Question

The low-frequency speaker of a stereo set has a surface area of A=0.05 m^2 and produces 1 W of acoustical power. (a) What is the intensity at the speaker? (b) If the speaker projects sound uniformly in all directions, at what distance from the speaker is the intensity 0.1 W/m^2?

Answer 1

a.

The intensity of a wave (I) at a surface is equal to :

I = P / A

Where:

P = power output of the speaker = 1 w

A= surface area of the speaker = 0.05 m2

I = 1 w / 0.05m^2 = 20 w/m^2

b.

The intensity at a distance r from the speaker is found by:

I = P / (4πr^2)

Solve for r:

`r=\sqrt[]{(P)/(4\pi I)}`

`r=\sqrt[]{\frac{1W}{4\pi(0.1w/m^2)^{}}}`

r=0.892 m