Question

an audio speaker producing a steady sound at an outdoor concert is 18 ft away from you. if you move to a position where the speaker is 78 ft distant, by what factor will the amplitude of the sound change?

Answer 1

The amplitude of the sound from the speaker at the outdoor concert will change by a factor of 4.2 (78 ft/18 ft) when you move from 18 ft away to 78 ft away.

This is because sound intensity decreases as the distance from the source increases, following an inverse square law. The inverse square law states that the intensity of a sound source is inversely proportional to the square of the distance from the source.
Mathematically, the formula is: I = I0 / (r^2), where I is the intensity at a distance r from the source of intensity I0. This means that when you move from 18 ft away to 78 ft away, the intensity of the sound decreases by a factor of 4.2 ((78 ft/18 ft)^2).
Therefore, the amplitude of the sound from the speaker at the outdoor concert will change by a factor of 4.2 when you move from 18 ft away to 78 ft away.