What is the evidence that sound travelsbj)f2 pohr*jr ./eo6l as a wave?

What is the evidence that sound iu 1)knsgb n:m96s qz-es a form of energy?

Children sometimes play with a,77ub /8olpusec6jvp homemade “telephone” 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 vuu/7 7,6s8ebocp ljp–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes *b df1:5y l9e7dn)bywn3trz w k,h:uhfrom air into water, do you expect the frequency or wavelength to3 wwbnt)l9rheyzk1 f dnb u,*y:d57h: change?

What evidence can you givm tjlx1hj* 6)yb9yeolkq 2t 2+e that the speed of sound in air does not depend significanty2 te1j) *l tjlbokx9+6 mq2yhly on frequency?

The voice of a person who haq*51w(4fcgqayr7x izgm3 u z/ s inhaled helium sounds very high-pitched. Why?

How will the air temperat r* f qcc5y34.3stqfjeure in a room affect the pitch of organ pipes?

Explain how a tube might be used at0 uh/s.)ugzu+prt)c s a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufflerp)u+tz .t h u)rg0us/c.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as zaqw, n it64n4w by32qswwpv5 l*v9l7 you move up the fingerboard toward thwqi97p*6v4 bsz 4yaw3lt wnnw5, q vl2e bridge?

A noisy truck approaches you from r 7tq 3a(m*dmlkri ;9obehind 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. Explain. [Hint: See Section 11–15 on3mr7q ( d;aom* lki9tr diffraction.]

Standing waves can be said to be due to “interferen5suc b mks7x/6ce in space,” whereas beats can be said to be u5x6m 7 b/skcsdue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the p.6*ps7uj*x dvr9ckchj tid7 *oints D anp j9*c*7idh x7*d vrjku.st c6d C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wor m ewn3p6l ho6fm (c*8bbcr*g4n 4yc/pk 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 /34n6 bwphg8m(cn6c f cl4*mbpy *oe rnoise. 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 shk: 0uvbnr zh8k8,/hrv own in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fu /vkz8 hnr8:0rvbh, kig. 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 obser77p: a uciq,0 hdra5zq ft:qy.ver move in the same direction, wiut dz q,q ahfq57y7a::ric.p0 th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a perszdueqjlx l/dc oig:); b cp;2nw5d8+ 3on at rest with respect to the source? Is the wavelength or velocity chan)j wq 5cb/u 2iedldzgo8l+x p:d3cn;; ged?

Figure 12–32 shows various positions of a child in motion on a swigy4ep;b qp9 p*7 z,kting. A monitor 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? Explain kpy qp9gz* p,;e4ibt7your reasoning.

  A hiker determines the lengt9 94ro:. atecfz*ukk ,w- wx,fv taw*ih of 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 sh,f.uzca9r atv:-k ww *otei *4wf,k9 xouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterl7nf :z)vik)f sine. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary signif 7fsf)i:kn zv)icantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airvim5 vmkl,po+ 7,e3z t 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 just axxwet51(ogkh 2)ct9loi z /u/bove a school of tuna on a foggy day. Without warning, an engine l i1uxt/kgcho9x (to5z)w/ 2ebackfire 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 cliff. The splashr84 h24i wznx* tp4awyjz+r( /bepu t) it makes when striking the w+p844 y wntwathzzj()u2r4x/ r pe*biater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to2kx85nsjc tc0 the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 5j s2xtcckn0 812–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mil/ (4qgvakplm. fs* hm9e of distance by the “5-second rule” for estimating the distance from a lightning stm9 /.*q gmpl h(skafv4rike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120sheg/7ee( : -9yucdq 4+luudk 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 fnv( f(+w qpm5intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce5o zc l2+oorj* a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hino*2o5+jrc ozlt: Add intensities, not dB’s.]    dB

