What is the evidence that sound travels as a wavet-s 43qxchmb6/k1 c;zh t) huf?

What is the evidence that sound is a fo :(kauq yf3dnopff6m cot+5 ,. f6*6fspiwl:orm of energy?

Children sometimes plb11ove +z jved c:ie0(ay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be hear(+bivo0deez:c1v j 1ed 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 iesrfd e u2m2 ; z2j9hto0/ypin2+v ql+nto water, do you expect the frequency or wavelength to 92sqfj ree2n v/timl2;d+hz 0 yp2uo+ change?

What evidence can you give that the speed of sound in air does nzro 1(sjc4z9 8:pqwi pot depend significoq8: s9icpzj rpz4w 1(antly on frequency?

The voice of a person who has i mettczu.kx8 5ttd8 q 0nso(3-nhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ yf,.2ued7 ye z 2h(qns07.8u qd vfmgepipes?

Explain how a tube might be used as a filter to reduce the ampliiy7p7wm70w z- mnm6natude of sounds in various frequency ranges. (An example is aw6z07mmn-iw 7ap7nm y car muffler.)

Why are the frets on a guitar (Fi)dt 4pnwr;d)/b l 6vbug. 12–30) spaced closer together as you move up thbdtd;/) rvb 6nw plu4)e fingerboard toward the bridge?

A noisy truck approajts22 cedw *8pfyc)(vches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explainjf82c yt) sve 2*w(cdp. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference i,- dy /8uu6fzgub/u;fhv7vb on space,” whereas beats can be said to be due to “inter;z-f7 v6u/dbfb,/vu go 8uhuyference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pou; 8rs ,oxyr1x :ohvh+ints D and C (where destructive and constructive interv hsyoux+r1: o;h, xr8ference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wpv q /p.6(thriith 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. Insteat/hp 6vi(prq. d, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a supdvk bh4tqt3y*mg5z l* 6pscj ss4:n01erposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), ares*zs3hgv b:5 d4sp6n c 4t1my*kqj0tl the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and o4 n-4e3wpaujht:6m+jq zqa pd8 h4jw8bserver move in the same direction, wim6aj -dj h+ t4q3wpq:a484pehnj8 uz wth the same velocity? Explain.

If a wind is blowing, will this alter the f( 1 px:nmabnj58i 9wcyrequency of the sound heard by a person at rest with respect to the source? Is the wavelength or ac1bw5 pny9xjm in8: (velocity changed?

Figure 12–32 shows various positigp2c tnj7c6q1 ons of a child in motion on a swing. A monitor is 7cjnq1g ct6p2blowing 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 l+ +fz+dhqk1oj istening for the echo of her shout reflected by a cliff at the far end of 1+f+zo kjd+qhthe 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 ji z2e9 z5n bm swhixv xi2pnp;xw/34-1ust below the waterline. He hears the echo of the sound reflected fro wz-xnix5 9bi/ph4mw2i pz es2v;n1x3 m 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 mbfr ,-lk) zb.5nmi a*$^{\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 sc po0+yvwoy4c 3eh l)v7hool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awa) oye3ylv4 0+pcw7ohvy (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 oca/) 5jboh -iywi/y,a cliff. The splash it makes when striking the water below is heard 3h-w, 5ib/c ijay/o)oy .5 s later. How high is the cliff?    m

  A person, with his ear t- uukr ; ew8q c9noux8.hbee0,o the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Tabokneu-uc q 0. ue;8r89 xb,hwele 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent eruh *th:n (/uww7ryn /pror made over one mile of distance by the “5-second rule” for estimating the distance from a light//rnthwp(: w uuy*n 7hning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain leveld)/ gm+ 5tk:5rm f20 tcehgwwuv+1t do 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 q kmwfs-/3qlkds :p.p fgp4-gzz4n-k57rk1rof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult+ba4kekjnqk: /o+cq/ aneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, e++/kknqbcoqj/ :4kanot dB’s.]    dB

  A person standing a certain distance from an airplane with fop7ijdoi/+ b x)ur equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would bpi+o)/dji 7x this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is sadte)ad1fd7. .fi*u62dju0 zp u 8 ypqkid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Whau1uf ikjp.0 68eyzq)udp2dd. d*t fa7t is the ratio 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 from a person gb(- sp/, ycz i4rs1rospeaking in normal conversation. Use Tablrg4o,(ipb sz1s- rcy/ e 12–2. 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 an eardrum whosedh: o yk*erj(2fdtb vy /1ejp/26hxyhw81v;h 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 mo4 o .9 8 fm2ui;nu+xg6q fmgzgkaox*8cf.mgs:dest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you omus g nog; c2f8 8mz+f*gf.k m6u.iqxx94ag:would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when pz.lp82zcdta m dx5g1*laced 2.8 m in front of a loudspeakez*g xt.m dcp18ad2 zl5r 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 typical/i0 (itaps: 7mrm c9kqly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secti9i(m0i t/saqkcpm 7 :ron 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) zlcs-) dr.xdg)b-4pk by what factor will the intensity rcl4 .zbs) -gdp kxd)-increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaceml,.:nxob -zb(3zla*ykc;v h dent amplitudes, but one has twice the frequency of the other. What is the l *z:z.x(b,v yh3cknld;aob- ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air th ;eg*ut yb2dr:at corresponds to a displacement amplitude of vibrating air molecuryt; d*ge:ub2les of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem asuj6vwoc 8i9 ( b jlh 1)u.a/,g)n t/.iksrskbk loud as a 100-Hz tone that ) ik/sg6j9cuhbk.)in /voa rut.8k (swblj1,has a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detev7egpd4d; q p 8b+z/ejct when the sound level is 30 dB? (See Fig. 17e8dzpv + /pdjqe;g4b 2–6.)

