Before you ask for a formula try to understand what displacement means.
"What is an Amplitude?":
http://www.sengpielaudio.com/calculator-amplitude.htm
"Soundfield Quantities of a Plane Wave – The Amplitudes":
http://www.sengpielaudio.com/SoundfieldQuantitiesPlaneWaveAmplitude.pdf
Here are the formulas coming:
"Relationship of acoustic sizes associated with an acoustic sound wave"
http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf
"The Formula Wheel − Formulas of Acoustics (Audio)":
http://www.sengpielaudio.com/FormulaWheel-Acoustics.htm
"Particle displacement - Wikipeda (with formulas)":
http://en.wikipedia.org/wiki/Particle_displacement
Cheers ebs