)t u zm5,lclosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1i fy64ckjhii e4kuul19e;:0y.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What ek6f0lkue iy ij:; 41chi4u9yis
(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 cv*-g8)ia 75 gq zoxih$^{\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 pre p6f0aojqkwb9w:k ((y sent within the audible range for a 2.14-m-long organ pipe at 20 a9q ok 6(0(bj:wyfkpw $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximxx*bl; qd9 z4mately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in thel;xm z9xd4bq* audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 sfa2t95b vzh1h. mo5:1caiv uk when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± k v5 1 hmtb5ci9havf:o 1z2.ua   Hz

  What is the beat frequency if middle C (s; 4h-kqa /i 0nbdnw:v:ioon2262 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 at5.fcqzpg-bhh3m;ibp; * f xg4 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separa*ghixqbh;pz 3b pf4 .5cfg-m ;tely, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produceb *1 t:hw5ajz,ye-zuse tsu, ;s 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? Explain yours5-;e se t wb az,utjuy,z*1:h reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension ij0s) q nzwvam z(ui462n one string is then decreased by 2.0%. What will be the beat frequency heamz0qj w( iuzsav6)24nrd when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle Cvm3f94 3efzdet7 kelxz7ue 37 (262 Hz), but one is at 5.0u47de379e7z3 x3t fvfkle ze m°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bic7 ar:o cpy(6 has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz 6cpy:i (acro7is 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 frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker and 2fn 1mqnq8b)i 3.50 mfb8q)2i mqn n1 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 supposzpc- 6ckmlnb2.+o(wt ed to be vibrating at 132 Hz, but a piano tuner hears thre2p6(koz -bncc.mlw t+ e beats every 2.0 s when they are played together. (a) 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 5ka vp*m1b8pxkhs 2n9 m in air. How many beats per second will be heard? (k sn1 5pah8vkpb9m x*2Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz vwe :/dtt ))(mkvfqtn-6wjf9 when at rest. What frequency do you detect)mfnkd/-:vv tj6 t t e(q9w)fw if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginej1wrw4p .d8vtsfviz 1 n+ed/ 2 whose siren emits at 1550 Hz moves at a speed of 32 m4it1v/r2+ 8d.j1wzd svne fwp/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frztzd v. c;4b:jequency 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 frequencies exactly the same? Are they bj.;t:4z dvzc 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 freque-*5dv b2)zid6fgt 2yuj8l r ifhe r(o(ncy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assubrh *fg5(olut2 (idiy-jf vz 6r2e)8d me T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrd c9k;zyz z;;iasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away f; 9;z czdiy;kzrom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spee-wr, xbx9cadn mv8 u+ja 54l2d/m;qysd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency dombcrjna/2wasy8 x+ 9qud ,4vl;d5x- mes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playc9)omcqq ),sj0lq2/6biiy( dzj, w9 h gz*joo ed on a moving flat train car at a (ho69 md,jygj ioo9b,ci s j)z)z2 qcq /*w0qlfrequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasok;2yer /am,;yh 1rrsq und 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 floq;eray/ y1r;hk2m sr,wing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of1jer0i;q q* l8vzvl9c b12zd*wo z:gb 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 ) /8bncbzi6oj570 Hz. When the wind velocity is 12 m/s from the north bzc6/)njb8oi , 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 - s2pghg sc;+isr.aoq0g9s4 bon land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Wha z fap6* lr)ot2by6g;bt is the angle the shock wave makes with thlfatbp;r z yg*6) o62be 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 wheafblim8 i q 6jj4ek*//g82qpsre the speed of sound is only about 35 m/s i j2eisgb8/ 4f kpl8j6/qaqm*
(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 sg3gi xe :+ij, rk4ibea)*rcx+ trikes the ocean. Determine the shock wave angle it pr,g4i aik *ijr+): xgx3rc+ eeboduces
(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 x)1wbos 34 oy uzx ly; pib*io;pc-71y$/theta$ 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 exactz j07 tqn4uu25un:fg yly 1.5 km above the ground flying faster than the speentu:u5yf qg0 7n4u2zj d of sound. By the 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 apx5b cd +4pz020,000-Hz sound pulses downward from the bottom of the bpaxp+0dcb 45 zoat, 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,+v; l;*eyh2oyfzcf pwo1plq ) f4x v0 there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympho-damdt q)s5h -ny. It consists of many plastic pipes of various lengths, which are openha-ms)qt- d d5 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 ms+l /0irx.jr gq8 9,+evmm qkfrom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 su9 s.g kirv0+ jlqm+8mxmerq/,ch mosquitoes?    dB