  Your auditory system can accommodate a huge range of sound levels. What is td.vee19q d- uh/ne tu-he ratio of highest to lowest intensityq-ueve dne-.d9 t/h1u 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 of 4v7s8ct2j s9d(i +wg +m o12btu4 oxcji40 Hz. The length of the vibrating portionjs wdx+tcti+bo187gjs 2c 4i9m (u2vo is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenta;w6exe+;wp;9 wi lrkpp+vfe 8l and first three audible overtones if pewipx6wkfw +;e r9l p;e +v;8the 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 woulx +1sv6ctrgqhx nn3 ,az0x b:)e8+avdti gl78d you expect from blowing across the top of an empty soda bott vxatg ,i:vglcszx1d qrxa+en0n)8+6b 8h7 3tle 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 s au n,5hwjz)-t 5tj (fh;afe;a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what woul,ej;u5hhn) aja tfs;tzwf(- 5d 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 tig q*nyd 7+/w0vcx2:j f db8hharmonic. What will be its fundamental frequency if it is fingered at a length of onlyw +d*d/yb: q8j2 xv7ghfni0tc 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long vm bw .1a,*w/qjyc;eq and is tuned to play E above middle C (330 Hz).;w/1 ey*c,mvq .jwabq
(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 that5/dul nd6dg8 5yb-qx m;r6rgr7*gtis f;v n1e emits middle C (262 Hz) when the temperat55y*m6 e;v ; /dt8 b-d71gnfq6g xsrdlrngu riure 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 azrwluyg .em q0b2f1*if(tg16t 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 12–1 hbl6fw.djx;50 should the hole be thajd5w6 lf;hb. xt must be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, burzsjwr: g+b:24r /tdwt not at any other frequencies :w t+gz4 wbrdrsj:r2/ in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two sucxz ne:0sl c(f:lznr/); kbit;cessive harmonics of frequencies 275 Hzzlklefr)c(xtb;/: ; n0n s: iz 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 -l nod92rmiz .$^{\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 t00ow lsvb;fp:fe;oh+8xm 3 vpresent within the audible range for a 2.14-m-long organ + v0wb3pexo80 : vsf;;hofmtlpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelyq/.l,n:n rch .+e no95qep ufq 2.5 cm long. It is open to the outside and is closed at thunq:ce .hor,5enn/q q9 f.pl+e other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when 0ixe cmpp5 /vqx3t7-z5dv6+h a gt 1fttrying to adjust two strings, one of which p 7zecxfmvxd160t/55a3ht t pi - qvg+is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262trg *en:t5 )xo 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 op;ux f8c vrr3,zerates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard zr8 xrcf;v3,uby 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 tu g(- 9dnb*zh wcg+oti1ning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Exoc ng+ t*hz1bw9 dig(-plain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, odtpfko+1* 2;y:nl6m ikpqo )294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playeppqoyo t1di;f:k2lkm*on)6+ d together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hd5 ;or8e0j qedeard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other a5;erjod e d8q0t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, andk r0rji )6d 58f6.okkid)rcsn 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 ki 68dk kcdjn rs6 rf0))o.ri5beat 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 speaker zl u*oqbp::7c-h2xj7 ,lstkq and 3.50 m ztb7*qh2 ou, jp:qcx7:lk- ls from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hearg 48kwa7ak 7c;8 o:real,wfaf s three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequenc: e 8,7f8arakw7fg4k al;coawy 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 wavelteinjb34+ jq1 fptj rs961h5 lengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assumrp+ ji jt6ht9q j14sf b3e51nle T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of af-ss/xhx)b (nxv8 ,x d certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move witxx xsnh d b(-/8s,)xvfh a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wh5 z1w ec*buem9at frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 wm 51ezbe*9uc m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-oiigy) dq9,: gHz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenc9,o:gdqyi g )iies 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 the same single frequer 2 y3vrpj ueh(/ v0.(d)qvkyency horn. When one is at rest and.0k e qvyd2huprer(/yv) 3 (vj 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 wavesia0xcu49y-rzm5; ry vxr+frk,d)a:y at 50.0 kHz and receives them retuy5-yxzk v94 rf)c+dyr xmr0r ai, u:;arned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wal3mjj1zl ze 7d7hh* vv7l at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequen13j 7hevzdl77 z*hj mvcy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plbdgxi:, xm idbuadm0+8-2m:(2v u chsayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played t ubs+28x - mcmmbii 2:: avuddx(,dgh0he 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 blood-flow speeds. Scftja1beyi)(a-435er 0l yz wuppose 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 -) (c3yijft w0r1ye l5aabze4 frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency yd fjhexko0 ;c*;l0(qhp* l8o $2.25 \times10^{ 6}$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 Hjhsuyh. rg x; .a(5v13n3/i d heevrx5z. When the wind velocity is 12 m/s fromdang ;/j.(.er5vh3e3yus i hr 1hv5x x 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 speedpqn eu7-qb(aqq9-y t/ 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 3jd(t c)kvx13o10 m/s (a) What is the a c)3xv1k jto(dngle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a i w3n1 5zd-2eknke ,df ni37poplanet where the speed of sound is only about 35 -w1z2f5od3id7e,3i npeknnkm/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 th6hwnk wn3 *x kv2)2 fznlf4s9pe ocean. Determine the shock wave angle it prx4 fh9p kz3fw6n*)l2ksnw 2 nvoduces
(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 2 6r:rw nfg;n5hphg-g$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plau+/c,n q 2upmvam97 qdne exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, t+p,qcv 9q/ mau2d7nmuhe 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 q1xbb 0 qm1l4xpulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is db0q mlqbx141 xesigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in 9. i1 gg vdsulz+gby8-the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consijy6vdfa3 at ;2sts of many plastic 3yafd; aj62tvpipes of 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 .8u 0iprtvl*didm*g is/w vh8 j-t-d 8m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquj08*t-i h/v l w8-sdvm*. i8pgruitdd itoes?    dB

