What is the evidence that sound travozaiyu0 * r vro703k2kels as a wave?

What is the evidence that soum,h ,a5zlxxor(- fdt: nd is a form of energy?

Children sometimes playm2( mk eu:.aon with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child o.uekm (2:nmaspeaks 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 into water, do you expec1osbdy)wpa0; h(z m9lfr d5 )bt the frequency or wavelengtlbrhaspod;1z)bm 9fw)(d5 0 y h to change?

What evidence can you give that + cmy0(zcwc8tm( slo8the speed of sound in air does not depend significantly on frequency?wcmy((t8 cscom+8l 0z

The voice of a person who has inhaled helium sounds very abkqy5z87 g4w high-pitched. Why?

How will the air temperatureynszt*, iu(- tdpboc+//-u su2 c:kur in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude b(8w4 dibft5tl8ignmb,m 4 4 eof sounds in various frequenclt (4 bd4mbet5fi ,wb m8ng4i8y ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movyd6gkj9 )wmg 24 3.wrb.;ca5frhgqude up the fingerboard toward the bridge?g b)ag;5.3y2mwqwkug6r9cjfh d d.r4

A noisy truck approaches you from behind a building. Initially yo0w.r91fjbld+sx i a b0u hear it but cannot see it. When it emergesb+swj dx.0af b l9i01r and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference i:y5g/le a boc,n space,” whereas beats can be said to be duec:,5aglb/ y oe to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowereyo.i o0by *:5l9xrpm pd, would the points D and C (where destructive and constructive *oil09 ym5p o :bprxy.interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoplixeu/,gkfz- 8dtxr /5e 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 am5xd,r-g z/kifu t8 e/xbient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as am-f fv9u9op2p l+3i i3gih p2m superposition of two sound waves with i2fp+ i39hg3 i oupl9-f2m pvmslightly 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 x-*;op, tgavp+c;q qf same direction, with the same vqt+p-qo;ca pvgf *;x,elocity? Explain.

If a wind is blowing, will this alter the freq1i;iloo0t oi;uency of the sound heard by a person at rest with respect to the source? Is the wavelength or v o;toiii1ol 0;elocity changed?

Figure 12–32 shows various positions of a ch pf,p*s2j fa3lild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A thr p*2sj f3l,fapough E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of 2 b.p vd33amcrtawa:*a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengt a2 .apmcbva r3t*d3w:h of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shi.t:dp*r zse/m7)td7 u. xz5cibvtl;v p just below the waterline. He hears the echo of the soun/ b;75e7 .z)dlxtvv*spic:ud r.tmz td 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths7uqg f3 kfo4 9wrk2zr+ in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting jusi 8+(*rqfplv st above a school of tuna on a foggy day. Without warning, an engine backfi q irv(fs*8pl+re 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 top of a cliff53 socfv-ju9rtibvj+ ek;cv ,4;ua i+. The splash it makes when striking the water below is heard 3.5 s later. How high u-f, asoiivjt 3 cvc95 jk; vu+;rb+e4is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the c f t(sz 7xt2ta:vsa -z*tl99o-gkar3noncrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–9: tsn --*ao( gk2 3ltsrt7vtzxz9afa1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ove 7 orcd7wa3fm-r one mile of distance by the “5-second rule” for estimating the distance from a lightning7 daofcr7wm 3- strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound l.sxd0 ey n0.qat 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 k6hur+ 5q)ye2 uob4zzgu ysa 2i;c;f+ whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound l u- a7qvh0o.nzevel of 95 dB when fired simultaneously at a certain place, what will be the h7nuv 0qzoa.- sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a gkbdm;7e0+ pdw 84 eldcertain distance from an airplane with four equally noisy jet engines is exp4k0wmeddlb+ 8e;7pg d eriencing 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: Add intensities, not dB’s.]    dB

