Answer:
The intensity of sound 2 is 67.6 W/m²
Explanation:
First we convert the intensity of sound 1 to the intensity level in db:
For this we use the formula:
L₁ = 10 log₁₀[I₁/I₀]
where,
L₁ = intensity level of sound 1
I₁ = Intensity of sound 1 = 38 W/m²
I₀ = Minimum Audible Intensity = 10⁻¹² W/m²
Therefore:
L₁ = 10 log₁₀ [38/10⁻¹²]
L₁ = 135.8 dB
Since, the intensity level of sound 2 is 2.5 dB greater than intensity level of sound 1. Therefore,
L₂ = 135.8 dB + 2.5 dB
L₂ = 138.3 dB
Now, we calculate intensity of sound by the same formula:
L₂ = 10 log₁₀[I₂/I₀]
10^(L₂/10) = [I₂/I₀]
(I₀)[10^(L₂/10)] = I₂
where,
L₂ = intensity level of sound 2 = 138.3 dB
I₂ = Intensity of sound 2 = ?
I₀ = Minimum Audible Intensity = 10⁻¹² W/m²
Therefore:
I₂ = (10⁻¹²)(10^13.83)
I₂ = 10^1.83
I₂ = 67.6 W/m²
