A sound from a source has an intensity of 270 db when it is 1 m from the source. what is the intensity of the sound when it is 3 m from the source?

Sound intensity is inversely proportional to the square of the distance between the source and the receiver.

That is

I = k/r^2

where

k = constant

r = radius

When r=1, the intensity is I₁ = k/1 = k

When r=3, the intensity I₂ = k/3² = k/9

Therefore

I₂ = I₁ / 9

In decibels,

I = 10 log₁₀ (I/I₀)

where I₀ = reference intensity

When r=1,

10 log₁₀ (I₁/I₀) = 270

When r = 3,

10 log₁₀ (I₂/I₀) = 10 log₁₀ [ (I₂/I₁) * (I₁/I₀) ]

= 10 log₁₀ [ (1/9) * (I₁/I₀) ]

= 10 log₁₀ (1/9) + 270

= 260.5

Answer: 260.5 dB (nearest tenth)