What is the evidence that soundl vt7 pfp49xa0 travels as a wave?

What is the evidence abnx2ey2k w18 that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attachin,/ox0pjl+yhb z2g,jg r2,k 3jj4nna rg a string to the bojjrnpbhj,og24/x +3,akn,j 20g r lyzttoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wattjs7n7m)*/zz fh:3thxm bo u- er, do you expect the frequency or wavels:) /3j7fmhumxzh -tz7bn*o t ength to change?

What evidence can you give that the speed of sound in ak6 xa - ,djgh22jsi2yair does not depend significantlygj-sj22, ihykx 6d2aa on frequency?

The voice of a person who has inhaled helium *h 0tu biq.l9ila 4.oksounds very high-pitched. Why?

How will the air tempe ;kih 2r8eabsk;5-d01kc cwcjrature in a room affect the pitch of organ pipes?

Explain how a tube might be used b7gk(u9u r8u.;( sxpawnj+ k yas a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.)x p sgn7a(u+ uwk98j.k(r buy;

Why are the frets on a guitar (Fig. 12–30) spaced closer togwwg rgrbd 4fi1f6s60 hp39 8bdether as you move up the fingerboard toward the6 p618b siw49gdf 3rh0bgfwd r bridge?

A noisy truck approaches you from behind a buc/:8 buq)pbo xilding. Initially you hear it but cannot see it. When it eme) u/xqbc8 b:oprges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfer 1 jfkn29 jaf;*rh-7lrlc:oorence in space,” whereas beats can be said to be due to “interference in ti- h:llo rff9k 1*r7oc2jnja;rme.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointscc2r;92d sirt D and C (where destructive and constructive interference occ2 r;2rcdct9 isur) move farther apart or closer together?

Traditional methods of protectingspmalf7+)zlob( fgn22: 9fwq5cgdm* 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 relativ5z (f )fm7cbdg *2fw+nmlqg osal9p:2ely 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 addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves9h.4dgwh;2 a )nfju4pwtu hj 3 shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves w j gd9uwuahn h.)4wtf;2jp43h ith slightly different 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 d4vwj ngva4/ h .zv2cu+irection, with the same velovu2vj h4n.v/a4 cwz+gcity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a persp(8p cczx) p a1xpbi1.mp20v. xr,hyion at rest with respect to the source? Is the wavelength or veloci(pppvp)x0 ym.c8i1a.1pr cbhzxix 2,ty changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitog8d mv* s/lvx6eh /.etbh+h8ar is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hvm 6 hte*b8s8+lx gah.ed/h/vear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of-g) rlo)mp7n6ckjhs7 a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengp j)smcok nh6l)g-7 7rth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the si0rv fcyim w1c*ad )5r2de of his ship just below the waterline. He hears the echo of the sound reflected from the oc )ym 0i5d*ccfrwrav2 1ean 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 wavelengthszg,.s1t(o0bq fw o9ou 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 a foggx blu gi1aw.-+y day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33g l+w-1 bauix.). 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 makes when strikiv hq02efn +/bbng the wat0 bf/n+q2vbeher 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 uli d7 b80ggyu,6- osithe 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 awa i,dg67yuisguo80l - by did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ovejjkb53 *c spq-r one mile of distance by the “5-second rule” for estimating tsk j b5qj3*cp-he distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the qw0vak32u rp- 830jumykbm; zpain 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 levey5sy:eft6qz3wy: *w3)tv iunl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sou4a2gcy*o8 p ycnd level of 95 dB when fired simultaneously at ay8c oygp4 2*ca certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wit x4xp-nscx)4ih four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? 4n- 4xxsxp)ci[Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal, 4voqi- fpjkk)uv)7b-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of),j7 vvboqf-k)i k pu4 intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of so.n f((5rr kilxund from a person speaking in normal conversation. Use Table 12–2. Assume thinrkl f(x .r5(e sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strike7 lo;h ;mysy:n) 9qxvhvo48rks an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifieru/ 39c9d *pz9b 6s ;kkdkg(fi.gsxskn B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a po(9zdbp/xi9 s.9kn cu3fs;ksk kd g* g6int 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 when placed 2.8 m in front of5l g (p1zin1nkc5o3pr a loudspeaker on the st inzr 5l5p1kc13p go(nage.
(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. What is,lm(o h sxgklb2sr6ml,3dm/ 5 the ratio of the a ds6 s(m lk2rm5l lmgxob,3/,hmplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)9iqd:l5ptzch w*k3ai..t ;dv by what factor will the intensity increase? Increase by *hdkc z 5t;qai3p.i.l t9:wvda factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement a17up /tw rrf+qmplitudes, but one has twice the frequency of the other. What is the ratio of theqpf 7 u/rw1tr+ir intensities?   

