What is the evidence n) zq (uz-yim)that sound travels as a wave?

What is the evidence that sound ipbh46neocq1 3s a form of energy?

Children sometimes play with a homemade “telephone” by atta /oeqf /sy+ uex4cm)nq3 9nw-eching 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 q3neqeyfe9 o ) cw //-smu+4xncup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air intc/r/w e9 nm)d:-rf2krru dwv +bit),ao water, do you expect the frequency or wavele ):rc-/r /bdu)m+aek2rwiwr ,9ntdv fngth to change?

What evidence can you g/ jh6k2 vxw7(,eua foiive that the speed of sound in air does not depend significantwi7j(o/, kx 2av uehf6ly on frequency?

The voice of a person who has inhj9;9h de ( cemzq+nua;aled helium sounds very high-pitched. Why?

How will the air temperature in a room 5ih udc.a( io2affect the pitch of organ pipes?

Explain how a tube might be used as a filter to r bllas8 p .wlg,xty1 2w0 x+0dlihb1b76mry t2educe the amplitude of sounds in various frequency ranges. (An example is araw 1y.87+l1lp t0y l62bb0 gwxsl2 bxhitm,d car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mos79k2p r9 l0*cb)4qumvy wejeec.t* v ve up the b9uj)* 90 lpy7tc .s*2cvrewe4kq mevfingerboard toward the bridge?

A noisy truck approaches you from b 3dg6s 5:gts9;fwfxs .rvi2 ubehind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly:5x2rsgu;wvfif sstdg936 . b “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 “interference in space,” whereas beats cgqxx:aju6 h*o)4x h)oan be said to u)*)oj gxo6qax: h4hx be due to “interference in time.” Explain.

In Fig. 12–16, if the frequen0n b 7b44ltvkncy of the speakers were lowered, would the points D and C (where destructive and constructive interfeb 7bkl4n v0nt4rence occur) move farther apart or closer together?

Traditional methods of prjfqq+7ekng :71nyg )yotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block orgejn+k y 1)gnfqq7y7 : reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in 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. Eo8lrzle+ ydzqtgd43:8k96 lnach wave can be thought of as a superpositlgk 38yt zd qln+ 8l6roz9d:4eion of two sound waves with 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 observerja3ac8 p-o4 yx move in the same direction, with the spa a8y4oj3 x-came velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heailfj c e7p7a5q;q23u yrd by a person at rest with respect to the source?e72q3 ua;c jl5iqf y7p Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitjd2tj+c(g )j j6g jgd8or 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 whistljggc j jj6j (2dd8+)tge? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ec5v 6c kyrlm*s p;+6gsxho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s 6skgc sxp6vymr *5l +;after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wd mm, y+ sdi : rhy18lofjg8d.vat1g)-aterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with dedjdhy)a.m88g r11-: o tgf+vyis,dmlpth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at pm:**g5 he4m nc nsuz;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 j/lf hl /gii:i5ust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How muchliil /5fi h/:g time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the to asno,; u4oei*p of a cliff. The splash it makes when striking the water below is heard 3.5 s later. Howaouis;*o ne4, high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concret;hwi.tfr3t e 7e pavement. A moment later two sounds are heard from the impact: one travels in the air and the ot7.r ifh3t ;wteher 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 madsp3n bs*/s.zi0qzag.le;xv ,e over one mile of distance by the “5-second rule” for estimating the distance from a / be vgsiq*.;3nsz,p0zsxla. lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensityoxzbl+61.wf i of a sound at 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 intel2 x10rsm* 2fxuq: 6poaj2nxr nsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when h2vbm 6a cot;-cg fm:.fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Addfo .m:cvtm c;a 2-g6hb intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wiw1uhrm1smh6 u s toyi(u381d3th 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 dos8m31 od(6u1mut3y1 wrs ihuhwn all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is ac5dbv uqw1,* ;jr .vqsaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background n*51aj v,b;uwv.qdc q roise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe y./m)h 4plli6haow z,r output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spw/ i laoh zpm)6y4.,lhreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum dvdd9(wkl ivv md/* *i e5/cz*zwg4c1whose 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 z.l*yfyw ohykb 5 (2r ,vzc(y(is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m r5yy .k(( *l(z,z2bw yy vfohcfrom 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 wi 4uxai88u dh 24(ss*)apoh)cd9gfjfront of a loudspeaker on thefg )w4uc 8u2s j8dxi 4*h(oa)dia9s ph 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 sgah c1 3:-dvib0q 2grbound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 1i gv -:g1rba3hcq2d0b1–9.]$\approx$   

  If the amplitude of a sound wave is tripled,8q8f0 is *efgb (a) by what factor will the intensity increase? In 88*igfqf0esbcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displ(-2 i )m5gqorwd:wke-jfmau6acement amplitudes, but one has twice the frequency of the otherug q a-d(-mrwi:) e5ow6jkf m2. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound w vpzq9+ itgv kiffs (+7oa-+i5ave in air that corresponds to a displacement amplitude of vibrating air molecules oszf-oaq( v5g i vit9fki 7+++pf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 10jv66qc2jmt s50-Hz tone that has a 50-dB soun6q2 c5s6m tjjvd level? (See Fig. 12–6.)    dB

What are the lowest and dz um)w6lkvfr 86b:k f6zb15 ghighest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6frwzvz6 5b g) mfb6u68 kdl:k1.)

