What is the evidence that sound travels as a wave?ihs;u 1es/:ne

What is the evidence that sound is a form of energy?f64w )qkb-kzg

Children sometimes play with a homemade “telephone” by attachingvt xn),io: .np 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 :n)i. ,xpnvtocup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into v r;qux) +3 yra a(0nnbbj11vvwater, do you expect the frequency or wavelengt v ybj0(1)1auxbrrn; q anvv+3h to change?

What evidence can you give that the speed of sound in air does not depenjmhmmtn; ik t4exnds7-69d t6lu+6,wd significantly on fremt 64, tk xjnmnuwmd+9-ist;hel676dquency?

The voice of a person who has inhaled helium sounds very high-r v ma xzdeeq06f9z;2:3cr5adpitched. Why?

How will the air temperature in a room affect the pit oyt j6oi/eq,w7jjgnxc.ut3u( *h 0 .. lyoo9fch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds i/.*u 0jlg o xszzh3f +5dsnn(zn various frequency ranges. (An example iszd*/of 0znuzn. sh +sj (3gx5l a car muffler.)

Why are the frets on a gu*w frubm vy(skmfrzg )( bt zu;y;)b6l6cg..5itar (Fig. 12–30) spaced closer together as you move up the)fmf;r(g s.vb w c5.l)zrb( *6u z tb;y6ykmug fingerboard toward the bridge?

A noisy truck approaches you fr a6 0wft2/uaudom 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 more of the high-frequency noise. Explain.6/a tuwu0d2af [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherele)a +;q mde0fas beats can be said to be due to “interference in time.” 0em ;elqfd+a)Explain.

In Fig. 12–16, if the fre o*a..nuogy1n quency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closeg.* nn1oa u.yor together?

Traditional methods of protecting the hearing of people :d avf6dv .-n+mw l yurmhrtf4j(+7p1who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electro 6(- :7r++hlm tdpymrn a fwvu4.jfv1dnically, 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 h1r w7vr6rr(c in Fig. 12–31. Each wave can be thought of as a superr(vh 7rcr1 w6rposition 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 observer move in the same dira1- i a1w,dpm*puqp0section, with the same velocity? Explaiau1,pi s*a1-qp0mdp wn.

If a wind is blowing, will this alter the frequenz+lfo .e x84w3p7fl)mr5scpocy of the sound heard by a person at rest with respect +z7pcp xeo5o ffl4r)m8s 3 l.wto the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monxpl 654jz dtb3if *lr(itor is bl dz (3rplti l5b4f*xj6owing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the 6eu-/hbg;4idag4tq x +cn (wa9e2pvi9jlg 2gecho of her shout reflected by a cliff at the fiiecaelgq jbdap(x- 4w 2g9 h26g9/ t; uvng4+ar 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 the ec-sl efkcq r*k5, s/olzc6l) v5ho of the sound reflected from ckl )s5q,l fslvocek * 5-6/zrthe ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave(iicw-vtk: -plengths 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 foggy day. Wiqo,k8m drd,axffmn,o2 /kyi7m).* ho thout warning, an engine backfire occurs on another ,*8dy, f d7m haf/imk)2okxmn qo.o,rboat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the wyk 1z k83zf1ytop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is kzf1w1y8 y 3kzthe cliff?    m

  A person, with his ear to the ground, sees a huge stone strike t+p9dj-4qpwyczgnn13 he 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 awac g4w9pqznp+31dn y j-y 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 npjq6:3( dsz7grfv( prule” for estimating the distance from a jn rp(36sd:(f7zv pgq lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of ibd1j- (jey4f tmpt 9*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 levelfk-2abil9rb-khb2c( ss- m: q of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta ceu-fhyyd)j;*w pd28 neously at a *jwycdyp; 2 u d8)-ehfcertain 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 with four equally noisy s-i-,dr;e8e4yw qae f jet engines is experiencingy4qfes-w erid- ,8; ea a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said tot h-kq,bed+vme mqc,;1 f8as8 have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rati1f,h-qb8 q d+8 tka,mse;evc mo of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound f79.kodsj :vf,o) u;at7myp zvrom a person speaking in normal conversation. Use Table 1jy; as9,zpmuod). ft 7vko:7v2–2. Assume the 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 strikes s,fb byc:i39sml7-md 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, wt p .n h6xy* zpiial8oo65ln/:hile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a p iayopx6nl: 5n/i tp.ho6z8l* oint 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 reg5n.fm5q m(ool istered 130 dB when placed 2.8 m in front of a onl .m5 (5ofqmloudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dBc(8 di s59x.hk/ px7qor kl2hi. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11i5hxp k( qh 7dx2okc.8/ i9lsr–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensvbxdcmh-v84 rfte 5t,7 9 mwk3ity increase? Ibdx - 3tc4mr9m k7v,hfv85ewt ncrease 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 twiciwsk: *59y:vgjf a 8xme the frequency of the other. What is the ratio of their intensit9a:wgsxf:5y mi *k8jv ies?   