  What would be the sound level (in dB) of a sei+y3zc-b4r9nyz7 0sqvs o*qa9lmo*gk, t 7pound wave in air that corresponds to a displacement amplitude of ,kqcg-to+4773 ny*l9 s i as rezz0opqv*bmy9vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wha8i;y7j iuo:-d4hv lkan2vw 2w t sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6;v:lnv kdja 8iwhwo-yu7242 i.)    dB

What are the lowest and highest freque b;u3hgh/l5yq4(1pq d s wby.pncies that an ear can detect when the sound level is 30 dB? wy5b pl gdbu/.3y 4ph;( 1sqhq(See Fig. 12–6.)

  Your auditory system ca/9(irf wsg6q.ym z 4wyn accommodate a huge range of sound levels. What is the ratio i6rf (w 4.yq/wmgy9 szof 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 frequency obxesg6cv ) mpa6)a/x-f 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?c) p6smv6ebx /- )xgaa    N

  An organ pipe is 112 cm long. What are the fundamental and firstvaooc mri * i6j10 w)//qgm+ce three audible overtones if the pipg/iqv6+o)r me/io w mc0ac1 j*e 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 acbd,hahf6 6, bjross the top of an e, ,af6bhj dbh6mpty soda bottle 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 r 4da1- hkyuw*)hpo h4open-tube pipes spanning the range of humandho p)yh*-ku1ahr44w 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 Hflu3i2 1e3gsv-s0uhtr. 6isqz as its third harmonic. What will be its fundamental frequency if it is fingered at a length ofe-ui32 qf g0iusr 3l16ss.tvh only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 1hu) :ht-g:5if c )y9jy 0/3pmbh5zciz lektnm long and is tuned to play E above middle C (- gmz )h1ky5t3h unz 5/:i ht9cp:ije yf)bcl0330 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 middleq9u iy/qt0w1d dnx/;h; h)jtg C (262 Hz) when u0x ig;1q)w/ dt qjh/nh;ydt 9the temperature 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 20 b ,biy(g6uc2 i$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o/q 7 wbhoa67/qm8pgiof the flute in Example 12–10 should the hole be tha 8/a7/ h6oi7qgowmpbqt must 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 264 Hz, 440 Hz, andi;tqa2m cj-r, w. :n vj/lf,re9mxt9d 616 Hz, but not at any other frequl,feax; rt:2 i,.r wc9t jdj9mmvqn-/encies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonaikpf7 yp+ ksqjx7 -mb,lip.88tes at two successive harmonics of frequencies 275 Hz and 330 Hz. What 78p+p qbim 7xp-fy .,lk8ki sjis
(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 dt:v(iy.t1x5e1.jmqw hni2 *d yn0u p$^{\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 aj32r1*j qx0slarnc m yw3npo/e:;z 3m 2.14-m-long organ pipen3y:r2lscw;p 1 * 0r aoe3z3mnjxjm/q at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It idt6x0)ptu6v f57oint ei (ye 7s open to the outside and is closed at 6tpn fdve5 (et60ti77x y oui)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 graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, oneb0d42oxhu2u2vl;z d e*/m hpk of which is sounding 440 Hz. How far off in frequency is the other string*b do0 ud2vx2p2u4e;hlh /zkm? ±    Hz

