Question

Two waves carry the same power, but the first wave covers 3 times the area as the second. How do the intensities of the two waves compare?

Answer 1

Answer:

Intensity of first wave will 1/3 the intensity of second wave.

Explanation:

Intensity of the wave is defined as the change in power with the respect to area of the wave.

Mathematically,

$I=\frac{P}{A}$

According to question, the power of the two waves are same but the area covers by the first wave is equal to 3 times the area cover by the second wave.

Therefore,

$P_{1} =P_{2} \\I_{1}A_{1} = I_{2}A_{2}$

Now according to question,

$I_{1}3A_{2} =I_{2}A_{2}\\I_{1}=\frac{1}{3}I_{2}$

Therefore, the intensity of first wave will become 1/3 times the intensity of second wave.