  What would be the sound level (in dB) of a sound wave in air that correspond4 eyrxo 0uqzq p4)1iz-s to a displacement a 0pzui4 1-exzq4ory q)mplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w4 )vl.l pw:iu ivoch*d63h v3ehat sound level to seem as loud as a 100-Hz tone that has a 50-dB souh* d.l6o w3 hc4)lvp: 3iievvund level? (See Fig. 12–6.)    dB

What are the lowest and highest leu0acbb 869w frequencies that an ear can detect when the sound level is 30 dB6ba8ew9 bluc 0? (See Fig. 12–6.)

  Your auditory system u3lf8xy0ln+ b)hl u 7ncan accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity ah07 f+yn lx8 u3l)bnult
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundbjg)u 8 jw,-ai)knd48f 2wrq*h oznu-amental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g.hz- *qn a2f,8)jn)ww8r4budjkoiu-g Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fuem8u(ml9 : djqndamental and first three audible o8qj u:dle(m9m vertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acov(l,ra f 1f)h,ee np.ross the top of an eflnh1(p,r ee,o. v)f ampty 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 orgyf6ksd4x 7qhfs l81b ,0v:oxdan with open-tube pipes spanning the range of human hearing b7sl 1hdy d0s6kfx,4:v q8xfo(20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmo dezciq7 a 2jkea lk3j 7t)4/(5t*hxovnic. What will be its fundamental frequencyi/)ka (k2vzqx d ja e*753t7t4ochlj e if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m longgtyzgl+ my,3zf/ a-5c and is tuned to play E above middle C (t+y,3zg/g 5m-lac z fy330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) +lvx *9dfw) m5)x jyhjwhen the y xx5hw*)f+ l9jmdj)v 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 ato*cy77, tmk z.rnl.i k 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 p6r- 8 r*puhcqo -v(af12–10 should the hole be that -*huvcr(8apfoqr6 p - 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 2fgr)f4;eyy. )td 4yyd 64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a)) dyf)yyfe4 tgy;.4r d 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 boiyc1 ./glbl4 rth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whcb/1.ily r4 lgat 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 ,m8fbus y7wv gcnm1,/$^{\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 1 4upq2kr6-gsdq;w durange for a 2.14-m-long organ pds4 rpgud61q kuw2-;qipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxiy;4/byoa* cixsyzg a )ida7 r ;6vkl);mately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in yd4s*) / rx7a)v;a ;gliyy ciz; b6aokthe 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 whn1y6j fl3fc7f en trying to adjust two strings, one of1 fc7 ny6l3fjf which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequenc b2wg*,9( eaf 6fikzvqy 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 kHz, while another (brand X) operat adz)nitt .84,b,lbfzalg/ 3 ues 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 pluza,dlg3 4b/n 8.lfatbi t,)zayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s wqx7gevu5d4jrimd s (z;f +68p8dx j+d hen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whugsv+fed85 zjd6(m7 ;x4jiq8r d+dp xat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz.: a;otn7xdj-l The tension in one string is then decreased by 2.0%. What will be the beat frequency ;to xj-7 dn:alheard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middl e az0tyw kdlgzg )c ed:.b*jvbx-iaxh594774e C (262 Hz), but one is at 5.0°C and the other atg4by 09tba4eli)xc. -vdxzg7dah7 kj ewz:5 * 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. For m/gk7+jd mx/tk 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 tom7/kt m/d xjg+gether, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one(bg skquf-u2h r/bc7: speaker and 3.50 m from the other. bc (-:ku/ husqbfrg72
(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 vibratin8tt 2(g 9ru (9abz;a 9atudmfjg 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, what must be r(udb8u fatgt 92a(9m;tjza 9the 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 bph /t.:wjd5f /d0wg koeats per second will be heard? (Assume T =5t/dk:0pw.wd jh gof / 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of 5gi)bygj nz.9g dyi/( a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect id5( zjiyi)b yggn g9/.f 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 o riw m45*jq m nep0w,n;yhm;/detect if a fire engine whose siren emits at 1550 Hz movesym;hn4;5on w /eqmwmp ijr*0 , 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 c5*3t;e0x)j ri t i5dytkch9j toward you at 15 m/s versus you moving toward it at 15 m/s Are th cyttii5 ckd )r39e0h;*5tjxje 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 t m6/+ f.wv7ad mofgnj)he same single frequency horn. When one is atmf. an +6wgvf) o7jdm/ rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wave8laf y,l;ldl:s at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the rec ,ll8lfy;: ladeived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at lr +dsty(0g y4a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecte+g drlt( y4y0sd wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was mn ck3,bt9b7 /6 ,;bawbisneq played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba playedik,csmben6 /q7b9 aw3 b;tn,b 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 waves to measure blox3b8o-od .(dlfc s*z;m( z kjiod-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 artl-m;c .zs(3io (j8*dxfkdoz beries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencywm a:j(csoq,uv,kvje9j 87; o $2.25 \times10^{ 6}$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 soundco;n:x-ua0 kdw 8e l uc(a+ m*8fygh;c of frequency 570 Hz. When the wind velocity is 12 m/fku0agd+;c wal8:(-;8umoxy hc n* c es 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 mil/wtg m 8s3f;la:gt1oving 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 8+q/q wxmftn1 (a) What is the angle the shock wave makes with the directionqx wt qm18f/+n 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 atmosphe6ep-4 qjuqpt g;g1 i0yre of a planet where the speed of sound is only abou4u6q1 gq;tiepj-0pyg t 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. .6xk ; jzbtywn,x6kq2oo8 *c iDetermine the shock wave angle it prodizyj2o;kctxow6 6n,b8. *kqxuces
(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 89.1 b 97jjjzvjl dtfq$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and seefy-xe*ap)w3 v mte ait33 l4m kdnq.9: a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic bootapm*3-eawify dq9x kv)ml4et33 .n:m, 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 :*t(/rql4:)fzhz c g v5)t a:vxcpdlc sends 20,000-Hz sound pulses downward from the bottom of the boat, h g c azcqpc:fvltt):4v x(l5:zr )d/*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 are tawz0sa: ky 7n.lcp; /l 3*awuphere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipfl*8adg dq,g 6e symphony. It consists of many plastic pipes of various lenga8g*l dd gqf6,ths, 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 the threshold o) ;6gbmf)cen ft 4ovwh 0f+7tff human hearing (0 dB). Wha;7ff)+bhtnmc)we v of406 g tft will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundnp)ltmn8 - 8qc and an 87-dB sound are hea) n88-l nctpmqrd simultaneously?    dB

