E l n constructive kl 2 n 1 destructive kl 2n 1

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Unformatted text preview: ves. . Two sources (speakers) . . Can be louder or quieter(!) than sound with just one speaker, depending detector on your location. Here’s why: (your ear) s = A1 cos(k (L1 − vt) + φ1 ) + A2 cos(k (L2 − vt) + φ2 ) Let’s keep it simple, take: use get A1 = A2 φ1 = φ2 a−b a+b cos a + cos b = 2 cos( ) cos( ) 2 2 L2 − L1 L1 + L2 s = 2A cos k ( ) cos(k ( ) − ω t + φ) 2 2 i.e. ∆L = nλ Constructive: k∆L = 2π n 1 Destructive: k∆L = (2n + 1)π i.e. ∆L = (n + 2 )λ Monday, October 14, 2013 Beats Superpose two sources with different frequencies: 1 1 A cos(ω1 t) + A cos(ω2 t) = 2A cos( (ω1 − ω2 )t) cos( (ω1 + ω2 )t) 2 2 Over time, sometimes add constructively, sometimes destructively. Hear beats. Inside, average frequency. 1 2A cos( (ω1 − ω2 )t) 2 Monday, October 14, 2013 modulating wave envelope. Doppler effect You’ve all noticed it when a moving siren passes you, frequency goes from high to low. Police radar speed traps also use Doppler’s effect. So do bats and dolphins and whales, with their sonar. Monday, October 14, 2013 Doppler, cont. fobserved if then vsound − vobserver = femitted vsound − vsource vsound ￿ vo , vs vsound − vobserver vobserver − vsource ≈1− vsound − vsource vsound Aside (later), for light: Top sign if source is coming at us (blueshift), bottom sign if it’s moving away (red). Monday, October 14, 2013 fobs = fsource ￿ 1 ± vrel /c 1 ∓ vrel /c Sonic boom! If Mach number = vobject /vsound >1. (Concorde, mach 2 around 1350 mph!) sin θ = vsound /vsource Monday, October 14, 2013 = 1/Mach number...
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This note was uploaded on 02/11/2014 for the course PHYSICS 2C taught by Professor Hicks during the Fall '09 term at UCSD.

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