For an ideal gas the continuity and momentum equations are ∂ρ/∂t + ∂(ρv)/∂x = 0 and ρ [∂v/∂t + v ∂v/∂x] = −k2 ∂ρ/∂x , wh
Posted: Wed May 18, 2022 7:24 pm
For an ideal gas the continuity and momentum equations are
∂ρ/∂t + ∂(ρv)/∂x = 0 and ρ [∂v/∂t + v ∂v/∂x] =
−k2 ∂ρ/∂x ,
where k is a constant. Linearise about the point v = 0, ρ = ρ∗ ,
and then combine the linearised equations to deduce that sound
(density-velocity fluctuations) obeys the wave equation
∂2vˆ/ ∂t2 = k2 ∂2vˆ/
∂x2 .
∂ρ/∂t + ∂(ρv)/∂x = 0 and ρ [∂v/∂t + v ∂v/∂x] =
−k2 ∂ρ/∂x ,
where k is a constant. Linearise about the point v = 0, ρ = ρ∗ ,
and then combine the linearised equations to deduce that sound
(density-velocity fluctuations) obeys the wave equation
∂2vˆ/ ∂t2 = k2 ∂2vˆ/
∂x2 .