  The sound level 12.0 m from a loudspeak31;8dq hsdq iwb z0k/her, placed in the open, is 105 dB. What is the acoustic power output (W) of the speadb81/wz3 ;q0ks ihqdhker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated ae rur 5+m,,qx(/lgwdj t 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output i(jq+/ l m,5weu,rdgx rn watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective ,j7 qlk k,few,devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 q kkjw e,,7fl,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 communicatil3395vdjl rpf xj 8w2jons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1co*e2d 6am2jr r eo7m/ow/ nj1$\frac{1}{2}$ 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 es8 aw ayz+i62a fundamental frequency of 440 Hz and a mass 6wz+eys 2i8 aaper unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wate/5q(11:v y; vrefkcqel- v03vja3 s1eunurxjr (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 wee yv-3njf k;aq1r1(vu30v:u qsvx1rl5jce /hen 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 strt ,5toyiyc*nec ;k:-j ing of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonn:* c; y i,-otc5tjkyeance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ly )m5e yz *q8wv h6h14ul1ygcfull 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 coma:uynl2le x.3ing from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the freque:en2ual.lx y3 ncy is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One tslz1;77pa d9ifne zl:rain is stationary. The conductor on the stationary train enpzf7 97;: ld1ilz ashears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you isw9m fhqu ,-j po68ndr- 538 Hz. After it passes yoj8q fr ud -won-6,mp9hu, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you cyj q wbh c((2d;+/kp7k zlysu1,yf a7dan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the strayykacqd(k;( 17wph 7 2+sduyl fb/z j,ightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Th ns8) pjii-)g wesh/f;e shorter one is 2.40 m longfis;-n /wje his8p)g). How long is the other?    m

Two loudspeakers are at nfl i3f0.xc8e opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (0 efx 8inl3.fcc) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta i / t04 ljq)iv81e5savgt znvu+s normally about 0.32 m/s what beat frequency would you expect iu zaq1e) +05ngvtlti v j8/sv4f 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flyin9.gz,6y+ jwj mjr rn* gmt9 ;4mvdilp0g toward the bat a*mr.m9 4w+mnzy9 djigtrjg0;v ,pl6jt 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it apprlmmtj(4o b0v 6oaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 mm 6b0o(4m vltjs 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+fvr c9:v p u+ndokk70 once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used t9kp:dnvo + kc 0vfru+7o 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 listening can be compromised by the presence o 8u*kx 3b)plh*p xyz7naj3 av,f standing waves, which can cause acoustic “dead spots” at the locx b 3jx h*payl3,up n*7ak)z8vations 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 “singiqgqe6vm 3m:2a,wfi 0zm0su:v ng rods,” involves a 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, thiu qmmm qs60:fe3:v, zv 0gwa2e 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 he:s,gn 1 4knfyw szzp 1bs9)lvt l.er(epg+:2iaring for the human ear at a frequency of about ylgkl)sz t 41snz,p::rw(f vg.se bp91e n +i21000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hear:z,;e1aa: anwjpln7**uksc ds the sonic boom 1.5 min after the 7 1d :napk*j awuns*lz a;e,c:plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 x yp/en)ki- at+kzx ,:t9s(gu5 sek5c $^{\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