At a distance of 5.0 m from a point source, the sound level is 40 dB . Determine the sound level at a point located 50 m away from the source.

Step-by-step solution

The intensity of sound from a point source varies inversely with the square of the distance: I 1 r^2 The ratio of intensities at distances r₁ = 5.0 m and r₂ = 50 m is: I₂ I₁ = ( r₁ r₂ )^2 = ( 5.0 50 )^2 = 10⁻² The sound level in decibels is given by = 10 ₁₀ ( I I₀ ) . The difference in sound levels is: ₂ - ₁ = 10 ₁₀ ( I₂ I₁ ) Substituting the given values: ₂ - 40 = 10 ₁₀(10⁻²) ₂ - 40 = -20 ₂ = 20 dB