At a rock concert, the sound intensity 1.0 m in front of the bank of loudspeakers is 0.10 W/m². A fan is 30 m from the loudspeakers. Her eardrums have a diameter of 8.4 mm. How much sound energy is transferred to each eardrum in 1.0 second?

To solve this problem we will apply the concepts related to the Area, the power and the proportionality relationships between intensity and distance.

The expression for sound power is,

Here,

A = Area

I = Intensity

P = Power

At the same time the area can be written as,

Now the intensity is inversely proportional to the square of the distance from the source, then

The expression for the intensity at different distance is

Here,

= Intensity at distance 1

= Intensity at distance 2

= Distance 1 from light source

= Distance 2 from the light source

If we rearrange the expression to find the intensity at second position we have,

If we replace with our values at this equation we have,

Now using the equation to find the area we have that

Finally with the intensity and the area we can find the sound power, which is

Power is defined as the quantity of Energy per second, then

it takes about 30 days for it to break down