Rayleigh distance Rayleigh distance Rayleigh distance in optics is the axial distance from a radiating aperture to a point at which the path difference between the axial ray and an edge ray is λ / 4. An approximation of the Rayleigh Distance is formula_1, in which Z is the Rayleigh distance, D is the aperture of radiation, λ the wavelength. This approximation can be derived as follows. Consider a right angled triangle with sides adjacent formula_2, opposite formula_3and hypotenuse formula_4. According to Pythagorean theorem, formula_5. Rearranging, and simplifying formula_6 The constant termformula_7 can be neglected. In antenna applications, the Rayleigh distance is
Acoustic wave wave becomes a travelling wave moving rightwards, for formula_14 the wave becomes a travelling wave moving leftwards. A standing wave can be obtained by formula_15. In a travelling wave pressure and particle velocity are in phase, which means the phase angle between the two quantities is zero. This can be easily proven using the ideal gas law where Consider a volume formula_18. As an acoustic wave propagates through the volume, adiabatic compression and decompression occurs. For adiabatic change the following relation between volume formula_18 of a parcel of fluid and pressure formula_2 holds where As a sound wave propagates through