  A cassette player is sid0k ),kk s:cn1 ied(qaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise forek:ndi,dc)i q1 (k k0s each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conver,lz(w -s.edw;hl /u5m7ewcr s sation. Use Table 12–2. Assume the sound spream/s lweus- clerwd,.w(h;5 z7 ds roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whornderq1z r 5n770cey.se 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 ,xpoc rg)t)+;ghr8bjt-of l9 at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspg+,f 9tcr)jo)hrol 8x b-t;gpeaker 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 whe)- vh-l xe j4ac-i+txgn placed 2.8 m in front of a loudspeaker on the stage.ei +g)c--av htljx4-x
(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 a9/ca wbrzqt4dh v 2 : m3j7)kzt)g4fyhv:n ob/ difference in sound level of 2.0 dB. What is the ratio/fht9bh 3m wtc:z4 7q zb)g)vjnyvorad 2k/4: 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) by8moa hc:pc n ;hxmiz43)ok2 y) what factor will the intensity increase? Increaccyzm:8hn m; 4ho)i kp3)oa 2xse 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 twice the7pxzx )94nvic-u 4g3j.lnbdf frequency of the other. bp4lf)37ung-cv j i .x4xz9dnWhat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave v9gzc+..kjydy 1 q 0pdin air that corresponds to a displacement amplitude of vibrating gc9d+zj1 . k0qp.ydyvair molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hatsj034i 6 pvwkve what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.6jw4t k3i 0vsp)    dB

What are the lowest and highest frequencies that f 1xp9eg-9x dkan ear can detect when the sound lev-dp kefx1x9g9 el is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rany, phdnw5e 1+qge of sound levels. What is the ratio of highe,wp 5qy1d +hnest 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 fundm:z:pk/ qj latp6i32u9o2o gpamental frequency of 440 Hz. The length of the vo::ot p9gkp2p2ujq 3m ia /z6librating portion 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 d4unv 5tbg ,4vn/ l8izfundamental and first three audible overtones/v5ng 4i4tu lbvdn,8 z if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the topyp:yy*+5l :b x7w fjdp of an empy5p:x f:y jw7bdlpy +*ty soda bottle that is 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 spcx24:rama3crq x; p(ianning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pm a(cqpxix;43 crr: 2aipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmoniwfyt(a jn- a :h66g-qxc. What will be its fundamental frequency ig--f6yhqana xt6 (jw: f it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string *z4*rv acexl4je oz-lohk5 y+3p8o2 yis 0.73 m long and is tuned to play E above middle C (330ke4z5l3+8 -vrze 4j* 2o*yxc oaopylh 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 midda .8 ;g:zsrnjole C (262 Hz) when t. nzr;g8s:ja ohe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at ksn)d j**j8 n(unyh6t20 $^{\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+tc/+9isbr c ilo0 4st 12–10 should the hole be that 4+lcob/ sict s 0r+9timust be uncovered 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 616 Hz, but no nsdmn .w6. 5 hji2sg:g d7scm:.4mamht at any other frequencies in between. (a) Show whyc 7s:j ahn:wnsi.m.2m5 .d6gmds 4hgm this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two z; ya qk iyl-he5h)9g)successive harmonics of frequencies 275 Hz and 330 Hz. What il;hk59)y-egqi)z hya s
(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 -06z x0jiys:zbehh)p $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.yjca0o(t +7qy w2k ,qa14-m-long organ pipe at 2c j0k7+ayytw q(,qao 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 outehe; ey,r 3f kx8pv x3*6 vj*.buizkd/side and is closed at the other end by the eardrum. Estimate the frequencies (in6 d8* ;.k/p*xvri 3zee y,uhv3jx kfeb 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 ,+ a7kgibflq9uar()en 9ft, vadjust two strings, one of which is sounding 440 Hz. How far off in frequency is the oth97auqbn ,)+a ek (l,ftgrv9fi er string? ±    Hz

