What is the evidence thaxz oah(): n3p:3torggt sound travels as a wave?

What is the evidence that sound is a form of3(t5ut:l(*qv)evtx akd n5 gq energy?

Children sometimes plal6tk e:jsa 5me))sk xx07 t8ocy with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (F8k:x)x)j mes7e tk6socta5 l 0ig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wate it9a kkle(-zyue1-0c(* o2kky5kn c xr, do you expect the frequency or wavelength to changkl (e(kyz xi-y5k 9*cto0 12-anceukke?

What evidence can you give that the speed oftg1u bn c7a1,g sound in air does not depend signif c,a1ugbn7tg1icantly on frequency?

The voice of a person who has inh2v2p8ml v x35r o-rqa7jz7uotaled helium sounds very high-pitched. Why?

How will the air temperature in9r.af a)p6 +iov/ pbasn7 at.e a room affect the pitch of organ pipes?

Explain how a tube mighx0n)+lrv ds h)az8w r9t be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler v+n9 8)drxah )w0lsrz.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togeth;: ffwwm3xn-1r 4u-a7ksd*ob8koh xt er as you move up the fingerb34:1kr 8x -ftund mbo;s k7* owawfh-xoard toward the bridge?

A noisy truck approachesa dcm7lsr *r6etyt8.4 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 mosy6c md*a r7rtle48. tre of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due 3 0clzr88iuan 2t:iypto “interference in space,” whereas beats can a ztnlp r03icy:28 8iube said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency rifz 2 j2dp i6rqf8m7-lz 7)efof the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer tojrzi- 8mq27f7 fe6 pr2 zdlf)igether?

Traditional methods of protecting-: +g9v 9t.jhrw gkckk the 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. tjk9r9k k+: vhc gw.-gInstead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can bcdaop e- ojo(mo3,8- claw5o6kq90l ae thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–adowm qlloo0j,c 8 p3eokc-(-ao5a69 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 directiojp2pg4na oy8 agm4 :-mn, wi a8ypnmojp a4-m:gg2 4th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bp5c*l6hfu1 / tpp4jlo y a person at rest with respect to the source? Is the *hlf5topc/461 p ujlpwavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A5e rnk *rjcq(*lpol(7 monitor is blowing a whistle in front of the child on the ground. A r5 nqlpce*((7ljrok* t which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines thetc,* x1ew xx bnbc6b.8 length of a lake by listening for the echo of her shout reflected by a cliff atec* b6t,1xwx cx b.nb8 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 just below the waterline. He hears tt-3 6yz , w;ggniae-bshe echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this poing t-;w,n bz3 6ig-esyat? 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 x45ki1 hc5x9i c2zjrzs25su o 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 a fx z,f)x 50q* ci6xj0nabyhw d6oggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How mucbfyxx*z) wch6n,d 05jxiqa60 h time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the t7e0jp6jn7otuuo.x q 4d, o k(wop of a cliff. The splash it makes when striking the water below i, j4uu 60xt. n(o opek77doqwjs heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge ston-lnvd)w y;nu.x*l ,wc e strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far n ,wyw*.vx -ulc;dln)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)(/u5q 0 l-xpub uubnr rule” for estimating the distance from a u05nlu(qb bx-urp u)/lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atdz,g q2taozzp;fy4)e1jsv5ajf*d m .tz2 :7q the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity is is(-72d gqe n+wnsjsvudb-iz8qc3 99 $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ataq l i2de-+pa6qvqu6j ,gh )qpdv7i9k0( ;yoc a certain place, what will be the sound level if only one is exploded? [Hint: Add intensiqqo2i0j6-d9a),hie uavv c 7q gd6l; ppy(qk+ ties, not dB’s.]    dB

  A person standing a certain distance from an airplanesmv5k , r)ki5wqiy1t1z6:qzl with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB.l1i5 iq qsv6m1kwz,) t5rzk:y 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 dl2( 7jb5upew tB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noiseebw5j(7 u2t lp for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a5 bf x92ayv3qx1i q5kf person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly3i1q xxq5fv a5f2bky 9 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 wh6q4 6 vsb5flpgose 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 nd ,h6m0x3y yvrh r;z8rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from r68;, yhxv dnzmy3h0r 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 d5mnv73isz j7fw7( rr m1hsak et:f1y8B when placed 2.8 m in front of a loudspeaker on the stsir z(hrnwjt5 e7 ma3ffks m7:1 y7v81age.
(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 leve:ul53del6vq3zu 7t tpwy -/fdl of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this tt37zw :l 5vupq y- 3e6dduf/lamount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a so-mt1t :b3d w kbvxi0t*und wave is tripled, (a) by what factor will the intensity increasb: 0txt*dmwtk-31bi ve? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twickq,i2 a cgznc324ig;-hl pvwjbz- 98m e the frequency of the other. What z -qmv;ibhpk 42 3aj82-9iwc,zl ggn cis the ratio of their intensities?   

