What is the evidence that sound travw,xa*eozg5 bo*vt t86t(.xn tels as a wave?

What is the evidence that sound isam2 ),2bfzmrt a form of energy?

Children sometimes play with a homemade “telephone” by attaching a strin q1;ouzt y7cy,g to the bottoms of two paper cups. When the string is strettc;1o yz,7 yquched 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 pax0t2cqliex:l( sg u:p-q q7j*sses from air into water, do you expect the frequency or wavels e quj(q2-cpx:l*i 0: x7lqtgength to change?

What evidence can you give that the speed of lw9v:- wg i jv zg)/b)hpabpj09l2,pmsound in air does not depend significantly on frevbhz 9)0wwi,p/ )m -:jla g gbp2pljv9quency?

The voice of a person who has inhaled helium sounds vepkbn*uind-1 ) 6;fd k5 pvz3mdry high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pu-h:bj :+6byru gx2 cpipes?

Explain how a tube might be used as a filter to reduce the amplitude of sob,mr6*0 01jbeqkt 9vtgfyi xg7e ch ;6unds in 0gyb1jhx 6tb0qe; fremt g,97cv 6k*ivarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig.yyvvxg5:s kfcdg9g4 q o96:+r 12–30) spaced closer together as you move up the fig69 y:q9v5yrgkco x+gfd4s v:ngerboard toward the bridge?

A noisy truck approaches you from behind;td1ogpqzcc1px;+ z 2:5b z( lylzt+cvmb z48 a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explaipd1z4lvqzc1gtxz; t b28ol5;:+(bcc z p+myzn. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said tori bd1 z+kd0t)cci-(jom0 lu8 be due to “interference in space,” whereas beats can be said to be due ro0ld(0tij8 k cmbu1id-)cz+ to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the point t.2cucnh(b;ms Dcmh2u( .;bn tc and C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work i3spb 8,0kil4eb+vsda n 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. Insteades03 kbpb +84ias v,ld, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of ae1l-5lh+ hwdo i/tyv3s 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? Ew5e 3l-1h/ov+yd ihlt xplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obhgl)95sz*nbx+ h ro+j server move in the same direction, with the same velocity? Ero lb95 x +hs*)hnz+gjxplain.

If a wind is blowing, will this alter the frequency of the w/w5mt gd) dt8sound heard by a person at rest with respect to the source? Is the wavelength or velocity changeddw5wgt)/m 8 dt?

Figure 12–32 shows various positions of tmt-ef2bbr0npt.; zx0 es*f( x7h0 oua child in motion on a swing. A monitor is blowin .fx7r0 h m2t- (0nptbox*ezsf;e0b tug 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? Explain your reasoning.

  A hiker determines the leng to0+vv. duow/th of a lake by listening for the echo of her shout re .wu/o+ ov0tdvflected by a cliff 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 ssg km6wp3/-.iseap ( qide of his ship just 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 1560iag.pm ksq se6p3(/- w m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20ilrnzqlin ,m:z5:4n8*1d cu a $^{\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.: cd1xqdq 2ws7awog6(h i7(ff 3kfr l( Without warning, an enkw216 oh7(:3qfa dwf( scg l(qridx7fgine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the tok8u)hbmntvms(i:7-sj. y :tap of a cliff. The splash it makes when striking the water below is heard 3.5 s later. H(:m a-)7tyi8. mk tuj: bvshsnow high is the cliff?    m

  A person, with his ear to the ground, se(hej.5b iqda7 pk5 2xnes a huge stone strike the concrete pavemb.2a x n(dek5qh5i pj7ent. 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 away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance b574qs 2l98 pt ,kwk q 0 r1uc8c7cc,ppgthkebhy the “5-second rule” for estimating the distance from a lightning s8 8h 74t9h 5k0 cqcbup7tkkpcel21,wg, cpqrstrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a *hrfrnb n )46jfhgqv;7 k:dah*)8rdk sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intenpr1.z0j *slq2z kj braar5(6fsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lev4bu a4 whzuf7+el of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intens+wu4bf4z a7uh ities, not dB’s.]    dB

  A person standing a certain distance from an aikdy o.b;xk; rhiobg c.i8 -o63rplane with four equally noisy jet engines is experiencing a sound level bordering on pak ioibx;36r8 ho.cb gky- do;.in, 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 h75r5.cgp ai1e mreh.have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB 7grhea1 rcm p5..hie5. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fromz49z6fn rl8m v a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o rz8vf9 l6z4nmn the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area isn -+kpl 10 ws q1:aazs4qco,sa $5 \times10^{ -5} m^2$ (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 modest amplifiel nq+t6jnki r83r h;v22g) qbmr B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspit qk) 82rl3n n6qb2+m;vjgh reaker 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 placeddd-0h7btn5hvq, e/t v 2.8 m in front of a loudspeaker on t-hh t,bve5nvd/t 7 q0dhe 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 idrz/(14+ whplvmq.5dj6 fbndqqa7- detect a difference in sound level of 2.0 dB. What is nfwml6/ +(pzvq.d q4r aih 5j-b7qdd1the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) ed+g3l*i 5l29g4jje d;1d jzy-wsdkp by what factor will the intensity increase?ijw s g; pld51e4de yk+9z*ddj3jg2-l Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twic vd2;*jbebf q3e the frequency of the other. What is the ratio of their intensities*2 bfje q3db;v?   

