What is the evidence that soos8py;gboez-t . ,8dkund travels as a wave?

What is the evidence taq8wkze m);)b hat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to , 5mv.- kexoajthe bottoms of two paper cups. When the 5o.kjem -av,x 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 expect the frequency or w4nhxdi+vyy y7xb/r * n )9g(zsaveleyghb4+ nrnv/zx7 d*y9 y) (xsingth to change?

What evidence can you give t pxthw4yz;55z5wi3 ie hat the speed of sound in air does not depend significanz3 5z i5p5wtewxyih4; tly on frequency?

The voice of a person who has inhaled helec5hwas 1y;.vium sounds very high-pitched. Why?

How will the air temperature in a room affect tr9qjsl4o5;id ex- 9gphe pitch of organ pipes?

Explain how a tube might be used auw9 f nujbt :9l.v.l5qs a filter to reduce the amplitude of sounds in various frequency ranges. (twvlf quu9 5:n9b.l .jAn example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tquwh14 p/ 9qf1qulfs/ qpp ygve6+8-r ogether as you move up the fingerboard toward the bridge?ups9lu-f qy1eh1 pqrvw+p /6q/ 4qgf8

A noisy truck approaches you from behind a building. Initojx+vlyh-- ym69y /uc ially 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-fjy y+ -yv9lo/mxuc h6-requency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due t- t2-iw.sd bx,lc3jrfhwh(5y o “interference in space,” whereas beats can be sai 5s-fr3byt(h , ixchw 2jdwl-.d to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequ+v nx3uj2ip7yency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or xi+ njv2py 37ucloser together?

Traditional methods of protecting t3xn v;ip, ye;ihe hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in adey i;v,;xp3indition 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 though35*pyrl+rbduo .p 9 rvt of as a superposition of two sound waves with slightly d+up5v.y9blrpr d*3orifferent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directio6xsqhq x1+4v(/ 6)s hqxbdqwin, withx/v(w6 qs hsbh4x6+qxi q d)q1 the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the -2m iu -ym(c5qz )m9w-bfls rfsound heard by a perso)yfmqw9u rzl-(i b25cm-- f smn at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monf wjcce5wd6x r54fdb 8/. gu7fmgc58witor is blowing a whgx .wcr78f5e5 /wc cw8 mfj5u4bfg6ddistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of herxvg 0ml2 1ibr3 shout reflected by a cliff at tlvrm1g2 bi0x3he far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears th r:mgug+jdoz391pw0tm o,0z qe echz j0g:9gdqpmmrt ,0zw3 +uo 1oo 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wa3ncgw. 6t bj6evelengths 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 just above a school of tuna on asftyxog )m.qjrjl+.kes l2.s gbrk3;k6l5 /1 foggy day. Without warning, an l2ssq.x./5smkorlbjf kg63 j;)yel+ 1 tr.kg 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 mat4 paqi q4l:ddi;5b sz-(ht3rmp1ge 7 kes when striking the water below is heard 3.5 s later.hstqb dp;(te zr5iq4mg4 l3a-7 1pdi: How high is the cliff?    m

  A person, with his ear to the ground, see.a ph.2ocvvi+s 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. pv.v2aocih +, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rul,di2pixs:5or -c j4gye” for estimating the distance from a lightning strike if the temperature is (a) 30d5y cx or 4gi:js,-i2p $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1).8(sh jocpr0z5 vkmw 20 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 wh+0zt g n-vhpvy7; 5ex l9h- ljn0sr2tzose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fire2h;.urw; t, jfx;2m8n axk3. cb8svttcz 7nrcd simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Adcu jt;b72v nxr .r.;hskca2, t8c wmnz;3xtf8 d intensities, not dB’s.]    dB