  What would be the sound level (in dB) of a souj jfy tio)9 9:sfn77eund wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz? s nu9fe)o tij:7j y9f7   dB

  A 6000-Hz tone must have what sound leve au+d( 0+adcai*yp*)smy6m wvl to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6( p+)dd c u *samyw06vmi*ya+a.)    dB

What are the lowest and highest frequenciaiei3 ,-whk,jy8i a(a2ai-o res that an ear can detect when the sound level is 3ayao-ki 2i3 i8-w aa(he, ,irj0 dB? (See Fig. 12–6.)

  Your auditory system can ac +-rsk1ub m.uhcommodate a huge range of sound levels. What is the ratio of highest to lowest intensity1 b.kh +usum-r 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 d -i0 piq.eu t5v):zsgfundamental frequency of 440 Hz. The length of the vibrating portion is 32 cmie 5)s-d q.u vtgz:pi0, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible *pvmd (dd kpoao84,8bovertones if tdmb(da8, op*8od 4vpk he 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 expecino;doo hv.f 7g58x7nt from blowing across the top of an empty soda bottle that is 18 cm d 8ni7n 5v.xo;df7hg ooeep, 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 thebp ly12xx(g ,u range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required(l, bxpuy1gx2? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a+ ws*tsiro7fdd +prnq -oe 1p;gq((o0 frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a leqs 1p (g-en0+ oprrdf( ts;dw7oqoi*+ngth of only 60% of its original length?   Hz

  An unfingered guitar string isk6ui,6 -*; ldjtruzv d 0.73 m long and is tuned to play E above middle C (330 Hz). ;,v -r6*ku6j iuz lddt
(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 middles v-ka3 intc8( C (262 Hz) when the tempera-i3atvn( kcs 8ture 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 a0o9abflr u wh 8vbu1+.t 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 12ba 1s4q ykq:4v–10 should the hole be that must be uncovered to pl14 :qqbsy4v kaay D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 4( g23k-a (vj00mqb oq v,cv neaj:kz8o40 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open oreoj 08j:q(cvzv2mvqa k-0n b, oakg 3( a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It a.i8u1 c bsee( y0fth)resonates at two succesu a0)ehs. ibeyf8ct 1(sive harmonics of frequencies 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 yhicdw-p9vn 0kz(a+ : $^{\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 +nq h 7jp1tv-paudible range for a 2.14-m-long organ pipe at 20 7-p pvqh nj+t1$^{\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 ton.47l v 231uiite* ebnog8y(ibd c2 fm the outside and is closed at the other end by the eardrum. Estimate the frequencies (in th e7gv1ft 3*oe2u(.8bbnci i 2inldmy4e 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 tryinl4bf+.iumxn) :y qeg0 g to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other qf0bl i.y)x4:g e nm+ustring? ±    Hz

  What is the beat frequency if middle C (262 Hz) and (y()-a yqydb gj 8r2tf$C^＃$ (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 23.5 kHz, while another (brand X) v,.1r7lf 66ryehj m6 k 4cgrnuoperates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, esljk 14,r66 h .me frngyrvu7c6timate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/4 twyr+ t 0agqoreq72(lqfuk;++5:, w lgbh fgs when sounded with a 350-Hz tuning fork and 9 beats/s when sounqr+f0;yqt7(5 a qrtbkh llu + :4gfg2geo ww,+ded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings ar86hhk/rmdr2xotm l :s l)+2ice tuned to the same frequency, 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 to8h)r +t:m2id2sk m6rolchlx/gether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be r4jxt:aa54ym5 o+lrb heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0b+x5o 4 ram4:lyta rj5°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 jl41k7pt cd ;dxt+9 czHz; 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 possible when A; cz79+tjl4xp1d ctd k 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)lu4o2b h4 nwg speaker and 3.)un4lghwb o4250 m 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 tpw 3cd7fywl*n;srzo6 +6oa * 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 Hzos7* zda*w 6cly n; +f3wtpo6r, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many bvuu a5ts,m2 -e/rx19,frvaahror ;5 xeats per second will be 5fm 1u2;tv aev rsx9,a,ro arrhx-/u5heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque9t+elt,2 x( 0dsc slasncy of a certain fire engine’s siren is 1550 Hz when at rest. (lstla d se,9x20s t+cWhat frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine x1y7k kss)mojg* e2(xwhose siren emits at7ms1y2o)jx( sek *xk g 1550 Hz moves 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 source is moving tyz)ch4pn(uv4o*s5 x uoward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly thu4) ho(zuxp* 5vnyc4s e 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 frequencymt27w qbof8.xj ;roh- horn. When 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.j2f ot. r;-qoh78 mwxb5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives n: srzq2mc4:y f r8lv*them returned from an object moving directly a lr42c8:n qfv:*r yzmsway from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5+/ nb ((yxqeac m/s As it flies, the bat emits an ultrasonic sobax+ c (e/(ynqund wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experir15 vkg3 bzl9jments, a tuba was played on a moving flat train car at a fzvrjk9l g51 3brequency 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses 5sn3:zf vmwl.y cvxig0 8c2b,ultrasound waves to measure blood-flow speeds. 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 sougc 8325nvb izcm.sfvwl0y:,x nd source?   Hz

