What percentage of sound energy would a listener receive if they moved from a distance of 1 meter to 3 meters from the source?

To determine the percentage of sound energy received by a listener when moving from 1 meter to 3 meters from a sound source, it's essential to consider the inverse square law of sound propagation. According to this law, sound intensity decreases with the square of the distance from the source.

When a listener is at a distance of 1 meter, they receive a certain level of sound intensity. As the listener moves to 3 meters, the distance has increased by a factor of three. To calculate the change in sound energy received, you need to apply the inverse square relationship: as the distance triples, the sound intensity is divided by the square of that distance change.

In this case, moving from 1 meter to 3 meters does the following calculation:

Intensity at 1 meter = I (initial sound intensity)

Intensity at 3 meters = I / (3^2) = I / 9

This means that at 3 meters, the listener receives only 1/9th of the sound intensity they received at 1 meter. To find the percentage, it can be calculated as:

(1/9) * 100% = approximately 11.1%

This rounds up to about 10%. Therefore, the percentage of sound