Q 11-14-046JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
A point source at the origin is emitting sound waves of intensity $16\times10^{-8}\ \text{W m}^{-2}$. The difference in intensity (magnitude only) at two points located at distances of $2\ \text{m}$ and $4\ \text{m}$ from the origin respectively will be ______ $\times10^{-8}\ \text{W m}^{-2}$.
Numerical value type. Enter your answer.
Answer: 3
For a point source $I \propto \dfrac1{r^2}$. Taking the given intensity as the value at $1\ \text{m}$ (as intended in this question):
$$I_2 = \frac{16}{4} = 4\times10^{-8},\qquad I_4 = \frac{16}{16} = 1\times10^{-8}\ \text{W m}^{-2}$$
Difference $= 3\times10^{-8}\ \text{W m}^{-2}$.
Solution by Sreeraj P, M.Sc Physics