  What is the beat frequency if middle C (262 Hzg* s/tynz /ohg,bhx.,) 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 whistlk/osc)o,l z he20 .rm0mek z6je operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans zo0 . zksme2cm)r6 0ol kh/j,ewhen 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-Hzza* vn+ e2)w*f 8vkqba tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vivk2+*zf* )bawqne a8vbrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one stf+4;n ifmu 2)hk-g vgtring is then decreased by 2.0%. What will be the beat+n gf4fmh2vuk -ig ;)t frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identl1ah4 va q/+ 5r b:;5rqbtfsomical flutes each try to play middle C (262 Hz), but one if ramoq 4s:t5rbh; v+/b1 lq5as at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; wgbxc. q78 c6q0kg.jyc02o5ch kb wu+fhen A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beab.7 8 q jxfgy6cc b0hc+.0guko5cw2kqt 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 oner5;n lvbjib./ly0 f(2htsr ) b speaker and 3.50 m from th;2bh/brt. 5vyf jlb()i snr0le other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano f y+,s;wvt. abtuner hears three beats every 2.0 s w.,+t;vwbsa y fhen 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 m in air. Hl 09is y(nme(g;dspl- ow many beats per second will be heard? (Assplsn-yg0ls d(m(; 9ei ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’hwo/:ir1yj*88r ( e bp**fm tly oe;yrs siren is 1550 Hz when at rest. What frequency do you detect if you move with a speedj bpry(re/1f:m*oy;rlot 8iw*h* y 8e of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequencdjlyt/ ;06f.gy)sd nwy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3lst)g6wnd.yjf 0 / yd;2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f wwit0(:7j yytrbs5+drequency if a 2000-Hz source is moving toward you at 15 m/s vejid syr 5 y0t+w:w(tb7rsus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When el7qqi1i9f4 nb qa53 hone is at rest and the other is moving toward the first at 15 m/s thei579 ia nlh 134qqefbq driver 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 waves at 50.0 kHz a: ho qwe6cl+a5y-g 7hvnd receives them returned from an object moving directly away from it at 25 m/s Wh:h7wg c5 ay6h-+lqevo at is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ulhm+z.-q*nryqqn ir k-) i*7xnr/m vl*trasonic sound wave with frequency 30.0 kHz. What frequency does the bat heq- nnh 7xm+i rniqml*ry.*v- *k/rq)zar in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments,h56w6slq 0fi4ffml; zy3w 2jz a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway fw0635 lszyz6hjl4iw fqf2m; 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 waves to measure blood-flow speeds. Suq h4)t s+yhk.1pp wu;sykm3 7tppose 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 flo)hy w14kpht+q pyukt; 3sm7.swing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasoni1jjf mpn3j)lxgdm+rh;7 2z 5l9 (de iyc 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 vel*c6uk(ly*)rcp bdz0 locity is 12 m/s from the north, what frequency will observers hear who are lo0 6py)lb*ld c*k(zurccated, 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 s:uo2 er7u, /;yisqhtdl v+p j3peed 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 m4 i16voi6w 9g 6irw2.rbx dvbg/s (a) What is the angle the shock wave makes with the direction of the airplane6r1 briowg6 g6d ivbx 4wvi29.’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 the spee 7cd+;itxd s7.8gbeyj a sb*,xd of sound is on 7;xtc, b+7ay bg*sx8djseid .ly 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 str38lmventro++10 ven d5k3gc xikes the ocean. Determine the shock wave angle it producesr3ne5xvc+e3m kov 0l +g8d 1tn
(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 peyoa(:u j:sj:85jf d$/theta$ 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 flyil3d5m ;djysp 4ng 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. Detyd3 ;l5j dm4psermine
(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 xwwdcv ain016 +m6*)leh*id kpulses 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 between pulses (in fresh wateri +mw16)*d*0 dl ixcvawekn6h)?    s

  Approximately how many octaves are there in +(,ou/92v4egt qxzk hf dd+cx the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calle* oc3c5t2 ntmlts)3hdd a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both e3t2cs nlt5)cd*mt3h onds.
(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 m b-x-o4*okx) jydk.rag h(u0a person makes a sound close to the threshold of human 0 o--*jm(ux g)bo 4hx.rdkya khearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB- 6ps9 1ar7fqwrx4orz; /92ju nlb kgx sound and an 87-dB sound are hear99qr6l 7s x1 -akg f2nx/uw ;4zjorbprd simultaneously?    dB

