What is the evidence theybft+/dleh5 ,;,sr w/p chg-t7f6btat sound travels as a wave?

What is the evidence that2+nfeaeabg,j ;/iz9. u8 tsze sound is a form of energy?

Children sometimes play with a hom ;uf 3;fb58tshchdtm+ emade “telephone” by attaching a string to the bottoms o8hhc ts3 b;u+d m;5tfff two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you etdwmod:n,e( ,b(yt 9dxpect the frequency or wavelength to chn: b9to(d(,w d em,ydtange?

What evidence can you give that the speed of so3k;-ep ) b1iqus :ynmd42 gmukund in air does not depend significantly on frequd4m)yk1 neum u s-3;:bq2kgpi ency?

The voice of a person who has x8 d (l4q 3u(tdxe)mq2pd*ijfinhaled helium sounds very high-pitched. Why?

How will the air temperatun5sza * vhok+2re in a room affect the pitch of organ pipes?

Explain how a tube might be used j -8 irf+rfet+.p 7elvas a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a l vfi +etp.-+r8erf j7car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move upt9sr vfv) x5 4eb8(+suftxvy7 the fingerboa5tvbxsyt sxv89f(e f7 4)u+rvrd toward the bridge?

A noisy truck approacha6 9wd qfvbn:j* htn wcqp7.c8-kw).zes you from behind 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 Sectionw8:q 6z.9v* 7ktpabh.d cqn )-wcwnfj 11–15 on diffraction.]

Standing waves can be sm ls;h2 7w9/ zqln0ltbaid to be due to “interference in space,” whereas beats can be said twlzh/7tb 0n qml2 s9l;o be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency o6sg9y9nc co+p f the speakers were lowered, would the points D and C (where destructive and c+pcg9csy6 o 9nonstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people whohmu9q(r4*3f 3z7ta0je rf)gag e l7o t work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detect0h(9ra)fttq3g g7a7reomjz l* uf43e s 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. 1* qnx0d nl++ocqd( q9x2–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig.+ d*9(qqcqdx o+x0ln n 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 s9p**tu*bo11b ,dgnc.p ub,iggjm +hv ource and observer move in the same direction, with the same velocity?g*b1im*1tcp gh b ud9bv o*j.,png,u+ Explain.

If a wind is blowing, will this alter the frequency of t2 m2 uqxkb5; 9c2 (8mdobo+wzfnvn6vr he sound heard by a person at rest with r(brv26 d9n8ub2 5mn z m;wokxvcf2o+q espect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various*q l y:7bmwghviv33c* w8vd b) positions of a child in motion on a swing. A monitor is blowing a whistle in front of the ch*) v3yg7v b:dwiqc3w vl8bh m*ild 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 leng7:mltusujr)l-zi pd6* 3ru j6 th 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 -)7uslpd6:r jrtmil uzuj36*shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ecs)shpz7 td*6q95e ushho of thquh e 5 )shdsz9p6st*7e 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2a5n ;5tuk6,ntb2quj d 0 $^{\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 f 52hozk.dls2cv-4 pc toggy day. Without warning.z ks-4pdtoc5c2hl2 v , an engine 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 top of a cliff. The splash it makestd qs7/w )z1lj when striking the water below is heard 3.5 s later. How high is the cl jtqzl17)ds /wiff?    m

  A person, with his ear to the ground, sees a huge stone strike the conu cps01,6 hb+- /plqzje uaus5crete pavement. A moment later two sounds are heard from the impact: one travels in the auq l56p,+ps/zja 1- uchu0sebir 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 mtndg 0( n:.5glqx7strile of distance by the “5-second rule” for dr sqtn.lt(x: 7ng0g5 estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound az)z (ix-80yyyw3rri ,,lx8bs dbdf; ot 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 yd-eogr+8a z6 sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lev2 1xob oqwnb02el of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB1nb2box 0woq2 ’s.]    dB

  A person standing a certain distance from an airpx morc- k2njjsw- 6o.6lane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, j-rnc-j omso k6.6 xw2not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 d - bh/hiibbho:*4amy9B, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal bh*oih yb4 b9hm i:-a/and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversxx *eoe;h/)jj ation. Use Table 12–2. Assume the sound spreads roughly unif*exhx o) /jje;ormly 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 xq+ )k hbeu6 gz1a.ag.an eardrum 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 is g)os96 fyiq4n 83mquv bv3588 ) jailkgi4 fwxrated atl8uq v 3jg gn 6fiqk5o4y3)av 884 wxs)9mbifi 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dq5om + x0ap ;bjndp3.dge*s7qB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stagbsdp.x75 ; +dgnpa3 m eo0qj*qe.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference i:( vgdheb28iyn sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectioi2h8g( edvb:y n 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factorg1i)s6lmbb- vrwe /m+. (getg will the intensity w vm/i(e 1b6mg +).brlg-gsteincrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but oy.)m8k6 kk*ms vac )rnne has twice the frequency of the * k .k)s8ay6rn)vmm ckother. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wavahlup dt90(*)npdqjc6h a;x6e in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 30qad9up6d)jh *6tl ;ap xh n0(c0 Hz?    dB

