What is the evidence that sound traveqgm-hf+2tp kw7c.+nuls as a wave?

What is the evidence that 7 9 x0kdac8dirpb ovn .nukst:*ba4) 0sound is a form of energy?

Children sometimes play with a ho. )c: r ycur9tb6ulvz3memade “telephone” by attaching a string to the bottoms of two paper cups. Wr )cy6v:zl.tc9u ur3bhen 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 js7ayqly5 + .roji7;,-abqqw from air into water, do you expect the frequency or wavyjasq wr+ioyb- alqq5, ;j 77.elength to change?

What evidence can you give that the speed of sound in air does not depend hy97w-tm d7krfrwa *0 significantly7tkm9r7 r0w yd*-h faw on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whye8 s0zzdb8uv+*u7*u /q2,wg rvl:awaz k)amu ?

How will the air temm i c3(ecoq cod h.d1nw.;vg-(perature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the a*95bc ng3iaqgt k*:x pmplitude of sounds in various frequency ra*gk : xpaq53n* t9gibcnges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced 9tqby3+9nry 9q y1f7l k */cwvgey*dpcloser together as you move up the fingerboard towardg3e+* lbwn1q rfqycyy7vk/* p99tdy9 the bridge?

A noisy truck approaches you from behind a building. Initially you 2;hi+ uk); y75nyhvylsioxz 4hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequey5;iz2kv+si7 ; yx4lh) hy unoncy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spak kjra;7x t*-nce,” whereas beats can be said to be due to “interference in tim ;*tnax rj7k-ke.” Explain.

In Fig. 12–16, if the frequency of the speakers were loww 6wsu3tbz * ,y:o1jlgered, would the points D and uj3w b zg*t,os6w:ly1 C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the nq568)vok sw5c11 hlbrc-vre r;xcg / 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 headp/cs -woer1 1vr 5);6r8q ckh bxlvg5cnhones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eacilh b/* ,v5y 47 j1)0 wmexoujxqe+szih wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are tijexjw)u 5,z 0imsy/ q4 h7v +*xol1ebhe two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sagt q d:jkd a56b)pipih 3/-s3kme direction, with the same velocity? Explk/bi:pphia t-s)dj qk3 g5d63 ain.

If a wind is blowing, will this alter the frequency of tf7mbmx,x/ 05gb hde0nhe sound heard by a person at rest with respect to the source? Is the wavelength or veloci0/m5x gb0 hmbdxfn7e ,ty changed?

Figure 12–32 shows various positions of a child in motion on a swing. A m jo1w ir;j3v*donitor 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 yi1w;3 d jjvo*rour reasoning.

  A hiker determines the length of a lake zq- r,ee m-3h-*stizgby listening for the echo of her shout reflected by a cli-qszem-ie3h*gr-z , t ff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship o 9 lar*g8my:sn e1-yajust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the lmo9y e -aa81n* :ysgrocean 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 n h6*/m3z0zr/4kgbt, +rrw -q/ -ypsp rgtnxp 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 jusm(h 1eiekn zipq.3m::9 bnfx9t above a school of tuna on a foggy day. Without warning, an engine backfeenii:3fmmz 9 1kn9 .b: hpx(qire 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 + 1, edbvy7pqp9i3ko mvt)c sk i*3rm7of a cliff. The splash it makes when striking the wa,pt irm +ivepkqo7ybc3*3k9 v )m17sdter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the clw y67nl* ux 9cel4m7u8rk4fuoncrete pavement. A moment later two sounds are heard 8w7nuc946ylfxe k u7lm4*urlfrom the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error maxn41nhk*geyw7fd)d / de over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a4dn/)kx wde fny g71h*) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the lxk:2gnjp5 -mailo6(pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound 8s1*r(gtl** fvbs yj cjh: m6cwhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fir shpj/7; lvw1led simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, nlh1 7lp;j vws/ot dB’s.]    dB

