What is the evidence that sound travel /t tpv2r qgfrza*y+.jtv q;79s as a wave?

What is the evidence that sound is a form ofg2l)8w h:ckkw 8fa i3m energy?

Children sometimes play with a homemade “telephodm8v(ak(,w vf ne” by attaching a string to the bottoms of two paper cups. When the string is stretched and a chil,k8vwvfa (( mdd 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 water, do you expe;) xffw ykn)x7ct the frequency or wavelength to cx 7f xw))fkn;yhange?

What evidence can you give that the speed of sound in air does not depend si;ww.wr) :da kjgnificantly on freqjw w)k:dw r.;auency?

The voice of a person who has *tc3t:;q8ct md.rr hly cwnp7.pgc*0 inhaled helium sounds very high-pitched. Why?

How will the air temperature in a ry:l bud4 u;m,boom affect the pitch of organ pipes?

Explain how a tube mi1iwgum* p ni5i/ntc+ 7ght be used as a filter to reduce the amplitude of sounds in various frequency ranges.75wipn*/ tmi1g+nui c (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30)0 27v5sgnt qsj spaced closer together as you move up the fingerboard toward th0gvqs 2njt75 se bridge?

A noisy truck approaches you from behind a building. Initially you hear it:6hgb f g*g+ k,bzm(wmg/9mnvc2 jo :m 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. [Hint: Seecgn/mmhm+z6*,g o:9vg w 2( b:mfjkgb Section 11–15 on diffraction.]

Standing waves can be said t*zi0ej ys5n2h6u/mmhx j l v95o be due to “interference in space,” whereas beats can be saideymviz925h x sl5jnm* /uhj06 to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowere u; i59 c)cvx0yjzprx;d, would the points D and C (where destructive and constructive iniz;yc0 xup)5 v j;9xcrterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in area:)x,d+rii-owbpz , ges with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With e:+,w rpd),-zox bgii 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 inpuevmh(d tw n)1/+ :ua Fig. 12–31. Each wave can be thought of as a superposition of two sn1d auw)+ te: u/mv(hpound 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 ty(.)bp 3s63mvavhvt,7g sjhnt7mi ,uhe source and observer move in the same direction, with the sam gv 6,v a(7)y,tbj mi3t.uhph sv37smne velocity? Explain.

If a wind is blowing, will this alter the frequency tan(* ge i a+z3xb2wi/of the sound heard by a person at rest (/+ b3iagxawit2en*z with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions o7t)xb:; sfagc9u igc+sc4;z d f a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Exp9 t;f ;icuz4+x:gg7bs)acscd lain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sb-poe9p hv5ga3g 9mg (jft3w1hout reflected by a cliff at the far end of the lake. She hears the echo tabg e3m(g159p-fohj wvp3 g92.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shipyhry4pt d5h8*l3 emj0 just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and do0 r8h d3h5 tyjeyl4*mpes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavell4ub(icnr0 q+ engths 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 s q)t9 4muavwffk,cj;(chool of tuna on a foggy day. Without warning, an engw( vk9 )uqc4;tmfjaf ,ine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it make2-;w e lj s5dwm.k- .(q:ud tz/xou tfb,afvr/s when striking the water below is heard 3.5 s lam ja5/.luw:2ud.-t/wr -zvkt ,eb ; fs(qodxfter. How high is the cliff?    m

  A person, with his ear to the h:/nxh jvcdn2 / s)w8oground, sees a huge stone strike the concrete pavem:nd/xh/ 8shwo n jv2)cent. 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 away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one tv vf+1gwm9m t u25jv9wtn d(c7nrp9* mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the w 9d2j9v7wfrp ttmnct1v 95+(* vngumtemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1jay ++a98utbl20 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leveln pg8,a+ec+ e;awmo5onb+y s6 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 simultaneously at9( upy m7zuav(*k)bj0ngzq3 w a certain place, what will be the sound level if on*(zz79(0 3ua) ynbpgmk uwq jvly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally b: snp0 -e(l0sdyms;y noisy jet engines is experiencing a sound level bordering on paies smby0n:-d;0(y lpsn, 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 0dj5 ncaioaqv /8/1uyto 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 noisjq /81 ioycau0v/d na5e for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal convxpgn.y :2e ;uo /z:zeaersation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cen/y:g.e:ex zauo p zn2;tered 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 earnbz4w ((kq ;nbdrum 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 amplifier B is w4 src/xr:mk 7rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loud7kx4/rswm r :cspeaker 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 x yk +-pfvh79axl25*(c yragu dB when placed 2.8 m in front of a loudspeaker ox9v+ x* agahyp2kl75ru y- c(fn 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 dif)flhjh7r7 6u cference in sound level of 2.0 dB. What is the ratio of the amplitufl jc 7hr76h)udes 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) bysk;qv q5a-hrt yp9c0g t /u-8w what factor will the intensity increase? Increase by ah pt ;a-5q9tsvkcq/y8gr0w- u factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bsvb 2pesh+9 7ph .1ftdzt0p,put one has twice the frequency of the other. What is the ratio of their intensitiestpz+pphpsb20,h v.s d7 9e1ft ?   

