Unformatted text preview: ves. . Two
(speakers) . . Can be louder or quieter(!) than
with just one speaker, depending
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
cos a + cos b = 2 cos(
2 L2 − L1
L1 + L2
s = 2A cos k (
) cos(k (
) − ω t + φ)
2 i.e. ∆L = nλ
Constructive: k∆L = 2π n
Destructive: k∆L = (2n + 1)π i.e. ∆L = (n + 2 )λ
Monday, October 14, 2013 Beats
Superpose two sources with different frequencies:
A cos(ω1 t) + A cos(ω2 t) = 2A cos( (ω1 − ω2 )t) cos( (ω1 + ω2 )t)
2 Over time, sometimes add
destructively. Hear beats.
Inside, average frequency.
2A cos( (ω1 − ω2 )t)
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.
then vsound − vobserver
vsound − vsource vsound vo , vs
vsound − vobserver
vobserver − vsource
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.
- Fall '09