  A person standing a certain distance from an c8pngbon w55 0(k5frcairplane with four equally noisy jet engines is experiencing a sound level bordercc0pn( gk5 58nfbo5rwing on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas foe-4v plnrv 71t7eqr+or a CD player it is 95 dB. What is the ratio of in7er l1 epq v-onrtv4+7tensities of the signal 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 na a-qd7-4yfroyd-* uc ormal conversation. Use Table 12–2. Assume the sound spreads roughly uniformlyqfu o*cy---adr 7y4 da 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 whose area is mw s*j4,,x9a/hdvki , j p9agb :6gkkb$5 \times10^{ -5} m^2$ (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 am 791seslxj 10;k -pzzehmcc m6p(ycr*plifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expezpcres p0l7 jekcsx 19y;hc16z- m(m*ct 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 registered 130 dB whe o(d40mae *t* d1qa/2nhcp nyen placed 2.8 m in front of a loudspeaker4n a(de*m *ton epq1/0h2yc ad 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 lev r:p c1l +w,awuowl3.sel of 2.0 dB. What is the ratio of the amplitudes of two sounds,p c : wwo1a+sl.uwr3l whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inn/)196 2u-*ct nw7ftygh ro+vph jjhctensity increase? Increase by a factouh6 + tc1ht*cpjj f7wrnh)9v g-on2/yr of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal5w;.so7jzd57 d2ctj4bqzhb t displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitbo7t; hw7 5zszj.54b cd2djtq ies?   

  What would be the sound level (in dB) of a sound wave in air thxmdub2o6h ;y7nm q59 empzyz .*ic18dat corresponds to a displacement amplitude of vibronex 7d6.i9* yz m52b; uhm1pymdzqc8ating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to8zsy5vm5dme 0we qjg3 cit/t04j)1r i seem as loud as a 100-Hz tone that has a 50- m4trjtvy/0 5 j1mz ce0igwe38 q)d5sidB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies nd m2s2rp,8p0h md+g00 g muszthat an ear can detect when the sound level is 30 dB? (See Fi2p0nspdrd h2mmzg m0 08,+ug sg. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the r /5+pi7w-r af*nrvk(dmn.xt c atio o7 d. rinw-5/f+va mx(k*tncpr f 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 has a fundamental frequenna x88yrywd-u .(u)ec yu f;e+cy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under whatwda -u.yenf y(+)ey 8ruc u8x; tension must the string be placed?    N

  An organ pipe is 112 cm long. What are tn0zpn07o2 ngp he fundamental and first three audible overtones if the pipe is o znn270pg0np
(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 y fsczc1z240m/;qm qibou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clos /mb4scqczf i20z q1m;ed 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 pxnkf r/tt+50 nipes spanning the range of humxnk tt/0fn5 +ran hearing (20 Hz to 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 harmoni:r 8itemn:me y ,3jl )yxqf9 64*irxpcj-ewx/c. What will be its fundamental frequency if it is fingered at a length of only 60% jtmre: y3e ,9 8x6r*n:)4ly/jxpi-cqwf x iem of its original length?   Hz

  An unfingered guitar string is 0.73 m long t *)xejujy7o swsg.63 and is tuned to play E above middle Cje *6 7.wxjsuy s3)got (330 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 -2i gzbp;e2se*g l ow;o0t-mq middle C (262 Hz) when the temperaturee --mog bgqe;ti0s 2zolw2p* ; 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 2qi fnw816j8vx 0 $^{\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 12–108 +h0 h4,m/tyeoo jdrd should the hole be that mudmrj+0 e48/ yo ,hohdtst 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 y v870tanyx(o264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an ot8 v ay(7x0nyopen 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 ist)xjw9i9m 7 ps open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whati swx9p)tj9m7 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 i*kji+6 u) mwcwh:2hb$^{\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-long orgarvoshq 9 bj6.9n pipe at 20j 9o6rv b.q9hs $^{\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 outsid2.0 ap asptjz.fhi(khy:+ 8ffdyt o,,e 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 pfh z d: ht(,+iso8fap0jy k,y.t.af2information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat eve41yx-c5bqvd s ry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frecdqy v4-5b1xsquency is the other string? ±    Hz

