A surface receiving sound is moved from its original position to a position three times farther away from the source of the sound. The intensity of the received sound thus becomes

Question

Question 11 options:

A)

nine times lower.

B)

nine times higher.

C)

three times lower.

D)

three times higher.

Answer 1

The intensity of sound diminishes with distance from the source according to the inverse square law. The intensity \( I \) is inversely proportional to the square of the distance \( r \) from the sound source, given by the relationship:

\[ I \propto \frac{1}{r^2} \]

If the surface is moved to a position three times farther away, the new distance becomes \( 3r \). The intensity at this new position can be calculated as:

\[ I' = \frac{I}{(3)^2} = \frac{I}{9} \]

This shows that the intensity of the sound is reduced to one-ninth of its original intensity. Therefore, the intensity of the received sound becomes:

A) nine times lower.