  A person standing a cert(xte nfm :s78tain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound levelf8es (nm:xt t7 would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise 8 mpey(,1hs n urkw+.hratio 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 for each device?,hp (ynr+ 8u.es1w khm 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in n j .cqecf,ibi vsv14b/9qz4m*ormal conversation. Use Table 12–2. Assume the sou/ii9v41js b.bczc *,qemfq v4nd 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 eardru f-ajm88pefg k; dv3q*-ou f;im 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 ratedao i0;ai acv: 4fhua(gn4*c-f 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 loudsc 4fg-:0*fcv aiu;h ( inoaa4apeaker 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 reg+qforvv3r4; t sv.2ij istered 130 dB when placed 2.8 m in front of a loudspeaker4f+orvt;j.irv 2sv q3 on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whliqc/ xm +.ig;at is the ratio of the amicx i mq;/l.+gplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triplcdpq 9a*jt*,1tj kvt0l zd.y*7*gznh ed, (a) by what factor will the intensity increase? Increase by a factortazg**t*l*t cyj0d znh k vq79d jp.,1 of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equo7s w1()k b(,6kvkao/itlu ycal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities?b sokulo 6/1tw(yvc,(7) kk ai   

  What would be the sound level (in dB) of a sound wave in air that corresponds to9t8- y+ia 1(ve vxkikpx)0n0kqb bg9c a displacement amplitude of vibrating air molecules of 0.13 mm at 300 t kgaxcqvk810 )9b -x+i9ek n(pibyv0 Hz?    dB

  A 6000-Hz tone must have what so5lr-+ys zjzw -m:hs0 (tkes: ound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6ols +w05s:h:ryzet -( zms-jk.)    dB

What are the lowest and highest frequencivsyrq3az;/4 m es that an ear can detect when the sound leve4y/mrq a ;s3zvl is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangkhmiq,q ;) 9p)5o wejot7 /gjoe of sound levels. What is the ratio of highj9)7kwq h gj5o)peq/mt;oio, est 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 fund-d o*q s0llwrvrvpf 2;o(uk-.amental 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 placed? r *pk-vv -fr0lq.o o ;2udswl(   N

  An organ pipe is 112 cm long. What are the fundamental and first th/kyip zi+7y ,kh0ssal ft+7j)ree audible overtones fpz)yij kih7/s+y+ a lt,ks70 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 top j68i-lhpil2wb -ce i2 of an empty soda bobcwj2l6-l hp ii82i-ettle 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 spanning tcqp5d6;0v8p n -minfxxj-. c ehe range of human hearing (20 Hz qm in5 v.6n-f0pc j-8pxex ;dcto 20 kHz), what would be the 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 its third q3r+vc; x.x57dbqb .9ik6 knk seas (mharmonic. What will be its fundamental frequency if it is fingered at a length of 3 q(6maksdxeck x5qbi;s .n7+b v9rk. only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long anaahh gq-2tf8i7ux y5;d is tuned to play E above middle C ( 8it;hx7-a5g a2uqh yf330 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 middle C- dhkmi+-*wb)0 5pinux z- ncm (262 Hz) when the temperatur bmi-0xkn--*)nz5ic muw +hdp e 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 stv yt7m+w 1bfs5(2skyt kpx6w: p x6*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 12y*o/sp3ek tb t-te0+-p*qmqo–10 should the hole be that must be uncove tytppo q*k0e* b3qm-/+s eto-red 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 cah2l. t-0ii jetn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (aj02 el-ihi t.t) 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 both ends.kelqo9n6z xz - f:)p2jocx68o It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is oxj q-6z)9cz6kxlo :2pn 8e fo
(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 ;js9q* -pdmvp $^{\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 presen s7 oauh:ccee 7tl w3i)7qqo3-t within the audible range for a 2.14-m-long organ t w3lqi77as:oqh ec-)o 3c7eu pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately d 0dv )nk+fotr lpo3482.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph4or8 kfn +0l)potv3dd of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0ue81a d ;ovdny.n22 tckn x lvae24k:1 s when trying to adjust two strings, one of whicu 21: c a 4ov2yn8d.keta; nve2xldkn1h is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hesk +)ddpipbowx0rb8( 9q a,,z) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23 uxibyb77e6uqi /d)v36i l380ncbc ys.5 kHz, while another (brand X) operates at an unky6ud0)vub36lqy/3enbic7b8csi7 x i nown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces- 0qesfqm zjvhz*19t 6 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasq t0zqsh-6j1m *vfe z9oning.    Hz