  What is the beat frequency if midv6y qmfa,ak acf+9 wc.j,: ly3dle C (262 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 opk(tzz b0hxa(.6u.y; fiqn 4g.3dzjws erates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when playedayutw3f(4;. zsnqgd60hbz z (k.i. xj 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 4k 0 qfvitv77m9;82tlbs8qqq8uh-8pue dy 2 rl beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What iqm8 p; beqq2tk77t0 sd8r9uivuly 8-8hfv 2qls the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freque*,gku 4y8sp fvncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency u *vs,8yk f4gpheard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tryijdj/.ikj:i * to play middle C (262 Hz), but one is at i j i:*dij/.kj5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hashqj:8xe 0t3xzo6.vcpt nx7 5z a frequency of 441 Hz; when A and B are sounded togetxqzpx z. jx7ot8he:6v503n cther, 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 standse)qo/5c:sn,c5-e ixpqzs ovsv6k , )w 3.00 m from one speaker and 3.50 m fr,ekvq )cos/5swq- )oxcz56:,v isnep om 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 )3uc7(f7w3p 4 j9thpwxvqit) sp xs:e to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 )x9 w) hcfwpqpj si:37vtpt3e x7(u4ss when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and vyfyb58gi k6 uj 6zla, me09z42.76 m in air. How many beats per second will be heard? (Assume T = 6gvkyzz aul0jmi,9 648bf5e y 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of0 mq sya)azi*/mw*6db x4y9c-gtm2d f a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you )0acdfm zqmb/ w*96 ygtmi4x-dy sa*2detect 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 dhlhq md 6ckz85 .y+s3vo you detect if a fire engine whose siren emits at 1550 Hz mov6slq.hk5 c8hzydm 3 +ves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz souqn d1ao6ry*zp5 vb dq-87vh4 srce is moving toward you at 15 m/s versus you moving toward it at 15 o 84a 57*bq6-dqvyprvsz1 nhdm/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whe3 mr5lefnf*3a .zb25v/ wkrmnn one is at rest and the other 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 wbkfmf rlza5. n 3vm5/e23*rn emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wavehc :-,rll9:s.g gb7s zk4:ms npuda,ss at 50.0 kHz and receives them returned from an object moving directly away from it at 25 nd-cbh:sml: 9 7pk,z ,g4l:aug.srss 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 cb,jrhpxt6qd6 wt 1:9flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequenc9q txth1wrj p66cb:,dy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a gcsny qq f ec490 gyqn(w3mb2-d0a0:ituba 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 fr(qye9wmbc0gs4ng0-qcd2 a ni:f q30yequency 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 k-7qvr h66 v5/uqf, djby+yye measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound i75+y-uq6r/ v dqej,vhkyby6fn human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freqph s/ a 616e bu;tcu5-r:qk88yurdx hgsw :1tcuency $2.25 \times10^{ 6}$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. : rpqn eq+:ev7When the wind velocity is 12 m/s from the north, what frequency will observers hear req ::pe+v7qnwho 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 n(lq3 +fr +(6r3xquyuhxadv0 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 Machj h z;t.bjg udw/q622c 2.3 where the speed of sound is 310 m/s (a) What is the angle the 6ju/bc2 thw .gdj z2q;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 0.k6slo.fp ol2 y2/cwcbz *ll a planet where the speed of sound is only apl ol/lc o.6.20lks yfzcw *b2bout 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/ erk(qtz2hpebybr +*.(ys/ izw hi(7*s strikes the ocean. Determine the shock wave angle it pkebzwr2b7h*t+. yhy(*((z qeipris/ roduces
(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 -alejd3 378 *t3xacn sdx* kvv$/theta$ 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 exa : kq.ps tej.o5qkb7;gctly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the . gspbq;kqk57j t.o:e 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 d / th5 6-by3ritu:qqzievice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum iy3q:ubit/6h5t-qrz 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 arsu4r 1k+)w 409sbl w u /hufq+vcm+vnce there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disgu2uoesn j v2r+6w) n0play called a sewer pipe symphony. It consists of many plastic pipesvwu2)ej 06n2 nour+gs of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a persg1ks2zf ) revwo9dz;njw6r2)on makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosqui) o2degrww6jz2 1vrnksz;f)9 toes?    dB