  The sound level 12.0 mu7m- m:h2xs3 ojgpivy9 l ko( (,nu/vp from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directiogovn y92x(3 lkop,(mp-m iuus /vjh:7ns?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outp3d+w*l7r d yb8,rc 17ezwrmxbut drops by 10 dB at 15 kHz. What is the power o7rwr, z7dlbe3+r cbxdm y81w *utput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. :t sqw lbxl4((Assume that thewlb( (t sl:4xq sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicat oiicb mm( 8m/mqva672wptr 4j vt xwve0:215jions 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 is tun lt t9 rl/ ur4ktcdc+5-zw:k6oed 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 points with a f/9o jh 9f/sg.dds bgm6undamental frequency of 440 Hz and a mass pe./9gfd omh j6b9sg sd/r unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fil7i*p)j -p(9vr w+gko1znez fuled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so,zeurv9kpg 1i 7(wo+fnp*j- )z 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 b3w1uy z5+0j+egdn k l9ekug(one end and also0lk 9gw+n3 y5(ede zjg +1kubu 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed toh0w3xnxvofqb d 6dh+ )g82, iwp*+ ajd resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from tw46uz.xthzdd f l-w9jdrt* 0pd5x f3b)o sources. 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 minimal at a point 0.34 m farther from one source thz jxlb0f * fh5 t4zud.6tr9xd)d-3p wdan the other. What is the frequency of the sound?   Hz

  Two trains emit 424-3frpk s0t5,a qHz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches.3s a0 ftrkpq5, What is the speed of the moving train?   m/s

  The frequency of a steam train whistl*e1,rkpn6vq4 :yhtb z e as it approaches you is 538 Hz. After it paszn: hrk*1pyeq4,vb6 tses 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 cars just by listening to the dif)cg8v5yf f m/uference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by onvu)ff58g /cmy the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freqfgn4xakwu) x6p/ar il *.as7 +uency of 11 Hz. The shorter one is 2.40 m long. How long is 4+a6sn7 *x/ ur i.xlkgafwp)athe other?    m

Two loudspeakers are at opposite ends of a railroad car as it mgim0tokhw 0ll n, ,;)soves 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 car, (b) he is between the speakers, at B, and (c) he hek0 l, ho0);,nlswgtmiars the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what 54r zlvk)pq ghrbv+:1beat frequency would you expect if 5.50-MHzqlvg )p54k h:+zr1br v 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 towa1u 60fhepouc z m4.gz,4md *hu0* 1ugqwnzc;srd the bat at speed 5 u4n0gu1w6h*zh0u e;q.pso* cmc ,duz41fmgzm/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moyeac,f (l -qg9.a lw(mth. The pulses are approximately 70.0 ms apart, and each9fmqal - .w,l(yecg( a is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Aevps,i 9p0 vcl5s17aplpine village to another. Since lower frequency sou0vveass5l,p9 c7p ip1 nds 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 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 stereoxs 4y k jc1-7n)7muik/s:ygk c listening can be compromised by the presence of standing waves, whichcux4 1 ykjs7gs-nckiy/: mk7) can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvesb.f8agn unyet :7 hsy3(xk5/fc 0wo 89kwhg s8 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. Fora(0 8suknhy osth f3k gxbnycfe9.wwg5 /88:7 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 thresholx 7)v ymdpp/*ud of hearing for the human ear at a frequency of about 1000 Hz is)* mvdyp/x7p u $I_0$ = $1 \times10^{12 } W / m^2$ 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 observerm3sc-o;1p 7g3c kxts s on the ground hears the sonic boom 1.5 min afterss;pmt37 x- o cc1g3sk the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat-a-s jc( 5n1eoaou-j q 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