  What would be the sound level (in dB) of a sound wave .b5n.a1sr;yl h+ l(qcktt 2diin air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 3r5(b. nlt c;qk s+a2 tydi.lh100 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud yui,opdy9*6itv3;.+ 6 v z5myhlh mowas a 100-Hz tone that has a y9,3ovih;tdm6yopzm6 wih*v y . l5u+50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frld3khxx:b7* uequencies that an ear can detect when the sound level is 30 dB? (See Fig.x7bd:u 3l k*hx 12–6.)

  Your auditory system can accommodate a huge range of sound le4yd2gtobjrqy:rrrw 9* 1 y6 e0vels. What is the ratio yd 4qyro w*jbrt2:6erg0 ry1 9of 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 ofwgu.imd:j5yb 2q;b/ w 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wh5b/w dmbu;yqw i:g .j2at tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the f*n.y;mq/y a30:eqw;mz gy oq9t cst+wundamental and first three audible overtones if the pipem:z* w y 3yqq.9te;s/q0mynwaocgt;+ 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 blowingk a1pwt1jp.btqy-9- wf2 h sf2 across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube2h 1y9qj sttw fb2a-1.p pw-fk?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build k wa*48.l4zlqbbqxs. a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the r8*w b4lxb. s4aqqz.k lange 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. What k6 t*rcv frrux4z(85i will iv4tru z85 6kcr( rf*xbe its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long1tsfsyg zb5xayf: -(; and is tuned to play E above middle C (3a-1 fgfszbs : ;(y5txy30 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 H* eyb qi5**gxdqk8+(okg-h okz) when the temperatb-* e k oxk8hdgg5*+*ko(iqqyure 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 y94ud1z h4axi20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the psho/+wkn 3gn-n/ x.x flute in Example 12–10 should the hole be that must be uncovered to play D above middl/p+sxw.no3ng h/xk-n e 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 a3m-44g6; xdbrpv.rym f;q tjlcwa8e- t 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) 4 dmcr-mr y4jxv ap3-fl;wq .6e;b8tgShow 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 nh0x.k0u h1 08ziv0(qa bgkzeresonates at two succe8a(v0 xg0hkekh .u0q0z n ibz1ssive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 kxhy .y4, n5kib,zk, .xn2dtu $^{\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 6;q- ucrgp1 u hg75d w.ta n,q0z1gxhmaudible range for a 2.14-m-long organ pipe atgndqtpuu50.a r-, 7zw6gm1h1hx; q cg 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lon -t 5rcvo+5)*fp1dxqklw bh 1ag. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the at1bwao5+ dlpf-xq)* v5h1 c rkudible 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 strinznub g6 gx )xg,m+dv5)gs, one of which is sounding 440 Hz. How far off in frequency is the otvx5g ,xu n6b) +mg)zdgher string? ±    Hz

  What is the beat frequency2bmdr) ,g amojxye y7- 246kne 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 op0ljvykv*;.wk 1jxr 5 kerates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can bjk0v.vy*wx krk5j1 l; e heard 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 2x fbt+brvlf15ej 14w id4l x-with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your jbvxxd44f5-i1f wbl 1 lrt2+ereasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension gu4oq eero)xe1s2( pj + -q0refpa.q2in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Rq+qge.p1 o)uprex2f0o s-(4jaeq2 r e ecall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flu w hn))r b*/:wcu3iihktes each try to play middle C (262 Hz), but one i 3b)w:nwk/rii)*uhhcs at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,x;is h74aka6nye2g7p.r ) owe A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of;p xs7 e.yaaor7k)n6wgehi 24 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands3ucos7xxpw*gf( :i v /tz1 0or 3.00 m from one speaker and 3.50 m from the other. z * 07(osgc/vox:fx wrtp1ui3
(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 bengr ev:87duyejz.d7x u2*+,c+;ytv r :jyp sx vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. vu.y ;er8*+n ycpdxj:s xrvyt7g,7ed+2z j :u(a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Ho h d2+zwal,b 9l0snu a9xad-t6w many beats per second will be heard? (Assume T = 20 s0lba9d,2au n+9 lzth6awxd - $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15fzxn 4hkhd 8k,us* s+(50 Hz when at rest. What frequency do you detect if you move with a speed of 30zsdx8 hk*,4h (kfsnu+ 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 vdauj/dtzz .z6 zpic32, qt-0 h6j*ksengine whose siren emits at 1550 Hz moves at a speed of 32 m/sj6hc qz/katd3.6z*zp, v0 zd2ui j- st
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcni m1jr/etucs;. ;ci:e is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freque1./c;jescim ;nt:r i uncies 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 tasg2+f0)yo vr, z/kluhe same single frequency horn. When one is at re/ko a0+ gl), vr2usfzyst 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 waves at 50.0 kHtj b9ttl2 89pbz and receives them returned from an object movinpt ljt99t 2b8bg directly 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 ofp:k u fw5u net t)q-s/6h1n*oj 5 m/s As it flies, the bat emits an ultrasonic sound wave with fru-thk :)/jswqo p6 1nuf5net*equency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimel v1bcs* f 3hei,d6,bwnts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. Wh hbflb i d3*w,,e1s6vcat beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter useix.vruca.n3 ejxul e:j14q: q.i.j3 vs ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the s n4.:. eejau13j3c.:v.xqlj uxvrq iiound source?   Hz