  What would be the sound level (in dB) of a sound wave in air f:3a1 (7nq;. vzwbiv dtd mor8that corresponds to a displacement amplitude of vibrating air molecules of 0.13 m7ntzqb;dwd av 8 i1f:.o rv3m(m at 300 Hz?    dB

  A 6000-Hz tone must have what soun87 kc+rn -0.xtgwj fq)tnu6zr d level to seem as loud as a 100-Hz tone that has a 50-dB souq- 6wznuxttg7r8r0.nk) c+ jf nd level? (See Fig. 12–6.)    dB

What are the lowest and hig i,ahi*uzj0 (ime3k3zme0 r,vhest frequencies that an ear can detect when the sound level is 3kumhe 0ri0,jii,zev(z *3 m3a 0 dB? (See Fig. 12–6.)

  Your auditory system can accommo;2sdaa+ q mdh ubt*mck2plv0c 6e:*2n date a huge range of sound levels. What is the ratio of highest to lowessh +c*6p eu:2bn* mmqcdl;a 0ktdv a22t 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.m(z ;yr51aam t;kzo1a The length of the vibrating portion is 32 cm, and it has a masmmk(za 5a;r 11 yoa;tzs of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fir4vpko7g3 n 6spst three audible op3 6vp sg7onk4vertones 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 fre;rxftw7/dhe8 5i l;8eot t2hq quency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you a8td2/l;ow ;ei f78 tte5rxhhqssumed 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-tugov1pw+ u(boo a,-l5f be pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes require w15vbgoflpa u, o+o-(d? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz p6q )98gxi+bsmjx h0 ras its third harmonic. What will be its fundamentalmrb6hjqgpx) 0s8 x9 +i frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitarn)x q/.34cnxkch 5ft0n kfr)ktuy2)t string is 0.73 m long and is tuned to play E above middle C (3hcrnfx5ckqn))y 0t 2 k n)t3f4k. t/ux30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits miqs/,+gr2cehh ddle C (262 Hz) when the temper ,erhq2 /h+gcsature 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 at8ddfgrckb;(pe9l u*,py x-c 1 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 should the hole cq1qh(; 0zds9 b4y7)uq j :8rsajpwt dbe that must be uncovez du8jqq r 4by01wdt (7h;:spj9csq)ared 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 resonate at 264 Hz, 440 Hz, and 61yulg)r,l,97 pe lu*gr 6 Hz, but not at any other frequencies in between lgu 9),*7rpy, eurlgl. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long isr0 )tl4koq*m2w ul(od open at both ends. It resonates at two successive harmonics of fquwmlo) 4 kot20*l(drrequencies 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 e.u3e;3inz u b$^{\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 audii pk 7 -w2dseuu,6j,xible range for a 2.14-m-long organ pipe at 2 -dskp6euui7i w,x,j2 0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside andlqf lyn+41k3nd:cp5+bg6qbrv68 h zc is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) l68fncy6r+ b4 qpd5l+gqk 3c1hb: nz vof 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*dpmp,umu a7 ).:z xfy every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the o):m yzupfxpud a7m *.,ther string? ±    Hz

  What is the beat frequency if middle C (262 ,m 5s.qrw kf9u3edhgp)+ep9zHz) 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 (brand X) ot3/)-icwzvq wsxvhu+;zl2 o5perates at an unknown frequency. If ne/uo523wsc)qv-it; vhw z+ z lxither whistle can be heard by 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 wit x+f cm)ty7 j-4xiqc;eh a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibr4-c7)jt iefxy; qx+ cmational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the;pc 3dsp2wawfqi ff k/c6 8q;* same frequency, 294 Hz. The tension in one string is then decreased by 2.0% wfw q*;pid/;fsq fp628 akcc3. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will b ,9 mnagzdd(0se heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the oth ngsm(a,0d d9zer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning f5v1 z( 0:jjuxh:x(s0ha z.xq)n xwxfiorks, 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 the possible frequencies of A and C? What beat ju.xvjx a(i :: 1z)fzh0h5 xnx q0swx(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 spv b.;d 5y:ekiseaker and 3.50 m from the othe.:5ibk ;y edvsr.
(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 vibrating at 132 Hz, but a piano;2vshjux rp4n- ;k b2o tuner hears three beats every 2o2;-brx p2vhj;u4 sk n.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 gd/jd: lrz0(tu/ q tw9and 2.76 m in air. How many beats per second will be heard? (Assume T = //t 90(gdrl d:zwuqj t20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a c(xiy :jml(6io t0z ku *it10wgertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 kyli 0(6t*0x wtig zmj(o1:uim/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whosep mbf-7nv 3vy3f7b6rfdjzc0p/w 61ow sireb1v-zfnp6 0p vbf r/7wd jo7c63mf3 ywn emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at 1)t ouadj n12qzj8r7fatr4ctk )g ;r385 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are n )72zqr3ja4t o8tfrjca )81ukd ;rtgthey 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 samext fp(2yjf9ac yfw9( : single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driy9f(cwatp:f 9 (yf2jxver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wax 3qq i)/mdfdapg:w 48ves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Whaif3q ) a/pmg 8dwqd4x:t is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies)wdcqtkv 2)gzy8:*t j , the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequ z :*yw8g 2vdkcqtt))jency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppl6x q(1z ygbz*m7im5 tker experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at res6i* gz(zmmb t qx15y7kt 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 ultrasound wabgzs f)yx3w47qk*; xhves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, a)k4q whb 7g*;zy xx3fsnd 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 directly away from the sound source?   Hz

