What is the evidence that so/waj m3a7 (cbmund travels as a wave?

What is the evidence that sound is a form of 8cy 7btax ht;;energy?

Children sometimes play with a homemade “tele 5qpmn s0zb7q;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 wb 5s qzn0mq7;pave travels from one cup to the other.

When a sound wave passes from air into water, do yo64 ia ypnomr8/u expect the frequency or wavelength to change 8paor n6iy4m/?

What evidence can you give that the speed okhp 2r46ybkugl/ . hs(8nbty;f sound in air does not depend significantly on frequency?kbgbh 62.8lrynkpu t;/h4 sy (

The voice of a person who hasqe s,g tkxtxwx3 y)0e;+z7 v:j inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipesjfsnp- s cp5*nb+6be5 ?

Explain how a tube mi;5qtwgyccwxyv8+7lvr 5 /rlfi g : 7:zght be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An8gc lx5v:z 5+w c7;r7tqywi:gyf/ vlr example is a car muffler.)

Why are the frets on o 3ibrnzh2.eeh r9 1t+a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bh.r1eh +2nebzt 9 ri3oridge?

A noisy truck approaches you from behind a buildiyt yc5kp fb.37ng. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of 3f5b .ptyc7kythe high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfeaadk:j4ax9a62ne rh4xn bwo. ng i20 -rence in space,” whereas beats can be said to be due to “interference in time.” E j o2wka:6ann4iegn9x xr h-.0da4a2bxplain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the point/tm/ :y ,*md+/lmpwa mtz;jsa o.1omss D and C (where destructive and constructive/1m.a*dom+smjm;a tlw/zo,s :yp t/m interference occur) move farther apart or closer together?

Traditional methods of protectnd (6 dxp7(+v /mler;myz6 *txar,fo sing 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 electronically76+nar s6;/ (xe,mrmtdo (*flx pvy zd, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thoum)zcinxn 3 .f-bq(z 5kh5( gvdght of as a superposition ofzz5ix n)-(g.nd fk bh3 cvm(q5 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? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dirqw7q80y7r luux/-/ v/nopw vg ection, with the 7pw0r-8 v nl/ 7u/wvyxqguqo /same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard b2y+mj ;k+vu7ucs67 oxjs:)1oysgnuey a person at rest with respect to the s j672s;j g: +xsouno7 yk)seucy 1vum+ource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mo adk+frl *ejt;yzt- //nitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Exf*je; ldatz krt-/y +/plain your reasoning.

  A hiker determines the length of a lake by lisyf8a 9(hb+ sm/xiyr.ntening for the echo of her shout reflected by a c8i.9nr fb+xy(yah / smliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He h yl b8vnsfr: ml(79w(eears the echo of the sound reflected frofe m((9ls vb7rn:8 ylwm 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 a6x en1 ew.nm)ft 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 :;boj1osds0 v v1x2na. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much timbjvd 1o os:x 0av;n21se elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fgwr-5g64a/w :z;ltkv l2luozrom the top of a cliff. The splash it makes when striking the w4gz r6kwgu: l/;5t2lwz vao -later below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the co24:qctftsrugss0**k e;h :gk-wi6 eancrete pavement. A moment later two sounds are heard from the impact: one travcssg4qf-hk2t0 a ewi:gu * s6*krt:;e els in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over on)ue* +k o0;vj16yqiaxt wlc9 he mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the tempera kwqyuvjoxet61;h+li9a 0 *)cture is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the nxll1n, x;2 oxpain 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 m30q63km(xp7p+ xer 4k. bzgylkve o: intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 de jk- ,pg,fafb;1j/c:jn.hjwj ik *t ,B when fired simultaneously at a certain place, what will be the sound level if only one pknjjw,-;g.h:* b1jki/atf jc,, fje is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a dx7u 9d2xvfk9zk/v )ziv ik8 0certain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: 0kz2iv vkfd9xk/ xzd) 8 iv79uAdd intensities, not dB’s.]    dB

  A cassette player is said to have a signalljozvp g5n36 4-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of inten3pvzn 54jogl6sities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe3xkpyzm:m6ip*/k d9qr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ovpkz/6 dpq 9i yxm3m:k*er 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 ear/e)e-a(l af+wky2 fxmdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the mora1 +imln7v)jxe modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wouldvj )1+amxi nl7 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 front of 0kboz4s; fy /m5omk isq6f n;3a loudspeaq;mk/si3 n6ko4; 5ymo fz0sfbker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB oeicpqp 6930n. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section c 960peoniqp311–9.]$\approx$   

  If the amplitude of a siwgf+j7l1zabs+o9 c ;ound wave is tripled, (a) by what factor will the intensity increasi+f19cw+ozl ga7;jsbe? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes,kc 6 boye2fr e3w5;mztjsi8/ ( but one has twice the frequency of the other. What is the ratio of their intensitief5r ioez6wbe t k(2c3/s m8y;js?   

