What is the scientific definition for intensity?

Answer 1

Intensity is proportional to the square of the amplitude of vibration in case of mechanical wave such as sound waves

But in case of light which is electromagnetic in nature, the intensity is the number of photons crossing unit area in one second

Answer 2

Intensity is a measure of the amount of energy transmitted through a given area in a specific amount of time. It is a measure of the strength or magnitude of a physical quantity, such as sound, light, or waves, and is typically expressed in watts per square meter (W/m^2).