What happens to intensity if the amplitude of a signal is halved?

When the amplitude of a signal is halved, the intensity of that signal decreases to one fourth of its original value. This relationship is based on the principle that intensity is proportional to the square of the amplitude.

To understand this better, consider that intensity (I) is defined mathematically as the square of the amplitude (A):

I ∝ A²

If the amplitude is halved, you would express this as:

New amplitude = 1/2 * Original amplitude

Substituting this into the intensity equation gives:

New intensity = (1/2 * Original amplitude)²

= (1/4) * (Original amplitude)²

= (1/4) * Original intensity

This shows that, with the halving of amplitude, the new intensity becomes one fourth of the original intensity. Thus, the correct conclusion is that intensity decreases by one fourth when the amplitude is halved.