  Two violin strings are tuned to the same fryj/bnr+ 4ak)j .n5bu oequency, 294 Hz. 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? [Hi)4jokrnyb.+5/aju n bnt: Recall Eq. 11–13.]    Hz

  How many beats will bex3/hf, wkcf:c7ca (k m heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other af7/3, m:kk(h wcxc fact 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freque idom7qes6l 2 3b)5hoency of 441 Hz; when A and B are sounded togethe3 s75mohe) q6ib2dloer, 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 possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one spkw85, b04 czh kck2ptwpd+d-seaker and 3.50 m, 2 54cdkb8twzd-kkhswpc 0+p from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, butv;bf-,dyrsm 2x2c-z)ty+o j j 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 jto2 x 2zsv),ymb-f+dy-jc;r 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 ) mk)csol7lei2f3 k4+hfma b; and 2.76 m in air. How many beats per second willf)lm2cih+m3l o) befs4ka;7k be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of ,:qcclnj chl+rofkx 1;6zn+ 5a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a spee6c xl hr:c;1cz5+q njo,fln +kd of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequ fn5ru e 4cu)ok5q-/zfency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/szuc5/4 n foer q5k-uf)
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift by/dszb/2d 5b in frequency if a 2000-Hz source is moving toward you at 15 m/s versu /bb5yzb d2sd/s 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 ul5ml u,o+z7s single frequency horn. When one is at rest and the other is moving toward the fizolul+,5 ms 7urst 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.mg2d ef0 fb(e g8i.6t6mlhi (u0 kHz and receives them returned from an object moving directly away from it at0imtfg( 2e8e 66g uli.fh mbd( 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at / wrvdp2:toymft 5p:7a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30d5:wo: p2mfvpytr7 /t .0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on phxqpk 6rd()4 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 wa4r6h)p (pxd kqs 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 speedzoxd xh97p4zp-(i 3lms. 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 from the hxzx-3p4l97imoz(d p sound source?   Hz