  What is the beat frequency if middle C (262 Hz) andh6(9 h1 nrdtbwxbn2ld/d yo(7 $C^＃$ (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 yf *i.yn 5f0 d2e3nkmmat 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurd.f*i n 5kfye2nm 0y3ms when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning foro;mia(0 nj:.yxka :ew k and 9 beats/s when sounded wit0:a ;imj(k:ey.an w xoh a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fqddax2k *nkb iyxn07.)bee0 :requency, 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? [Hibny be)7ie: kkxnq 0xa0.2dd*nt: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pt gd +f7d/nn:xf4(t)twa1m 1ox sp:vbn q (2rvlay middle C (262 Hz), but one is at 5.0°C b td+xfn dwxo 1rfvnstmq7a( vn2:/p(1:4g t)and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has ep 9*mi cij2m*5;at wxa frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequenc* *9a; p2jxwe5mitcimies 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 5w+fefq 5/u+gnana w77:nt u tapart. A person stands 3.00 m from one speaker and 35 ww:f+5uu 7a n+n7 ftqnetga/.50 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 s/9 e(xfwb*yq ikrfc 6uqb:)(bave w(,upposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, whaw f)qaf b (k6 e(bbeqiru,/v (:y*xc9wt 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 a( 9q)uhw xzi1lir. How many beats per second will z9 uwlxh(1qi) be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at hyg* 7q+sw)vm rest. Whatwv ) ysqg*+h7m 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 fikz6xd82sd: itb9-4m ect/ktmre engine whose siren emits at 1550 Hz moves at d i 6mctmxb:8st/ed tz-24k9ka speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift c6r7f5iyyomm/ i.im5 06mrfw in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you i.mo66w5 r5m7cyi /0 fi mmryfmoving 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 r+wyh d628tdmthe same single frequency horn. When one is at rest and the other is moving tomwy 6+dh drt28ward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wavbkw-t m m;ld.;es at 50.0 kHz and receives them returned from an object moving directly lt;wm .dmb;k-away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat ;7uz gf6g3pvl2 d irp-emits an ultrasonrf3;2ggpu v 6z ilp7d-ic sound 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 experiments, a tuba warkj jv+ 1x0 ,x8e8p.urpimu7j s played on a moving flat train car at a frequency of 75 Hz, and a second ipjk +vr 8r8,i.1xjuj 0p um7exdentical 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 ultrasound wa ytb;w 7bg-wb5ves 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 flogw5 b-wb;tb7y wing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic +: v-ucxzph2q 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 wind velocity)::fexdvh/,+cpc+ie t(u myq is 12 m/s from the norc,c q)v ui :f(yxd:emth/+p+eth, what frequency 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 mlr,ua1hj+e ep5l 7;r goving 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 ( smyx/m(wx*e 1a) What is the angle the shock wave make m1ex/s(y*xmws 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 whera0 w)g/gwr:o xe the speed of sound is only abowgo/gr wx 0)a:ut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oce*1q1he, i di/n7md(xcbg v6fkm;ric;an. Determine the shock wave angle itn;xdim/c hv; fb*iq1 6eg7r,mi( 1kcd 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 ,t;1xfp*h: jjqm86 oeqb1 o klzc7ah*$/theta$ 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 the ground f kaxea77ty 7:i*j1 vc vpr-;mklying faster than the speed of sound. By the time you hear the sonic boom, the*jye7ax -kakcr7v1p i ;vm7:t 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 iss(v10t dx; isound pulses downward from the bottom of the bos( tivxdi 0;1sat, and then detects echoes. If the 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 ajx9i8g99z w;7uu1g xwkh/w adre there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a .upte7n wcp,5sewer pipe symphony. It consists of many plastic pipes owe,7cpp .tu 5nf 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 person makes a sound close to 2lg7yiqg6a7 y the threshold of human hearing (0 dB). What willy7 2l7g6yigaq be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when a zfi,2zvno ,zj o9+bu(p7go z(n 82-dB sound and an 87-dB sound are heard simultaneouslj zz o,v,f2oo7biz+(z(gu p 9ny?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wfk)0 0xq kk8in ds9)doqh.iz,hat is the acoustic power o d q,dx .)o)s f0ikkiz0q8k9hnutput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rat ravn 9mall 9e3f1urm,wgsk- /;)*yeted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts aw) vyk a;r-l1t rm*/9l ef3nuesga9,mt 15 kHz?    dB

