The intensity ratio at point A and B will be 81:16.
Explanation:
Sound waves are known to get faded with increase in the distance. This is because, the intensity of the sound is inversely proportional to the square of the distance of the source from the observer. So, if an observer is standing greater distance from the source of the sound, he/she will find difficulty in hearing the sound.
So, as the distance between the source and observer increases, the intensity of the sound wave decreases.
[tex]I = \frac{1}{r^{2} }[/tex]
As here two points A and B are located at 4 m and 9 m distance from the source, then the intensity of sound at A and B will be inversely proportional to their respective square of the distance as shown below.
[tex]I_{A} =\frac{1}{r_{A}^{2} } = \frac{1}{4 \times 4}=\frac{1}{16}[/tex]
Similarly,
[tex]I_{B} =\frac{1}{r_{B}^{2} } = \frac{1}{9 \times 9}=\frac{1}{81}[/tex]
So, the ratio of intensity at point A and B will be
[tex]\frac{I_{A} }{I_{B} } = \frac{81}{16} =81:16[/tex]
Thus, the intensity ratio at point A and B will be 81:16.