  What would be the sound level (in dB) of a sound wave in air that correspondhf6v,. ysowl8 s to a displacement amplitude of vibrating air molecule.8o 6slwh,f vys 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 b9 j32/om,-c3v+dhe rb i acxfthat has a /bx -2 om,ecb 3 d+v9caj3firh50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thatkc)ve*/n g0bt an ear can detect when the sound t/v 0)bckegn *level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whattq5.ufc/ca ae)0 tp1l is the ratio of highesc5q.l)e af0utc1p/ta t 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 lengt:1i*t8mxl y)2odvtjm el.lr )h of the vibrating portiymdoj)r)vt2l1 :xml.* 8le t ion is 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 long. What are the fundas xbf) bjk5k 09t.pz7nmental and first three audible overtones if the pipe is9fznkbtk sp7)x50 bj.
(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 wouldqrp5-1qex-r l you expect from blowing across the top of an empty soda bottle that -re1rxlq p -q5is 18 cm deep, if you 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 spanningvd f 5 w9.vphi*rhn5+r the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requi d 9vr+n5w*fv 5hhi.rpred? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hak :25c.hid u4ump:qnk8gbqn)s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at qhk48q: bgp5dnkuc).2 nim:ua length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ( uz +0u3n+tsxw0tczeabove middle C (330 He wt (0zx+ztus30+nu cz).
(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 emi kkx)yx8l0+l:xpg e -zts middle C (262 Hz) when the temperature is x+ : xye l-)k08xlgzpk21 $^{\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 atg . pm+(ktdd b*qkv8.z 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the du z- dp4iduk1;v) my(jvz) m8flute in Example 12–10 should the hole be that must be uncovered to play pmkzdd1j-vzduiyu(v ) 4m;)8D 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 resonate at 264 Hz, 440vlu2u09ae. gg7p (qpk Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an p( ue27q0 .vpalgkgu 9open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates ;5pi; wyz -xqx0*5bv / sz+k)lrybkynat two successive harmonics of frequencies 275 Hz and 330 Hz. W i5)/k+pw*; k-5 zxvlbrysy bqn ;xy0zhat 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 o e;a/q.jqzjo gh6*.x $^{\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 presedeys;81 uk) ,hwcy )rnogz3w c),)uzent within the audible range for a 2.14-m-long organ pipe a3wgezs,uh1 w8,)z)yr y ncku;)d o ec)t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the ddag g;(6-bw gf5 r-vh9uqo2coutside and is closed avrhg;cuog g6(dw9d-5b2afq - t the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to 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 adjk13x c1 *kny1rj.godxust two strings, one of which is sounding 440 Hz. How far off iorc dg11xy3 x1nkkj* .n frequency is the other string? ±    Hz

  What is the beat freq *vjv kbgar, 81q. tq92nyb pzhax+;,vuency 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 (brandzcq,f tutb :da5,.u e*gb,:bz,+ ypl l X) operates at an unknown frequency. If neither whistle can be heard byq.c,bz:+ zp:,u,*t yfadl 5bb lt ,uge humans when played separately, 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 produces 4 beats/s when sounded with a 350-Hz tuning fork an,3**aecc+ 5tmioktdc d 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational freqdmeioc+ca ,t5ckt*3* uency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequeee8pzq5 cmso 9-a2+zdncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when t sezzeqdcm -5o+p298a he two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identic,czb3i d t 48k6nal r/g0*ebtnal flutes each try to play middle C (262 Hz), but one is at 5.0°C aad6*3zn n4bcil8g tr ,0/ebktnd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has ;tcan4d d7ko 9a 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 togeth7c9 tdk4; anoder, 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 starc.0 jyt 7)q5i1syw vznds 3.00 m from one speaker and 3.5swy.rz )1q v 05ciytj70 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 2s zec44e0r tux6y)f gsupposed 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 must be the frequ t4rge usxc6yz2 4f0)eency 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 waveljui;pf fzsqt4 *e*;r)/w/xf )gmuz. wengths 2.64 m and 2.76 m in air. How many beats per secozfqwmg xu*et/fpw4j*sf/r i);.z );u nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f4 0,7idh-c7lvz (deo;xa khihire engine’s siren is 1550 Hz when at rest. What frequency do you did va(i;d74 c07h o,-z hexkhletect 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 engin x7wtpj ss6+(ke whose siren emits at 1550 Hz moves at a sxsstk pj(6+7wpeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a4u+rbpc9p z pu /u9t6ugjx l79 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Agbp4z 6lr7 c tx +p9p/u9u9juure 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 frequencyly p vvqyv: byo5h2g);90 zk/n 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 bv)z2po9v;nhq/ky l 0 y:5y gvhorns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonibjlcxhq urzqzg*za; qd w(5 m/3- m*6)c sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received soundmqjzm z(az*uq bqw6 5)xg-l 3c/;h*r d frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sp+vyn,7tas* r8j9l/qed:a czt eed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the batvn/ a lj ,*+z8drq e7t:9sacyt hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler ekxf5ir i ax0kodpdc2,vv (s4).y9x0kxperiments, a tuba was played on a moving flat train car at a frequency of 75 pofa 00(x25xr9kdc x vvd)i k4y,.kisHz, 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 u3c4 gpv r4)p ebyqh ;*6ld+scrltrasound 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 isc 43 ;6yvr rg*pp4l+se )qdbhc flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr-dvp 8 (tbi 1kf4nhkt1equency $2.25 \times10^{ 6}$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 so.pkg uij,e:y/d2hqkavkf + n-3x ;-xgund of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obsefvk/pk-+hxk ,du2j-q;i. nxe :3 ga gyrvers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 0zw tyii1 i5o820 $^{\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, onbk fp77b4:ren ys( of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mn (,yrbne:fb 47spo7k otion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where t 8acmg:igh70k5 w j1:dyy; nbohe speed of sound is oan ;:5c7ibwg hydm01 jgo8:ky nly 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 strikic j;ry bwztq4.77dm d.- cr9fes the ocean. Determine the shock wave angle it produc;cb dty q4zj .i9.-mw7f c7drres
(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 eo7 0gbpf qtut).w4j4y 9b*hv$/theta$ 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 km above the ground flyi ;cpg.,j5qe1w.kc; zlccyz6 q ng faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig.zc . pg6l,;; cq15eyw jqz.cck 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 20,000lodg6 ht1 :(0ula7w)i b(vad p-Hz sound pulses downward from the bottom of the boav o pl(7(l)uab i:dwa1g dht60t, 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 aofls(n8.m (quxd: ,hgp no: 0cchr)2xudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dq/my3fwq;m7 fisplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on botmffqy/ 3; wqm7h 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 qyu.q phd3g0uvf ;,) lto the threshold of human hearing (0 dB). What will be the0y3q. du ;pqhgul,fv) sound level of 1000 such mosquitoes?    dB

