Question

The ratio of the amplitude of two waves is $4:9$. What is the ratio of their intensities?

Answer 1

Step 1: Given data:
The ratio of the amplitude of two waves is $4:9$

Step 2: Calculating the ratio of intensities:

Let us consider are the amplitudes of two waves such that they are in the ratio of $4:9.$

We need to find the ratio of their intensities.

We know that,

The intensity $\left(I\right)$ of a wave is directly proportional to the square of its amplitude$\left(A\right)$.

So,

$\frac{I_1}{I_2}={\left(\frac{A_1}{A_2}\right)}^2$

Substitute the value in the above equation we get,

$\frac{I_1}{I_2}={\left(\frac{4}{9}\right)}^2$

$\frac{I_1}{I_2}=\left(\frac{16}{81}\right)$

Hence, the ratio of their intensities will be $16:81$.