1
Waves
1.3
•Superposition principle
•Interference
•Beats
•Fourier analysis
Superposition principle
The displacement due to two waves that pass
through the same point in space is the algebraic
sum of displacements of the two waves.
The combination of waves is called
interference.
Constructive interference
– the waves reinforce
each other
Destructive interference
– the waves cancel each
other.
Superposition Principle
• When two waves overlap in space the
displacement of the wave is the sum of the
individual displacements.
Constructive Interference
distance
→
Wave 1
Wave 2
Superposition
The two waves have the same phase
Destructive Interference
Wave
1
Wave 2
Superposition
The two waves are out of phase (by 180
o
, or
π
)
Distance >
Noise canceling headphones
Noise
Antinoise
Wave 1
Wave 2
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Interference due to path
difference
path difference =
δ
=r
2
–r
1
In phase at x=0
Condition for
constructive
interference
m
δ
λ
=
Condition for
destructive
interference
1
()
2
m
=+
m = 0 +
1, +
2,….
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 Spring '09
 OKAMURA
 Physics, δ, 0.13 M, 340 m/s

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