  Your auditory system can accommodate a huge rangem(hok/0qiw(c9*b o k c of sound levels. What is the ratio of hiicm* kq/ch (okw9bo(0 ghest 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 frequen;yw8/il iie *jcy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string e*ji/li y w8;ibe placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three76 rg) 3iq kgca(rh-iv audible ov(a76h ig3q g)iv-rrc kertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect 3x/x*2a a3ft7/y 4ir sie 3tgk qkggt*from blowing across the top of an empty soda bqxtsg3ta etkx g/iry*a4 733g2f i* /kottle 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 pip6m;*ny n odx+a3fdd i+e organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz) m+fn*;i3ondy6x+add, 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 harmonic. What1iof xx750 dy5 *odu4ycwf+nw will be its fundamental frequency if it is fingered a4+*7dff nycyuow 5io0w dx5x 1t a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plfa h t5l9kn0y6ay E above middle C (330 5kfyh9 0 6lnatHz).
(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 pip b j ct7hq2 k9sj1a,eo 8/wjaovk6)4pce that emits middle C (262 Hz) when the temperajs/cb 1ka 6wh)4 7ooc j2a vt,e8j9pqkture 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 ;oqd.2.pxcrs 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fl:jr e-eoem *6cb*s yps *f2j1mute in Example 12–10 should the hole be that must be uncovered 6e r-*mmes *cpyjes:f* o 2b1jto 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, 447 r5k/i :loapn0 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. rl5n p/a7i:ko ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m m)xcjbi 63.amlong is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. W3a6 )cbx. ijmmhat 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 a0iuxd/5 d2t;jsag +z $^{\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.e0/oa )/pavg n z/ryo414-m-long organ pipe at 2n e)/rzgaap v/o0o 4/y0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm li9 j/h pm:9lh ka:x3goong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the aud/mj:x:9kha3i 9olg hpible 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 stringsk 7n)ry(0t5ud j g)gbq, one of which is sounding 440 Hz. How far off in frequency is the oy5t g )rg) (jbd0q7knuther string? ±    Hz

  What is the beat freque,wul vbt83)lm ncy if middle 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 operates at 23.5 km7 da2ciude vh86lr;f k:x3/bHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard /2edabi;l8vkduf76 x3r: cmh by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning ms o84:g-f4bch eq4kz b e,xk8fork and 9 beats/s when sounded with a 355-Hz tunineesb4-kzo4 ghbmx4 c8 8k:qf, g fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 vtioj7 g pp2z8*f8y.r Hz. The tension in one string is then decreased by 2.0%. What will be the bea8tgfy.j7ri z8 p*opv2 t frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fvty7,se4o3sa lutes each try to play middle C (262 Hz), but one is at 5.0°,y3vssaoet4 7C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, r7c8go +2iodw A, B, and C. Fork B has a 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 frequencies are possible when A and C are soucoi 27w od8+rgnded 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 speaker and 3b cfhd 4- mzcsqtefi2ac8.+(v7 j 0h:q.50 m from the ois- bt2fc4efq7(dh c.c8a+vm j :0h zqther.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132e0mto f :ln(ru54x km2 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratm:n20u(rmlfk5x t4 eoing 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 2.76 m in .j)lvvsys al j;z53uvqy679cu0ej (cair. How many beats per second9 ;0 c uc)(eq .l6yjljvzusa s37yvj5v will 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 15gc+(b +6gle*byzkax (50 Hz when at rest. What frequency do you detect if you movekx+egay*( 6cl+gbb (z 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 wxr*.j5qk t77p b)s xx 0wiint;hose siren emits at 1550 Hz moves at a speed of 32 m/s ip ).q0jr*5xbt 7xw x7;ktisn
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency ifj8pju :r9u d,x a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exar9ju: pu ,jxd8ctly 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 0wdb k pk5:pb6equipped with the same single frequency 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 5.5 Hz. What is the frew50 kdp6b:kpb quency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.02dyaz6mtl02t kHz and receives them returned from an object moving directly awz0 2ylta t2d6may 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 emits a36xhd j l0dxogk p1m0 a9oo .o3fb b)iyc9zl96n ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected9l1gd lk6yoo 0mo 3d6x)9fxhp jb9oi z30ba.c wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movl du :;6(f+, uwcszmtd0rpj lt5,ze:ping flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest z ,;sjz0dl wte tfd5 p::uclp6+m,r(uin 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 waves to measure blood-flow spf4 63v1plxw knw7 l/sneeds. 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 flowipkxnl1v7w6w s/l43fnng in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ulnjlwg o rq5g.dsnd2s ( kck64mc;,u ,7trasonic 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 is 12zk uwn * rj7.tl(:.ts yqk(h;v m/s:(kl.u7kn(wqty s v* ;zjh.rt from the north, 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 moving on land if its spkk0vb8pkfx:if3 t erl1- /h)aeed 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 spz3fl+g2uvd /ke a: e6ej1 as2feed of sound is 310 m/s (a) What is the angle the shojv:zue6gsa1 2 2e ea+lkf/ 3fdck 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 0mpdqtu,puzk9f) iu 2 5w; e9xatmosphere of a planet where the speed of sound is o zm ukwp9ie p ux9uf)5q;d0,t2nly about 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 ocean. Determine the shock ww;zc ityx:t2 + e1e70:cyu wsaave angle it produ2e;0xcet w1y7ystz u::cawi+ces
(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 sqc9 -oq yd-8g$/theta$ 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 groukdvh(5 q*+hlmnd flying fa q +5lh*(vmkdhster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses s )(hy7sibw6s downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is t s(sy hwi6)b7she minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there tv33ft) z k;1puj6,ruvt )e gfbk/1cain the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer 1/pw1jah4 p3ri8u (wms an8rqpipe symphony. It consists of many plastic pipes of various lengths, which are op81 1 iupsan qrhm(wpjrw3a84/ en 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 thrm:; l wh-d:ntteshold of human hd- tth;:m:lwn earing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soun,-mczj*n:m.e nz jzf 8d level when an 82-dB sound and an 87-dB sound are heard simultanz*men: .z,mjjn- zfc8 eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.d5v1hk knf:+l What is the acoustic powen+5 lkf v1:hdkr output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1080h e vf1n37.snepwkdiqs( (l00 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 1k( n1dfq.wsn38v7iepe lh0 (s5 kHz?    dB