  What is the resultant sound level when an 82-uru1+ixd-3rg 7mp*eb dB sound and an 87-dB sound are hea id*e3ubr 7u+m-rg 1pxrd simultaneously?    dB

  The sound level 12.0 m from a loudsp -o :mqvp 8e2hed6oh+weaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in al-d 6:e+wmhhe 8o2p oqvl directions?    W

  A stereo amplifier is rated at 150 W output aq9d0 7:*y;hvuba kss ovq /i.r5gc9d at 1000 Hz. The power output drops by 10 dB at 15 kHr sich us97qv;gdv q /oabky*d:a95.0 z. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft cejt+ie9jch1 wl n6f(6q (;cqtypically 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 h6e(q6 nw+9ccqj ;1flc(tiejear at a distance of 30 m from a jet airplane engine?    W

  In audio and communi;o u r+2okqqo(cations 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 to a frequency ,ml go0opngi9 6f2v sv 0k2u6p4cieg,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 vi9 jsmdjf:-cyi 05 5(cu ;nuhqmxxt/o :olin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass pe :jxc:5xftcjd0usym - u(hmoi5n/q 9;r unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with 8lm2o2ool l9c qcsm1/water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate womclo l2sl12c9q8o m /ith 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 *sz 6dirpnm4- mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tez - n*4sdi6mrpnsion 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 ob+g r6tax9nxn1)i tcl 0served to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming frna;z8p 6mo9iw om two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequimn w6o89p; azency is, the person moves 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 whiu:u)sw* 7 .c xiegxfs4stles. One train 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 tufx)g u7 w.xe4sis:c*he moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After 9,h)obdgkbpw71g/c*ngm p p; it passes you, its frequency is measured as 486 Hz. How fast was the trainbk;)gdp,c *7wn /o1hgp pgb9m moving (assume constant velocity)?    m/s

  At a race track, you can estimate t a3vm;/t qiak+he speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. Howam 3kta;/+ vqi fast is it going?    m/s

  Two open organ pipes, sounding together, pru1bx,+w5 cnv.ckd p1 zoduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lonx 1p,kd+5buzc.n1w cvg is the other?    m

Two loudspeakers are at opposite ends ozn2 x:w 8p*)7;,nlxfm sdb lkhf 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 fro klbx;pz:nmw7d,h2*l) s x8fn m 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 aortbhj :d8f/ o-fja is normally about 0.32 m/s what beat frequency 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 wd-j/j :8fofbh ith 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 mx1 y, bff9xwsyd(ju*8 oth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the freq9d,sbu y ffx* (8jyxw1uency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency soji 0h *g3jt(4z1bhtpmund pulses as it approaches a moth. The pulses are approxim301( z*tijjmhbh g4 tpately 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)w/ eno5+wkru xup ec//:sf3ph5t :)oz was once used to send signals from one Alpine village to another. Sf x) wukp:/h35 re//nt5 ewczopus+:o ince 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 which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo liv hk)w(koz- xq/ n8uu.stening 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 long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for t q8xuw.u z(no-/k hvk)he standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendebv p2ay 40az)vr aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the othbv)a0 2 azpy4ver hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear pmg jv;m(v0 p6at a frequency of about ;v0( 6vgmmjpp1000 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 the sonic bo3bu, kb:6ck)mt+v d voom 1.5 min after the plane passes directly ove mo tc:3b,vd6kvku b)+rhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 61-m1dj*u5zdkd 8 5irtzezm uis 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