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.
2 answers