  Workers around jet aircraft typically wear provutt-rxpd)/8 iv c .o9tective 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 effeito/9tpc xd- uvr8.)v ctive 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 communi7zh0v5 p;j gyzcations 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 tunedxmef5kb.y m 53 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 fixedxf k 83icew2mn(n1.fo7xgf2d points with a fundamental frequency of 440 Hz and a mass per unit length off8mni3df7wnx22.1c ( k gxeof $6.1 \times10^{-4 }$ 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 oi+7u,;nde 4ex(qg pdrpen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard 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 d uxi7 req(dp ,;+g4nefork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is openjr ;2 it qocywg2,lp:: at one end and also 75 cm long. How much tension should be in the string if it 2wg:y;:oqict , pj r2lis to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was e cu3;rn0qr fut53 cn6observed 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 froy4 rb .92ebhghm two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what.brhge 9b2y4h the frequency 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-icnixn;p 0jq- g14 fi1Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency whef01nqgn j p41-iii xc;n the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 g08ua0g v:mwg Hz. After it passes you, its frequency is measured as 486 Hz. H0wmgu:80vg ag ow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dif16fzjsh )2 coo8r,ll qference in pitch of the engine noise becl8)o2hs,1 j 6zoqlr ftween 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. How fast is it going?    m/s

  Two open organ pipes, sounding toc6hegl*jkb*+-l:dvo8f amgo/ (e *nmgether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How 8:hl+*vm 6m*g-f/ neab colgejk (od*long is the other?    m

Two loudspeakers are at opposite engdyytk 2e ,bn ;ccy7;s 1o4) wbl,q0glds of a railroad car as it moves past a stationary ob; 7g4ce b,0sdk )ylcy,bntqg;o12l ywserver 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 have passed him, at C?

  If the velocity of blood flvyxxe(*u y4ad8 ;figq;n.v f;ow in the aorta 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 thaty i 8;;;4qx*.nuxa(vgy fvfde the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mothnvva/xcn j +, o( 0chxrwue+9+ 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 o +/v ren(oc+0wh9,u +xcv jnaxf 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound puw st e1 538mk li*r0hr4wbe4tulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 t*s rk rhu wm038itw le4b541ems long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villa bec./nc9hzl9e/uq:x9c. mknge to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an opeqlm9e zcukcbhxn9 9.e. :cn //n tube.

  Room acoustics for stereo listening can be compromised by the mexfliw4em5i4gs7l( 8prrn1 (a3x, p presence of standing waves, which can cause acoustic “dead spots” at thepe47rw(slx3prinm81 gf xem l5 ai(,4 locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves al+eclb0xd,cd ov 2 3y8 long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can bc 2ce+l8yldxd o0vb,3e 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 d0rhabv )p;*fear at a frequency of about 1000 Hz )v*rp;ab f0 hdis $I_0$ = $1 \times10^{12 } W / m^2$ 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 a9w:bpl/(5rwz2 s i oq(srqrc,t Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the ls 9 qqc/o,:w2bw(irrz5r( sp plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15kw2lm3iha ;s+v ,)yza $^{\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