  The Doppler effect using ultrassf 802oqryoy 23idji1onic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the winv:m5;4p16nrv2u zbm x m0 xybdd velocity is 12 m/s from the north, what frequency will observers hear who are locatedyx6d;m0bz4vbp: v21nrx 5mum , at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed 4qky;bh:9dyj ghsu ar515rjj98a nh6 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 3jlqqs- bh/-h yx72/yt10 m/s (a) What is the angle th2yt-y hhlb /j-/ q7qxse 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 where the speed of sou;43irt+q x5od uy9xr cnd is only about 35x9t4+xr3r;d 5cyoiq u m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave anglqq ayzva.y3v5- /2r gse ir5qaz sya gqvv /3-.2yt produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 4.zr+hxvq zb5$/theta$ 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 .r0mz,lyq) tl the ground flying faster than th) yq ,llmr.0zte 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 that sends 20,000-Hz so ufg l4sv6s;c6und pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 20c6gf4l su;v6s0 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the9x 2v zo-ux9tt human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called ah;kjyu;*t tlpyw7b tkozczq /,l ;./. sewer pipe symphony. It consists of many plastic pipes of various lengths, which ajzw7ul qt p.h zb/ ;kt /y;ykt*o.cl,;re 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 sound close to the threshold (aj8nv rsk9 n3cfjlz s+ i-+o5of human hearing (0 dB). What will b+n9rkoz3j( v ifa8s-+j 5nscle the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soun6 pb8 (bu,8dm,mufdk dd are hear6mum (b,fd p8bddu, k8d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opes ns36q12 k(p vdv9ypfn, is 105 dB. What is the acoustic power outnd6vp9yp2kfv s s 1(q3put (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpui3z) -s n. .p cpiw.j/ ni2p3zamj;qene+ym f6t drops by 10 dB at 15 kHz. What is the power/i;z2azimjj .n 3wes .n-y3)efp+p6ni c .mqp output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectiveut voc+bl30 u( devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is(tl0 +v3uuob c 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatiox:,g0*wb*m, vcp do g1vaz2ya ns 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 viol9ijkvf.(d51 9 gf1ss/vbnemhin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with abyv1-es h b4rdytfe85( df1zna1 s2*z fundamental frequency of 440 Hz ar sh1y-1zfb fdy8s e az *et(1vnd5b24nd 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 ve pkuph 5.z6+g6 cbdh,urtical open tube filled with water (Fig. 12–35). The water level isp,guhuphz+ k.c56 d6b allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open ata1btv0ar/6dh mm:ik su9o5 ylk6 3 vb4 one end and also 75 cm bslm 4636mvut/y ad h:1kora50 9bivklong. 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 obserju6 9bfo(p ox4ved 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 pur30 -csdkp3kh3y3 l scc)ato 1we tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound le3 s 3)0l1 w-cayopck td3kchs3vel is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationa81/nogyx ok*tk)ny ( nry. The conductor on the stationary train hears a 3.0-Hz beat frequency when theo1ykyxg( 8 )nn/ to*kn other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches b;g q +y vogm.;zyxl37;6vjp5wlpm4tyou is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity p4lmy+;b; g t;5m3jwq7lvpx v.ygz6o)?    m/s

  At a race track, you can estimate the speed of cars just byg9jmu upnnuvs5mc3/ * b1( hn( 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 gc3j(ng9 /1b* unm5hnu(pvsmu oes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Te-8rv,ore :ot he shorter one is 2.40 m long. How long is the other? ro8t r,e-oe :v   m

Two loudspeakers are at opposite ends of a railrlikak c/tbq */136zp joad 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/q3balkk 1p *j6ic/tz the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/so9h f0+ rcsh2k what beat frequency would you expect if 5.50-MHz u9 c2kr+hs0ho fltrasound 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 mog1ez4z xk iz5 q6 3a8g)4c )k3kyvb wtp7ml4atth at speed 6.5 m/s while the moth is flying toward the bat at 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 mottq43i 348akp v zkl)xcgk7m5ezt6z) ay gb14wh?    kHz

  A bat emits a series of higc z zo3f* lr:5bvu)k*nh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can )cz k:*blr53uv oz n*fthe 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–-un+ otdxana/g 73lq038) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns we/dla7x 0t -+gu a3qnonre 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 l f jfifcu;*sp,xq:b 1.istening 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 frequenciq. ufpb;:*1isc fx,jfes for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumid+ u /fn2so5x *mwmngkk y/kin1av75/num rod held in the hand near o1 ufyk*n5ixn w a+ mm2ng/5/s7/v kkdthe 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 threshold of hearing for the human ear at a fren ljx x*(-9bj nw84mouwh tg95o,o mo6quency of ab8 b-,m o(4hnuj t59jnxo6g9omwwx lo*out 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer zqs7z)(gi/z zp wd9x/9m m 6i)fgtm8y on the ground hears the sonic boom 1.5 min after the planeizisz6z(dq9ztpmx//)w 8mg7gm f 9)y passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 8of)8pj0yna, nlr aseghl4zjj- 6tt r*vt8 9)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