  The Doppler effect using ultra-cuo)zq9noq c+a 3x4s jny;t ;sonic 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 emi43jiknwn * :emts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wille43j* nw mkni: 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 o ;ywui56 xp3jpn 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 mpfxn/r;c*:5q q6io.z xnga(/s (a) What is the angle thenrm*6gcnz (i5x aoq:;xqf/p. shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphe3 cdvxi0 ji (k8(gi s12e3zvqtre of a planet where the speed of sound is only about 35 m/s itiskd 0eq8 vj2g3z(c 13 x(iv
(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 *o,b 7cmch m(nshock wave angle it p,7* commbh (cnroduces
(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 mh89ne6h0kto $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andq2u+ gw;i3oay *il4/f9anczd see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time qla3i+*ing9 /;duf awy2o4zc 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 20,000o xl82*9juymccsr9.d -Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum de8ojc *l9m2x ycsru .d9pth 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 thrc5wk8wsqx0 /ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer 60hc v(pwp -t+lm1e c00- 0i5hyozw,yl bpn zhpipe symphony. It consists of many plastic pipes of b,ov im y000lywe5t pn6(ppz- hccl0-1h whz+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 mi;)bhluroim)zb/ y 93akes a sound close to the threshold of human hearing (0 dB). What will be i)zrbl u) ;9mi3o yh/bthe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound leve9:v9t.l0(xm vml gycm l when an 82-dB sound and an 87-dB sound are heard siml(m9.m: cyxg9v ltv 0multaneously?    dB

  The sound level 12.0 m from a loudspeaker, plac:0nhz4lzwid: efia) 7 t-hh)ked in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radi-74z iz fn:0h):hh ael tdkiw)ates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drono .-n1xyv bq4o+x3ld ps by 10 dB at 1+nx y vb34xq-.1oondl5 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicallypt/(2hr4qx-; : saha zd gml5l;, cwuz 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, anddp; w2lr ;:zz a-a5 scht,gmh(u4 l/qx that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy 4 e.akz)y ge5w5aofu(stems, 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 tun .)xb9o(z a*a5zxhizled 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 )un88 +zfxs rs32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per u8fs+x8rnu sz )nit 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 vexxgb,wsz.btkz 7tr;d:8c5 : jrtical open 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.tgwt:xrk xs7j:,d z5;z8b bc the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at on,o r z fk2td+w86iaojp-q/s i-:ij0 oue end and also 75 cm i6iq +wti afuj-ro0:- k,jd/o2pz8solong. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as onepq ss oz*2e/t5 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 ce r7 lkt3j1ofnu , );vl7ux3mroming from two sources. The sound is loudest at points equidistant from the two sources. v,) 73of;tru3l1mkxurl j7e nTo 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 is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the sctnf-4m yh;3gtationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mo;f 3gynchmt4- ving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After8:y3mrd c2)dc z8a-akj(mi zh it passes you, its frequency is measured as 486 Hz. How fast was the train movingd2mz 88zajr- ( m:dch aki)3cy (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just co bu9 p7ab 8ie6-*2mzbf+a etby listening to the difference in pitch of the engine m9bo*u -fp z 6a7a2ibect8e+b noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a b7kkx.e*tt /9gc kmj p2eat frequency of 11 Hz. The shorter one is 2.40 m long. How l xek2g/7mpt ct9.j*k kong is the other?    m

Two loudspeakers are at opposite ends of a railroad carh2jj r9z cppu5 dh+biff,fc 4kcm565+ as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical soundh2c mri cjfh u6 jp55c,5dz+pbf49f+ k 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 blr0;z/ko3qf hurf*e l )ood 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 reflect3qe;z* )hr0/lkfo rfued 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 o xhjbng, 7x s*,m(5so6.5 m/s while the moth is flying toward the bxn*mxj s5hoo7 (,sb,gat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mk ,pnt0x bubwk:q)p*6 lk1p8eoth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp re):uxpe 6, 1*kbtklknq p80wbpturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was oltd3 q .g46t2lhfb ,zznce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to inzd,6zl2g 4hf 3bl.qtt tensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the prj -w )p+h*kyhrul+ce8xd)0f resence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing wal8 h-jr*ry k xu)w)cdf+0+hepves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “z, ,ra;vt;edfj7- d-js vxm;azuc;-y singing 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, the rod can be made to “sing,”x f-med7c,rsz;; y,uja;t vzvj-ad;- 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 thresholntr92pbn0c kb( e5tv1 7a phz*d of hearing for the human ear at a frequency of about 1000 Hz9a(tvbb721ezphn r pn*tc5k0 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 observ6q7qrs5 8 3l9ujk ssncc/:vleer on the ground hears the sonic boom 1.5 min after the plane :kq 68357rjcs qvsulen9l c/ spasses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatgg2l6tug 918wubgd1 l2u mlj- is 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