Final answer:
To derive acoustic velocity using acoustic pressure, utilize the relationship I = (Ap)²/(2ρvw), where 'I' is the intensity, 'Ap' is the pressure amplitude, ρ represents medium's density, and 'vw' is the acoustic velocity or the speed of sound in the medium. Substituting known values of density and pressure amplitude into this equation allows for the calculation of the acoustic velocity.
Step-by-step explanation:
The acoustic velocity of a plane wave can be derived using acoustic pressure by understanding the relationship between intensity, pressure amplitude, and speed in a sound wave.
The intensity (I) of a sound wave relates to the pressure amplitude (Ap) and is given by I = (Ap)² / (2ρvw), where Ap is the pressure variation, ρ is the density of the medium, and vw is the acoustic velocity or the speed of sound in the medium. By knowing the density (ρ) of the medium and the pressure amplitude (Ap), we can calculate the acoustic velocity.
For example, at 0°C the speed of sound in air is 331 m/s, and if air has a density of 1.29 kg/m³, by substituting these values and the pressure amplitude into the equation, one can derive the acoustic velocity.
Additionally, the bulk modulus (ß), pressure fluctuation (Ap), and volume change (dV) are used to express the relationship between pressure and volume changes due to sound waves, which is critical in deriving the speed of sound in air from fundamental fluid mechanics principles.