  Workers around jet aircraft typically j(yvq ( 8nnhv:2an1ekmgor(8 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 h8 rq:eygjhn8o (nm2 ((akvv 1nas 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 communica*yu6w- 5e8f2 sejahu lpeyj )jxz/-*qtions 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 violih*-dz/ 0de7)g6z5wbfj h-3pnwvcji bn 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 viowo1) awya etrsy- .q )6-osbs+lin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of .- ws+orswbs a)6qoy- )tyae1 $6.1 \times10^{-4 }$ 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 i* ukt)h/nmj+ q+b qk+wnto vibration above a vertical open tube filled with water (Fig. 12–35). */+mb)kutq +j wnqhk+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 fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is fs/jepjk5- e-open at one end and also 75 cm long. How muc-jes kj5 pe/-fh tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed ,afekn79yrjb-vn5 7dw jkx79tt3;h l 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 from two sourceb(te;;q )kai8k93 ice6hsab qs. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What kcbe(qk83eb;hsait6i q9;) a is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the s i p1v.pu9hcd)tationary train hears a 3.0-Hz beat frequency when the other train1h 9cp)pi u.vd approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as7ny 8 preq5 2q6jaeb*rv 149ta9pizd g it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume consta8q rge9piz2d1a n795pteqjb4 yv6*r ant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenim3;teowqnzm 5,d * l.jng 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 oco*deqzw5l3,nm .mt ;jtave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toge22im(qon00 d:bl bybither, produce a beat frequency of 11 Hz. The shorter niy2bmb di00bql2 :(o one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends o*7 7sdbmxq j*xf 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, wha 77 xsj*xdmqb*t 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 b ia6v uhpeog+ )/9bt4qlood flow 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 that the waves travel with a speed +pt4/be )vhq 9uagoi6 of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.nrrc-o ei:hj vxb+v0,)f r.:s5 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)rn js eoc:vr 0rf+v,. bi:hx- the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequsrg5j:i 0nygv4v.b2npr.x x: ency sound pulses as it approaches a moth. The pulses are approximately 7n x:rgs gjyixbvr.2 n 5v0:p4.0.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sigp.* 22jpe epnpt+k t)snals from one Alpine village to another. Since lower frequency sounds are less susceptible to intnpttp22 jks e+e*.p)p ensity 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 stereoz8 j97z.xiidlpo0m w1 listening 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 21 zzwiiom9x.87lp0dj .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 q4 y q wtzkyrt:4:1y(ia long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm:ky t 4qi4 z1(yrwq:ty-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 thresho oe3 mf*ivd8(kld of hearing for the human ear at a frequency of about3e *(f8dmvo ik 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 Macyg1 lakug 3u6s7n1g8- rr8ipz h 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes direcnggs 8u-rr1gu3yz 7 k1p i6a8ltly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ;/v 6yus9wi8 +gkyk wvis 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