Question

In a room sound is emitted from two different sources having the same power, determine the relative values of the sound intensities at a point 2m from one source and 6m from the other source.

Answer 1

The sound intensity at a point 2m from one source is 9 times greater than at a point 6m from another source, since both emit the same power and sound intensity follows an inverse square law relative to the distance from the source.

Step-by-step explanation:

To determine the relative values of the sound intensities at a point 2m from one source and 6m from the other source, we use the inverse square law. Sound intensity is inversely proportional to the square of the distance from the source. Since both sources have the same power, we only need to compare how the distances from the sources affect the intensities.

The intensity at 2m (I1) and the intensity at 6m (I2) can be compared as follows:

• I1/I2 = (d2/d1)^2

where d1 is the distance from the source to the first point (2m) and d2 is the distance from the source to the second point (6m).

Plugging in the distances:

• I1/I2 = (6/2)^2 = (3)^2 = 9

This means that the sound intensity at 2m is 9 times greater than the intensity at 6m from a room sound source.