  The Doppler effect using ug*8-(t7v zeunj:qbmt ltrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is bfz 0twu0 jr.fiv- w.512 m/s from the north, what frequency will observef. j5wb .t-fwviu0 zr0rs 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 spee)v h) yr5h+8fsejdiy4d 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 speemh6c 2, rkger+m7azfg: 69exy0w e3lnd of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of 3r rxg0 n2e6f6ym+7le g, mckhae:w9z 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 where t7ow h nc1gsvw(m6t; k0he speed of sound is only about 35 m/s hcvkt17 sw 6gn( ow0;m
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave an* mho,ttq3-m bgle it producest, *htob mm-q3
(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 4q f*vok:,pmg$/theta$ 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 grou6qo he;sesaax1,(1 p h by.bz(nd flying 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. 12–34. Determine 1hxe h(.sb(yo zp q a61abs,;e
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pu bl,wtle0//i q6gxrc8lses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time betwi/8/rgtlq6 wcex 0b,leen pulses (in fresh water)?    s

  Approximately how many octaves are there i2b: 9yk. t )crsberxr :4maavl.d6a o.n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sm u7lkq5v jfai ;762ymymphony. It consists of many plast 5fu v 6jyqm7ki;2l7amic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close t-t hjqoy1rbmd; 3 vn ih/*c,o(o the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?/ohb(1 n dyqrc;hj-,3 ov*t im    dB

  What is the resultant sound level when an 82-dB sound acl .gd )eeg+c8;gl b4und an 87-dB sound are hearb ;cg.g) ug cl+ee4ld8d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What iv6rs7 9oui5 tts the acoustic power output (W) of the speaker, assuming it radiates equally in all dir79uti r5so vt6ections?    W

  A stereo amplifier is rated at 1plln 3q2oph li3/wsp7q 75j;r50 W output at 1000 Hz. The power output drops by7s l3 hqi5p prq3;wllon7/pj2 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devip u /+)hhw5+yy*iauy uces over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an efuuy+hw y5)+ hp/y*iuafective 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 communicaa, )id5ibbx2m tions 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 viol1v 4 orvyy0*c m7tc6uuin is 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 violiqjdv e/v 9 )*x;od+ugzn is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit lenojzdu /d+q x )9vv;e*ggth of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fil bdsstjqhv8ji/-3biyh; )v9 -led 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 d)yqbi;8j -9 s3v-s bv/i thjhat 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one ent/;o0j1 .ina8hcuol nes j,4 bd and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmon;ic/s.08eu,o n1b 4on jhj tlaic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate4kdorl)98er f as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sv-c hd ):( tg.0g,qwccgay(poources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimalg,va g ) (wcdc:yhgtpo(0.qc- 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 tra afn88 t+s1maain is stationary. The conductor on the stata+ma1fas8 n 8tionary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is irftwibpql0fu5 w 2, ,r5j1,d538 Hz. After it passfl1pd50,ijr ,t 25 uq,rfwi bwes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of u,yq, ;mv3ekf 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 hk vf;e,yuq 3m,alved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequencym8c ur4/w zuq3 of 11 Hz. The mcu r48zw q3/ushorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car z4n*.;qc( ib 3sf,zdh *fgv amas it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers havemq(i*gz.sv4fa*n,c f ;3hdb z identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in t x5(ubjnuqsf)r7 vky1/w c f+5he aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50rwfj )5 7yvn/5cfux(1 sb+uk q-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 6.5 m/s while the moth is flying toward the bel /.0uk t+0hgpe*b. kv wlnn0at at speed 5 m/s The bat emits a sound wave of 51.35 ke l.n/n0pwbkhk 0vl+tu0* g .eHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freo*mx)n) 7v wj evp;v78bvqfa9 yoy:c,quency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each iecw: vo,pnjof9y7 ;xmq )yvvvb * )a78s about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was 1+ lkcrw0m/iw 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 aw 1+krcim lw0/ musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the bxui2sp i)ml* yn+*b)presence of standing waves, which can cause acoustbb uyi ns*li 2xm)p+*)ic “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, callj8jhzn9v3y( tq- sqfu5dw, o3ed “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. Theyzv3 foq3, hq5 -9 tj8swu(dnj rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humw05d1 wfcuc r)mi2z:t an ear at a frequency of about 1000 Hz f:2iuzm c ) 5ct1dwrw0is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonbbo :hs4korg 1;d;q) nic boom ohk4gsro;);bq n b1d:1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboytkq 77s5 flujvk( .j6at is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h