  A person standing a certain distance nhgs2m: qvbbfxoh o/ 8k7 l.0*6+z ece2lppq +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 mz6e*+ov 2hfp.q0gbx l ob7e/ l2h+ 8:pqcnksif the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is eju-lm4 gl ut kz39mv4t:b 88hsaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratioulejv3z 8h9 -4t4bt8um mg l:k 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 sound23 0m9kzgjwjn(tfg r+ from a person speaking in normal conversation. Use n( f3 tgm j9gj0+wrz2kTable 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum b:pbt; vdd.0y 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 more modest amplifier B mg/+,y s ;*l 4nqgz**bkdqnmj is rated at 40 W. (a) Eb4k /g n; ,zn+yjm **qdls*gqmstimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter regp 4eyamm;(l jt6l(lc9istered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ma 9 ;lltemlycjp((64
(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 difq )ofo2y3o dg3y0 l y9c4dae5lference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11 4oa) oqyyod902e llcyd3 f35g–9.]$\approx$   

  If the amplitude of a sound wave is tripled, o ez6 ao.*eud-g t7wsx4ha4)z(a) by what factor will the intensity inat)6a s4g-x4du.o*oh7 e wzez crease? 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 ha9/k ir7v, .ryj q*tzcjs twice the frequency of the other. What is the rark v.jy*t7j / ,rzc9iqtio of their intensities?   

  What would be the sound level (tduz .c4yin ,9in dB) of a sound wave in air that corresponds to t.z49,unid c ya displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone yqy vz0c+9ig) that has a 50-dB sound level?iv)+ z09yycg q (See Fig. 12–6.)    dB

What are the lowest an qjr8+;i.rt vb4kjvs7 d highest frequencies that an ear can detect when the sound level .iq;jt k rsjr+78v4 bvis 30 dB? (See Fig. 12–6.)

  Your auditory system hn9wxm(p 3c 7vy(l; x:5uwsat t:ol(gcan accommodate a huge range of sound levels. What is the ratu9: v((tswl (wcmn:hog 7 t5pl xa;xy3io of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin h/arvb(1wh,q rq s k 45hwx:5n+m:mk pjas a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be 4pxrshhv 1 :mbqq:nwk/mk55(+a,wjrplaced?    N

