If the amplitude of a wave increases by a factor of 4, how is the intensity changed?

it increases by a factor of 4
it increases by a factor of 16
it decreases by a factor of 4
it decreases by a factor of 16

1 answer

The intensity \( I \) of a wave is proportional to the square of its amplitude \( A \). Mathematically, this relationship can be expressed as:

\[ I \propto A^2 \]

If the amplitude increases by a factor of 4, we can express this as:

\[ A' = 4A \]

The new intensity \( I' \) can be calculated as follows:

\[ I' \propto (A')^2 = (4A)^2 = 16A^2 \]

Since the original intensity \( I \propto A^2 \), we can relate \( I' \) to \( I \):

\[ I' = 16I \]

Thus, the intensity increases by a factor of 16 when the amplitude increases by a factor of 4.

Therefore, the correct answer is:

it increases by a factor of 16.