  What is the resultant sou lqna7y0/io wa/3-c qznd level when an 82-dB sound and an 87-dB sound are heard simultaneouslq07l - yzn/cq3woa/iay?    dB

  The sound level 12.0 m from a loudspeaker, placed in the js:pz-8k,jdf 7/t7x pwwq: wwopen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it raqw8/7pw7tdw:j:ws-fp kzx j , diates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz -ve2,)qh/vgovu tlhz lh/yp m 15p7;s. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?,ehl /v;us7ovlg/2h - 1pq5 hy)vpzmt    dB

  Workers around jet aircr3aa*xst g-q /grm,u8lvn2x9( t mrg5zaft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, isn2rgz*a u5vgq(m agrxtl, -3x9 8t m/s 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 syste3yxvzbo ) 473 d5kr.rhkc;i0 jmq :ymvms, 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 isv2fx7g u *zba;( lbxe1 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 cm long between fixed po8t obxtqk k):;el 8a2oints with a fundamental frequency of 440 Hz and a mass per unit l:) l88b2a ;qoeo tkktxength 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 ,j, *r4ra t:ihqsv.u/g m9dnuvf lo; 3vertical 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 ,;. 3tisv :j4f,rqu*/9dhglnoru v maand 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 thatve epf+ 3zax6te2m9z . is open at one end and also 75 cm long. How much tension should be in the string if it eavf6ee+tz9mzp 3x. 2 is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to rdwvtj4 mgh1 jn-00t*l esonate 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 purs u+0-/ k dvq6vchxbt-e tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the t/u v kcxq0bdh-ts+6 v-wo 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 stationary. The conductor on thxjf 9)0bg hs)de stationary train he jfxdb)9s0) ghars a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it osq :- ry-5lazapproaches you is 538 Hz. After it passes you, its frequency is measured as 48 aq--ylr: s5zo6 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimm yq i tk06o2fsek*/*kate 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 y*fkk ioq/6m2eks 0*tgoes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sou,81yr.eu) y c giwsj6vnding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thejriw,s.18) gyu vec6 y other?    m

Two loudspeakers are at opposite ends of a railroad car as it xmc r52+mxoyy9 rh- 2hmoves 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 th29mh25c rx+oy hr -myxe 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 blooo a;fezsrv ha )5o)ry nx4 79own349fld flow in the aorta is normally about 0.32 m/s what beat frequency would yf4o;ofzxr he9wly7n a 9a) onsv)34 r5ou 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 mo lb0.h95b k+ggvt8 tjpth 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 ofbb k. th l5+0jgpgtv98 the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approach.k r-506 or8ma0bv rzg fom+fves 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 emitted? z b rr-gk5+rf.v68 of0amo0vm   m

The “alpenhorn” (Fig.gcenn 5 *rp2b0 12–38) was once 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 mus2 *bpe5 n0gncrical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereombt .9e 24n(ttxkyh/ k listening can be compromised by the presence of standing waves, which can cause aco(hbtxke 2/ 9.ykttnm4 ustic “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 p uz(r6: 3mm7vq)uc vne6p / 6l.leqwe“singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For au lr cenp:v3wzp 6()ee6q 7v 6l.u/mmq 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear a4(o dd7k quu;-fpp +w5vf)cm vt a frequency of about 1000qp ok74vpf+5u w(- ;vumcdf)d 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 Madvz,,fp l w-n.ch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is thezlvfp.n -d,w , plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is .ih)5i z+uefaw-mzwa1rp ,o( 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