  An organ pipe is 112 cm long. What are the fundamental and f7c lrk yql9c4)irst three audible overtones if t7c9yk)rl 4qclhe 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 td*me*k 3 ;wld mfi.r.1 hznj9ihe top of an empty soda bottle that is 18 cm deep, if you assumed it was a clos.jildkfdm9h .e3 r;wm**n i1zed 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 spanning thei44vc (kxz /o4d6 vdnu range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requ(ui dv6/k 44d 4nxcozvired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hwdpk22 ,qj )hgg7:sqvas a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengpsj2v 2w7g)qk,h : dgqth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plaj0 5d(1n+;nnhwe1 scmak3 rffy E above middle C (3wh5ns dnc+ a ke31;0njmff1r( 30 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 op fx5,- -y) ozpj*omqveen organ pipe that emits middle C (262 Hz) when the te *5)ox fz-m-jqpyve,o mperature 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 yv7if0+8 j +bity-sqj9e tv*sat 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 s);p ljc7odpl2 xr(fq 6hould the hole be that musqoj( 7dplc6 r)lxp 2;ft 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 2y o// plt88a vu 8s+fc-sxyai(64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is as+/ts8o-ypiuyf8l(c axav/ 8 n 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 en). 8sci redic9 n kf+yr.7caslr/( (mzds. It resonates at two successive harmonics of frequencies 275 Hz and 3zk a+() ss9m.lenif8r 7r cy(cdcir./ 30 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 a4) fdgkn;l*vyo68zh $^{\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 s6z) ,ob ab/p1vpgdo8range for a 2.14-m-long organ pip zb vdog)a,sp/p61bo 8e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside andjer0l60rh vq; qn 26zrwc r+t7 is closed at the other end by the eardrum. Estimate the frequencies (in the audible range)r0ncjvlh+ r0t66erqq2 ;r7wz 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 adjust two 5lw;ldpbm7 ez)1 b cu0strings, one of which is sounding 440 Hz. How far off in frwce md l zlpbub)0715;equency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and d-yt ( o-pu3*r8weuy k$C^＃$ (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 4+n1cg;feiu:(r tx a m eip4h2operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are pl(ue2+ixm;ctg4aeri p:hn f 41 ayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning ff8z nhjd3 e1b3r(9p gqork and 9 beats/s when sounded with a f9n3p(3rqh e b1d gz8j355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to bfio5 6h n7y)o lg1ss6the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat flongfb61hsy) 76s io 5requency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will due (4htez p;08c r/l2d5dvpp be heard if two identical flutes each try to play middle C (dz ud4 de8(h 05 2et/;pppvlrc262 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning lm:wsne9qvl; l*5 /puemqr6:* ujjx;forks, 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 tog 9x 6mep uj /qls:e;m*5l:rlwvqjnu*;ether, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m ffrv7i;g gd:tp ;a1hf,rom one speaker and 3.50 m from the 1hfr7:,gi;vd; tpg fa 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 pna9p,d8r : 4;dcud veyiano 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 frequ4adn d9 ,cv;p:8rdyueency 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 anp9wg +5n 0,givs6nn t* se0(k eeg3syrd 2.76 m in air. How many beats per second will be heard? (,sgtyge3eserwg* (s5 p0 0kn 6+ nivn9Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequen wiahz8hhpm77q-k8 2ccy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency dom8z7i8qh 2c -kpha7wh you detect 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 engine whose sirhn2:mpr fr5.ren emits at 1550 Hz moves at a speed of 32 m/s nf5r.m :2rprh
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 200k s v; w342l;cjfu6fcm0-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are 6fv2sc4 3lju;f;c mwk 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 one is atwosl-35i8+t rer3th1 mc+z yr rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of o5 hlr3 rswe-i8yrcm 3+t+t1 z5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonw(ym ufvjp9i k 2ca:wh(mgbj )4d1m9. ic sound waves at 50.0 kHz and receives them returned from an objectv h(iap9 (.km c1fmuy:wj)9gb4m d2wj moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ul;zfmkp m *q0* u8vbc,jtrasonic sound wave with frequency 30.0 kHz. What frequency does thez*,0jqfk *8;bmpcumv bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fl hj,3cp, fg)csat train car at a frequency of 75 Hz, and a second identical tuba played the same tonfjg3cpc, )hs ,e 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 ultrasound waves to measure blood-flow t*-dt ,(fiwbfi: 9n il5 vn0sxspeeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away fromin:fn5fb*,lx v-0iwidt s ( 9t the sound source?   Hz

  The Doppler effect using ultrasonic waves of frs:wuciy51 p8 m mj;9guequency $2.25 \times10^{ 6}$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 windofxg3(icmz- 8 velocity is 12 m/s from the north, what frequency will zi8 gc3(fm-xo observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on lwy6)zbtua04j n+s7;jjyw ,q band if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s eeajqex:6ee16p. , q g(a) What is the angle the shock wave makes with the direction of the airplaneqa,1peqg 6e e6e x.:je’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 atmosph/vjudak v0dp1tja8vf/ u3o ;6 ere of a planet where the speed of sound is on v1d u;03v/tpkfjau/ vdja8 o6ly 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 strikes rk7,:tkc x m-mthe ocean. Determine the shock wave anglekkmc,m xr:-t 7 it produces
(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 v73t-elkoj +o$/theta$ 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 exat2 .8p0otkmo zctly 1.5 km above the ground 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 Figt mop.28to z0k. 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 20,000-recqt72 iv )s1jp2)-xtvxcq*2;k v kqHz sound pulses 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 xvjx2 q2 7ps-ir12)qv v kqtc;tk*)e cminimum time between pulses (in fresh water)?    s

