beats of two travelling waves
classical physics – problem 3: interference of two sound waves, group velocity and beat envelope.
amplitude A
A =
1.00
ξ₁ = A cos(ω₁ t − k₁ z), ξ₂ = A cos(ω₂ t − k₂ z)
angular frequencies ω₁, ω₂
ω₁ =
800
, ω₂ =
630
ω₁ (rad·s⁻¹)
ω₂ (rad·s⁻¹)
wave numbers k₁, k₂ and window
k₁ =
2.0
, k₂ =
1.5
k₁ (m⁻¹)
k₂ (m⁻¹)
spatial window length L (m)
show ξ₁
show ξ₂
show envelope
space profile
– ξ(z, t) and envelope at fixed time
time trace
– ξ(z₀, t) at a probe point