  What is the resultant sound level when a 4(:hs4rqbt ou x9ck29zabo*un 82-dB sound and an 87-dB sound are heard simultaneously? xk2a4hr9 sq4uc :b*b t9ouo(z   dB

  The sound level 12.0 m from a loudspeaker, plac764:q i.ljcd uxko)kuv0nc:v1z3w p eed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all oc7u lvwxkdek:z j0c6:. v4)np1uiq3directions?    W

  A stereo amplifier is rated at 150 W 2bi;j n+5yftwoutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watt2;iyw n5+ fbjts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective r5 hvdl;.n/lmdevices over their ears. Assume that the sound level of a jet airplane engine, at a distancmv;l /n .hdrl5e 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 communicationx)9dmipie 3 dv0shfw-;(k( j hs 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 ismy70n gvc (ke* tuned 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 c 4u 5oy:a, -tpg:xp4kogsoq2pm long between fixed points with a fundamental frequency of 440 Hz and a mass pa2pt:4: qok5y,-g4 osupxg o 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 7fmd 9jeeyi)mu7ck4. vrs,2q a vertical open tube filled with water (Feiy7,f92rqcvs4 m ) m.dj e7ukig. 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at o( 12qw(odyut m5qvp6sne end and also 75 cm long. How much tension should be in the string if it is to produce resonance (i5sdo (mqyvwu6t1q(2pn its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as o)7s t by7( pkl3onb+k5vov aaejon-;4 ne 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 500–1z( bi woukkd:l1iu8;2 000-Hz range coming from two sources. The sound is zdb 8o(wik:ku1 l ;2iuloudest 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 statlyt6bv:0 gga(fb1h,c 1 mx1wo 5 e+rmyionary. The conductor on the stationary train hears a 3.0-Hbx:(1r c15 m,glbyeyt + 1 0ofgwm6havz 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 w qyrz1;tpmv/p,0 qb2you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the trqw1qvtrm;, p2z0 / ypbain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis7yy,/knrebwmur8;/ (r jh 0ijtening 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 (fn,yujhr y // 8ew7 rik(jrbm0;requency 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 of )ff (txjdc v16ba6 q(p eoh0d911 Hz. The shorter one is 2.40 m long. How long is the otherdteo pf(hbdfj6v0x)6( a 9 c1q?    m

Two loudspeakers are at opposite ends of a railr (0tw, zcj5x**e xvsme b)bj:aq+kwz0oad 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 t(aw we be5zjsc j*) xm +q0:,*0kzvbxcar, (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 normally ma*) 9e5u mtxiu/e owk6v,3klabout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow antuvi3mml o6,) xw5 eakke* /9ud 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 a.p(oya-i1gl moth 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 dg i.p-ay(l ao1etected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freque. oxgm 510r8qvrjjmz y0 3n)xnncy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emittv05q0x)8rzn .n3xjo r1mgjy m ed?    m

The “alpenhorn” (Fig. 12–38) was oncwc )acy* qnsrs9q;0yt .;-uyf e used to send signals from one Alpine 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 about 3.4 m)qqyy .c fcu0;*a-s t ;9wnyrs 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 comlluv uyk;i 2z+-f9fk95b dhb /promised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.zkiy/9 vlh;u + 52f-9kdfubbl8 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 “sing b;xnpdjgw-wr;s:.y )ing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpointxs- y.; pd;wnrg)wbj:. 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 hfc4ai)zu;- v6(s(tzms7)n jhq (y uul earing for the human ear at a frequency of aboucut(u)slvi6-a4 fsumq)n7( y zzj (;ht 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 Mab1gtxn g u1y7*ch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhe y*7 xtngb1gu1ad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 6ml 78)ngcxx gl;d9x xis 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