  Approximately how many octaves are ctq2y. bmo7uyu3 g-j8:(gugraz) x5rthere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.-kflg2cc ;o u. It consists of many plastic pipes of various lengtcck .olu2;f g-hs, 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 frn;w9c-k4hmx sg/t 9akom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitogtxmanhkc9wk - 94s;/ es?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soundzg bv -z,mb/w6 are heard simultaneously?bv /zmg ,-z6wb    dB

  The sound level 12.0 m from a loudspeaker, placeebdnh:c8;3yq x15yjwd in the open, is 105 dB. What is the acoustic power output (W)wdcyx58h b q:e3y nj1; of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpx9sv5b-r1u dcut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is ur-xscdvb5 91the power output in watts at 15 kHz?    dB

  Workers around jet aircrafqj pe0eb0)a kpos5:6w t typically wear protective devices 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 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? wjaeeqs0o0 : 6p )bk5p   W

  In audio and communications systems, the gain, mq i*ax96 krzlpw4f,5 $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned tomls.n v4)ouyv5:0 iq1xo o9mu 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 fundamentjgj(wy en- 9 :,e2zeq7vx j,qbal frequency of 440 Hz and a mass per uw 9j, -eeq vzq,j:7(2yxgb ejnnit 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 vi+002eqy , z fbwxypuq,me21p dbration above a vertical 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+wyxqd22, , pm0bzquy 10eefp 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 one end xk 5jbis*qgi9cca :31 and also 75 cm long. How much tension should9 qcic 1jbax:sg* ik35 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 to resonate as 7epoo86hqww 0 w ya*t6one 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 5 0ckhmw*r/u2a 00–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person *h0/ mk2arwc umoves 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 stationarepq v 6oxc,h3kt 2+y(ky. The conductor on the stationary train hears a 3.0-Hz beat frey+o2k qckp6v(e xth ,3quency 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 b:y, rqn4uoh g9;g5 /fsy/nepis 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume con/9/ros;g4qnen 5 f uyy bph:g,stant velocity)?    m/s

  At a race track, you can estimate thj.b s:8 -m-+.s/iimm gd9z2 jhsmknbze speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Supposmibm-hi n.ssjjk 9bg8. +z /:dsz -mm2e the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Thf v/y b5suc,,jk(*x qqe shorter one is 2.40 m long. How long is*qjc xbf q5ukv(/,,ys the other?    m

Two loudspeakers are a/i,qizub)i0qgl e:pl1r*.x dt opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b)i/qr b *zgxe.,ll :1qp0)iiud he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s whalgri vvbcoaig.z 9j6 tr+: //5t beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood /9ji r5vcba vggz6:t+or./ licells? 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 towar2 dal ,(7ku(ej,c)-ho.yp c+cc o ifckd the bat at speed 5 m/s The bat emits a sound wave.+ a,elcdyc 7okjc2,uic(cf(oh )p-k 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 moth;w2vdjs(3 tu w. The wwu 3sdj (tv;2pulses 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?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one aa blk iobkbb5hw2 -.edj6,;6 Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and ababhke-,b5 ;ko jibl6.w26dwhich overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listenin ms++ *qrx*4cwbip 2uig can be compromised by the presence of standing waves, 4x+swrq*b+ cp2mu ii*which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvesukb11u0*o+kdwa xmh 1 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 o+ 10 uuab1mdx*1wkkhclear, 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 9gp5dx34eu xc)tv bs8x3pp/ athreshold of hearing for the human ear at a frequency of abo3pxs bd 9p58/ave cg4 pt)3uxxut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears thq1a alu8m dd t2f h)wkde-32;le sonic boom 1.5 min after the plane passes directly overhead2fl2kemdldq)1awu8a - dt3; h. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat hu-k,6j,ivj t5x 9n glis 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