  What is the resultant sound level when86 vf,h 9rjx ym*i4 m8+wpnomw an 82-dB sound and an 87-dB sound are heard simultamn8* m wijxryv6 h,84po mwf9+neously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1i 1h0rl.lf5 wr05 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equall5 ril lrw.h0f1y in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output xx 3 nr;q0 )b7v1 mjb9;nnbttyc4cpe9drops by 1yx n3m9x;9 bnnj;tbp 74etc0 rb1c)vq 0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears )2gqg6x a2fxi. Assume that the sound level of a jet airplane engine, at a distance of 30 m, isiq)g6gfxxa22 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationsy/2nsw kq vi.4 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 1u xcy0(f g5nj o .tpb)1(qcco1$\frac{1}{2}$ 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 32xfsg +x(b0n( y cm long between fixed points with a fundamental frequency of 440 +fbg(sx x0yn( Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is setgb+i*s(v bk4j into vibration above a vertical 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 kg4svbj*+b(i 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 i0h 8l 3mku.enus near a tube that is open at one end and also 75 cm long. How much tension should be in the string if imh8uu 0l.en3k t 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 one full loop (*yqd,( -5bpw cox./ku e4xyopax . 5av$\frac{1}{2}\lambda$) 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 solx91l5r5jhwzn c78euu *g:na: d s1xzurces. 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. Wh 5u*sxldw 1nn9 arzgx 5jucl7 :1:ze8hat is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistl.gjf/b he9a*ies. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the othe /ie*h9b.jfga r train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afterxx c;aho b+*5r it passes you, its frequency is measured as 486 Hz. 5xx*;or hcab +How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can azki +(ph z.ztni8 4kkfh i c1w-b0y/x;6u.ghestimate 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 stpya.1z 8(6i k/wic hi0tx b;h4-+nfgz zhu kk.raightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together,+s gtnwazg6y/zqk:; / produce a beat frequency of 11 Hz. The shorte;twq:6ga /kzy zg/s +nr one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends oei+afo-x*/e):ml7nuy ph q7j f 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 listen p :-xq*oih+/j )lu77aemeyf ns from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aoy6rp -qz id/mm)lr(bes:g 9/p rta 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 oy l pg6qrr/ -em)dipbzm(9:s /f $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth hy.h ) -tdmpfw3t4i8arp6k/sat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave a m/rptft6 34.idhp k8-sw y)hdetected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of highki894kbk 7mqpd e+2 ik frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the mo8kd m2ibk9kqpie7 k4 +th be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12/dtxcytly gry ztq //(0.7 )ay–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns dyy/ qrltt 0/c7y.tx ya( zg)/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 p; kxe 5co.ab. ,59 ,drazcdven7tas 0mr d6u5cresence of standing waves, which can cause acoustic “dead spots” at the locations of th c, 6m9 ae7dd0,;zxov a ua5 s5tbrc.de.c5knre pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a vu1 rv, u.y i534z jqq7zcuh/ ;ii9yfclong, 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 9z1,qu7 uiryu43vvqf z.c ;5i /cjyih a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the hj4 y7d1whqg1k(a1moauman ear at a frequency of about 1000 Hz igjm ydkh1a q(1aw417os $I_0$ = $1 \times10^{12 } W / m^2$ 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 gros*ih kh:ot;tknl5cs:1w :l)s ijg. )dund hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s ank;.l:o cdk)wthg ij ):li s* 51sst:hltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15*u4gii a;z3*/ rz l fn;a 8kv7q0lrlvj $^{\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