Answer:
The correct option is 80 dB.
Explanation:
The transformation of sound intensity level into sound intensity utilizes the formula
[D] = 10 log (I/I₀)
Where I₀ = 10⁻¹² W/m²
[D] results in 100 dB
100 = 10 log (I/I₀)
Log (I/I₀) converts to 10
(I/I₀) = 10¹⁰
I is determined as I₀ × 10¹⁰ = 10⁻¹² × 10¹⁰ = 10⁻² W/m²
Sound intensity inversely relates to the square of the distance from the source.
I ∝ (1/d²)
I can be expressed as k/d²
When d = 1 m, the intensity is 10⁻² W/m²
Thus, 0.01 = k/1
Providing that k = 0.01 W
For d = 20 m, we can calculate I
I = 0.01/20² = 2.5 × 10⁻⁵ W/m²
With four neighbors mowing their lawns concurrently,
I = 4 × 2.5 × 10⁻⁵ = 10⁻⁴ W/m⁻²
The sound intensity level in decibels is represented as
[D] = 10 log (I/I₀)
[D] = 10 log (10⁻⁴/10⁻¹²)
[D] = 10 log (10⁸)
[D] = 10 × 8 = 80dB