  A 6000-Hz tone must have q kud7f *9c6ka*+2tyg pq( oz7dv engl grc+0/what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See 2a(zt6gpqf9kqc * og un+gvk*+7rd7 cy0/dleFig. 12–6.)    dB

What are the lowest and highest ae (:ze8epo -vfrequencies that an ear can detect when the sound le-z(oeeea v8p:vel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. v-lw4j*edj p2qgh18 ix2)qz/xsm5td What is the ratio of highest to lowe)qqwdx p 1xmj2iej /z 4gv*lt285hs-dst intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violi+nf lnmb4 w.*lld:1xsw o 8)ljn has 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 bmnl l w.4osb+ l:dwnx8flj1*)e placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fbi 9(tpdh r:n.irst three audible overtones if the pit(i br9d.h: nppe 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 top svj ztc.hlax*jm 7.6,of an empty soda bottle .7hjxvs* tlm., j6 aczthat 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 wtz)+u;tpkg+u 66 y ngu4ml:0;ve awqk ith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be t+gkpuat+;6nul6w gqemky )v4t;z 0:uhe range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as i*wt ,fv*67bos a/d9bvsafltuk5u;*a ts third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of i 7ot ,ftd9lusa*f6ksvw;a * ab5*/vb uts original length?   Hz

  An unfingered guitar string in v u)p..w*ltd2vid 4 1jahb2vs 0.73 m long and is tuned to play E above middle C (bvdl1ni au)4.w 2dvj.* vh p2t330 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 fol8)k8:;,gu n n rrclof an open organ pipe that emits middle C (262 Hz) when the temperar c l:r8onf)n,k;lg 8uture 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 n4u mna/2u3xvc avw0dq/z ony/00+tfat 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 c2o ma 9*kzg sk)jof5,; un+;he4on ydbe that must be uncovered tu4e;o )m 5ogj+y2ko anf n9,zd*k h;sco 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 rm+ pjkf s;7ug hj mk1j zv-f- uqjsi-78210komesonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between.v 0f 17iq-jh fjs1kujsk- k +z u8gm-pm7m2oj; (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 is open at b88 4tprhdxafh *ow/e :(r lwq*da 2pv-oth ends. It resonates at two successive harmonics of frequenciel*v: a t88/ dr4(x-wfeaw hd r*2ppohqs 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 x4n,/juuu gw6ec)r2 -0 en evg$^{\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 2.14-m-lontsq uffvjgi)g7*)m -8g organ pipe at )s7mfvj)g tif g*u8q- 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm loqy :hj .aod,)png. It is open to the outside and is closed at the othera,qjdph. :)yo end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adju/iovs 27dx j8x;b chr0st two strings, one of which is sounding 440 H7/d xx80vs;2irb ochjz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (266h ngy2pfhf6d.n,o9/o aj pe( 2 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operatrt- ic(a-i9bt y,wi .ges 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 occuc9i, .at w(g -yirtbi-rs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork a:fjo 76 *r ks nq0+ajyugl2sj;nd 9 beats/s when sounded w royaj6 luj*nskg;2:sjf 70q +ith a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz.pzcv0l( yz-v kiat* .0 The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Reca cz0-pz*0t (kvlia.vyll Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to playekjxlzt9r l ;:*gezdv:7r8+x middle C (262 Hz), but one is at 5.0°C and t7tle+9dv;8g le:j: rr zkx*xzhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fre:8re u*aqdxs*quency 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 frequencies are poss:uxdq*r 8e sa*ible 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 3.0umib:p to.6 8a0 m from one speaker and 3.50 m from tiut8bmp.a :o 6he 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 suppos b)n-qbi/,v5 n zqfwn6/vf-kj ed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the othv- kv5jqin-zbnq w)/b6n/,ff er ?   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 i*c qois cqfa9(d:p2s )n air. How many beats per second will be heard? (Assume T ad*qf):(i qc2scp 9o s= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whenuj8* w) iaw;oi 5yyp4x at rest. What frequency do you detect if you move with a spw y*jpw5a8x oi ;i)u4yeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency kji+j;*2y 7z7 eluq xcdo you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/zj c;eyk 72ij 7+xul*qs
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is .lsf8 kew*4p tmoving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two f*8 swpl e.k4tfrequencies 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 eq2x914eh gc gah;vk6p tuipped with the same single frequency horn. When one is at rest and the otx1pt gegh649hkcv ;2aher is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.l7ci +8;g jrmpc- yk9t/.bo yh0 kHz and receives them returned from an object moving directly away from it at 25 m/s Wjyt cirl8p-7m;/o y.hb9 gc+khat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 :ruf2 )k9et8yf7,j6 jfwt *y/ qnc tdem/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency doescej:)qdy *9t/6nw fkf ,8yrtjf2tu7 e the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments) 8 wcqan65xk*cnliqc *)aw(e , 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 station. What beat frequency was heard if the train car approached the station at a sl(*e58aca) )* xkq w qnic6ncwpeed of 10 m/s ?   Hz