  The Doppler effect using ultrasonic waves of fwdta(////iu *2k wdmzaarx h5requency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is )z+i.;gk d b :y9lv b+yopg1hs12 m/s from the north, what frequencyp++dysy.b:bvh91 )z ;g lgko i 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 movingw. 9i*olztv-evg axm1k vrc n:8 r73dke3()bg 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 at Mach 2.3 where the speed of sound is 310 m/s (a) Wu2fx1dk +vbqc3m +bnx+q*0 qehat is the angle vkfed+qnuc m+*1bq b+0 2 xq3xthe shock wave makes 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 the thin atmosphere of a planet wvl. likoljf *toj.6+7o h 19eqhere the speed of sound is only about qk7*j6.o9 vo. +h fl 1oiljtle35 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 l; goqp u:uuc(ofv061+ )jvdi*(cfgl strikes the ocean. Determine the shock wave angle it p v+0o(p6u gc1fof(gd)jvq lic* ul;: uroduces
(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 l7frfk2w q24,yw y )qa5 w3cky$/theta$ 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 thesyj*j/ tc186 llz(nmb ground flying faster than the speed of sound. By the tim/lj1ctj n8 sb *6y(mlze 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 that sends 20,000-Hz sound pulses downwardkbu43 xe;/:luw)wac p 4p xd*m from the bottom of the boat, and then detects echoes. If tcwp 3 b /dak 4x*p4uue);mxw:lhe maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the kfoobw1t7vzbm 5 o.whw 7z+(li ,2je9w;zg8f human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has atoyo0 .pc r5 uu5,.vzc display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open onouzu..p5 ytv0rc5o, c both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close ts g(dt5uqxn+( o the threshold of human hearing (0 dB). Whaguxs+(d5t q( nt will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8ijc0mn0 shkf/n-w9ox rx0 k;u.88gc j2-dB sound and an 87-dB sound are heard simultaneousl 0 r8-.wgnh8x kuc00n;/sjf9cxkmi j oy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whai23 y9e 5qiozft is the acoustic power output (W) of the 5y9o iez3f2iq speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 103h qzc 16 hlz91+ou7vdb*oew z00 Hz. The power output drops by 10 dB at 15 kHz. 1z+wzz*h u7ehb6 o9l ovd1q c3What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typi +si2w3t 69gkq 8kaqancally 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 3 ksnkaw 6g+q92i8aqtradius 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 communication5w btap 0/ tnykr+z*re69p n8es 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 tuned v sc *x11euf hb9c7fr1to 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 fu)qnw5pwp p96o ndamental frequency of 440 Hz and a mass per un6p5wnw p)9 pqoit 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 v2ohi ; ,zrix(wmrr uw).juqi+c 96s( libration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the z2wimr r;q9uo+.r,wx u(ch i) l sj(6iair 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 ishrx 9u9-ajxu 1 near a tube that is open at one end and also 75 cm l xx1h 99ur-aujong. 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 to resonate as on2tmc5ixfk/p or(v v* vu( dzzd 5935bgu0he/be full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Theam*hd ; blo0 7a6.pzxn 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 ;onb6m7phxda 0.za*lsource than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary.j*5i tj9ielt ;jc+y(+mfq7nw The conductor on the stationary train hears a ( i 5q; m*j7 cf+ettw9jiny+jl3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whist lytzjr1zkw5lr.3u1 /le as it approaches you is 538 Hz. After it passes you, its fr .ly 31rw l/u1zt5jrzkequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate th(cm hk/-axco94pxtrgh(k*/ ee speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound rmp k(/(hhgt*kc9 cea / 4oxx-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 tog 3p lq(zrtc3tl4o pcc0pz2 6p.ether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Ho z.o 43lppcczp t2cq60ltr (3pw long is the other?    m

Two loudspeakers are at opposite end:e )ct3l .nc9rljrm r-5*kitbhl1sun +isi)0s 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) he is between the speakers, at B, and (c) he hears the speakers after they .ij1 0n l3k ili):h nsbrtclr5 m*ut-s9)+ecrhave passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what qw 5xgh/l3a (zbeat frequlz3wa5/(qxhg ency would 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 speed 6.5 m/s whilo 5 vu,,na4+encpdjb 6e the moth is flying toward the bat at speed 5 m/s The bat emits a sound v,+56 ao, jnucbned4p 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 hilc,ezo pvew l07ve) k)q.sr0 .gh frequency sound pulses as it approaches a moth. The p7).l w0 erovpes ,lkqv0c.e )zulses 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 signatlzl 8j-yfk, ea- o+ *mqte2*xls from one Alpine village to another. Since lower frequency sounds are-myjxl, -+ao zeletq*t *kf 82 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 stereo lis(eq sf1upc ,88anik(jtening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m l88 eufi,n1as(qkc (jpong, 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,” inv4n (.;wj)lc u6 pczxvoolves a long, slender aluminum rod held in the ;lz 64ov(u.wj x pncc)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,
(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 thretf 6s qw2 zwy;o.g3wi2ysyv( :shold of hearing for the human ear at a frequency of ab f: yt ig;.s36wwysqvz2o2(wyout 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 obse63a-r-eg 5svbd* yzwd:8zwsbrver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whzra6gvzd wby*5-3-8s :b swedat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboj+5p hwqktu(: at 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