Question

The sound level measured in a room by a person watching a movie on a home theater system varies from 40 dB during a quiet part to 70 dB during a loud part. Approximately how many times louder is the latter sound?

Answer 1

intensity of sound is given as

I = I_o 10^(db/10)            I = intensity . , I_o = reference intensity . db = sound level

for db = 40, let the intersity be "I₁"

dB = 10 log₁₀(I₁/10^-12)

40 = 10 log₁₀(I₁/10^-12)                              eq-1

for dB = 70

let the intersity be "I₂"

dB = 10 log₁₀(I₂/10^-12)

70 = 10 log₁₀(I₂/10^-12)                                 eq-2

subtracting eq-1 from eq-2

70 - 40 = 10 log₁₀(I₂/10^-12) - 10 log₁₀(I₁/10^-12)

30 = 10 log₁₀ (I₂/I₁)

I₂/I₁ = 2³ = 8