  A Doppler flow meter uses , nxhb,dlnx,,l+ jbqdi 3ejmv;p -y)5ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is 3yb+,qe m;j-hvldd ,p lx5 ni,x)jb,ntaken 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 ultrasonic waves of frequeshaju8ue 4y5(ncy $2.25 \times10^{ 6}$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 of6.igq dxzx,u( frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency ,qx. ug6zxid(will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moviu5dx x+dc ( -+au l.qiqs5*weang on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at6o utp;b-sd)d8 d bjo- Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave make-j du6-od sd8);topbb s with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters thb9p6x6a0c6.zl 0gq: p8do0swqquiy c e thin atmosphere of a planet where the speed of sound is only about 35 m/s :lqw0z.c9 sci y xo6 0q bd6gpup06a8q
(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 stri8hg6r61cj:bm 2rfwf 4wmrsr3( yhg8ekes the ocean. Determine the shock wave angle it produh248frrr jmebwhf 1m(y68g3r:6cw s gces
(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 r2v dxr ;nd8mg1( +lvv$/theta$ 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 tddm+e1bvhs- .1*2 ifynwy 5iy z ru r(0d9j-c1.5 km above the ground flying faster tn09j5id1-uz.frb2 +d1 ywis*- yvr tyh dmce(han 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
(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 tl :cqr wgtv3*cgx04;shat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work its w;0qlvcg* r:3g4 xcs 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible k(l*p8 iedp t9range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It 6 4zdfkxv*9jj consists of many plastic pipes of varioukjz69jvfdx 4*s 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 soun6mdv7cbb hm uh2n*m 4,d close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes vbcd7mb 6m2mnhh*4 u,?    dB

  What is the resultant sound level when an kr;4xmxt l-xfs6au ;182-dB sound and an 87-dB sound are heard rxau4k xlfmxts ;;6-1simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10bjuug)gzdeh);i-m 5f 8mbeed 526 cll4;o6 q p5 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dire6ue5 8chpqzo5eg;mdm f 2)jl 6d;ib)- 4ubgelctions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops 8zs bxm*wiph.vs/o qpisuba.:; 1- :c by 10 dB at 15 kHz. Wha*:bxv./z;.a qsu1 is-pw ob:pih cms8t is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicesfa0pih v :25t9j mp*uui 6(ohh over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, 6i(iu j0p:h9hfa*humo 52 pvt and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sysugj j81t6fjisap kx9 h9:sh+*tems, 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 tuned to a flce8 m ho1z*m2requency 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 eiu72rfgmhp )s wjd i+-b:d47fundamental frequency of 440 )+fd 4sbmrpi 7idu-g h:2jew7Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filledb*gptx*9lc+cy ix14 l with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the act pci14bx+ xy* 9*gllir 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 ofube ajjob6vw z5( c6*8zpe75 n mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce re66e nuj bjc e7ba85*zvo5 pw(zsonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resi 9k5tc52ks)l3skl rxonate 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 av2w s q47zk8i)f5maq 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 moves about and finds that the sound level isk872sa4z 5qaqivm fw ) 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 trai*;;v ,4g,- bo 2 mzi1ufb acasuyzz9spn is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving g -vs2z1s9fi,u*mz bapyc4,oabz;u ;train?   m/s

  The frequency of a steam train whistle as txp l 9d/5m7zzuv ft,;it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Hodt5z79 ulm,pzvxt/f ;w fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by l3:bwb5 ks-ouiistening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straighta3 bk ibu-swo5:way. How fast is it going?    m/s

  Two open organ pipes, soundin1w7z ancu8) xng together, produce a beat frequency of 11 Hz. The shorter one is u8 x 1anw7ncz)2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends sd;:2c- /aujj:ocipu of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If thei u :cc2pajdj:-u/s;o 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 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 dkkmv/5x ow i6lt*:g7what beat frequency woul7k6wgo ltd 5:/ik*v mxd you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at vu tcqf-y+(;w(iyx:lspeed 6.5 m/s while the moth is flying toward the bat ayl+v(wu;qy fc( x:i-tt speed 5 m/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 appro;yp7e gz43l zyaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away cg;4ey7y zzpl 3an 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 4j;t .h5hh z og,9d v/bdxfc;kAlpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to creatfh . ,5cd dbzvo4;x;tjk 9/hhge 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 st()ff*xm xby3m1x0 igyereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations m* 3y myxbxf)xi1(g0fof 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,” involvesrhjb02gzia752 (*h2s pn62ixx a ppfs a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod, 2ifnjxhz2ar5 h6bgpi 2x(s *0pa7p2s
(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 t8x- 6* fw7fvjtk te3 07xywrnxhe human ear at a frequency of about 1000xevtk*j7 t6 xxf3n87ywf0-wr 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 Macjxu.1 c;l87i6 k2 xytlw: axkqh 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes j kcyq871 a 6. tku2xxxl;:liwdirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is,jpl f,zga w2u8 3- gxcd8e6lm 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