If the distance from a point source of sound is tripled, by what factor does the sound intensity decrease? Assume there are no reflections from nearby objects to affect your results.

Answer 1

Hi Charlotte..

The formula for Intensity is I=P/A P=Power (Watts) A=area (m²)

Let I₁= the initial intensity

Let I₂= the intensity at triple the distance from the source.

I₁ = P / A₁

I₁= P/ (4πr₁²) The Area 1 is equal to the area of a sphere (4πr²) as the sound moves away from the source in all directions.

Solving for P

P=I₁(4πr₁²)

I₂= P/ (4πr₂²)

r_{2 =} 3 times the distance from a point of sound

r₂= 3r₁

I₂= P/ (4π3r₁²)

P=I₂(4π3r₁²)

The Power is the same for both equations so we can set them equal to each other

I₁(4πr₁²)=I₂(4π(3r₁)²)

Your question asks by what factor does the sound intensity decrease.

So solve the above equation for I2/I1

I_2/I₁=(4πr₁²)/(4π(3r₁)²)

I_2/I₁=(1)/(3²)

I_2/I₁ = 1/9

Let me know if you need any more clarification :)