You are at a show seeing your favourite band. You manage to get to the very front of the show and you notice that the band has positioned 2 stacks of speakers; 1 stack to the left of the stage (your left) that contains 2 speakers, 1 stack to the right of the stage (your right) that contains 3 speakers. How far away should you be from the left stack (and from the right) so that the amplitude of the sound hitting your ears will be the same from each stack? Assume that you are always in the front row (and that you cannot go to the left of stack 1 or to the right of stack 2) and that the stacks are 5 metres from the front row:
HINT:
The amplitude (volume) of the sound at a given point from one speaker in the stack is inversely proportional to the square of the distance from the speaker i.e.:
where s is the distance from the speaker and A is the
amplitude of the sound hitting your ears. Let’s assume k =1.
Regard the stacks as points (the distance from each speaker in a
given stack to your position is the same). Take into account the
numbers of speakers in each stack and using the formula for the
amplitude of the sound from each speaker find the distances
s1
and s2
that are indicated in the picture.