Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 59

From the following operation

follows

(2.26)

With the equation of state (2.15) for the density we get the linear wave equation for the acoustic pressure p

(2.27)

Inserting the velocity v′=∇Φ derived from the potential Φ into the linear equation of motion (2.24) provides the required relation between pressure and the velocity potential

(2.28)

Thus, the relationship between pressure p and the velocity potential Φ is

(2.29)

Entering this into the wave equation (2.27) and eliminating one time derivative gives:

(2.30)

The definition of the velocity potential (2.25) and equation (2.29) can be applied for the derivation of a relationship between acoustic velocity and pressure:

(2.31)