Answer :
Answer:
The 80 dB option is correct.
Explanation:
The sound intensity level is converted to sound intensity with the formula
[D] = 10 log (I/I₀)
I₀ = 10⁻¹² W/m²
[D] = 100 dB
100 = 10 log (I/I₀)
Log (I/I₀) = 10
(I/I₀) = 10¹⁰
I = I₀ × 10¹⁰ = 10⁻¹² × 10¹⁰ = 10⁻² W/m²
But sound intensity varies inversely as the square of the distance of the sound.
I ∝ (1/d²)
I = k/d²
At d = 1 m away, I = 10⁻² W/m²
0.01 = k/1
k = 0.01 W
At d = 20 m, we solve for I
I = 0.01/20² = 2.5 × 10⁻⁵ W/m²
4 people mowing their lawns at the same time,
I = 4 × 2.5 × 10⁻⁵ = 10⁻⁴ W/m⁻²
The sound intensity level in decibels is given as
[D] = 10 log (I/I₀)
[D] = 10 log (10⁻⁴/10⁻¹²)
[D] = 10 log (10⁸)
[D] = 10 × 8 = 80dB
The computation shows that the lowest detectable intensity is 80dB.
How to calculate the detectable intensity?
It should be noted that the sound intensity level can be converted to sound intensity with the formula:
[D] = 10 log (I/I₀)
where,
I₀ = 10⁻¹² W/m²
[D] = 100 dB
100 = 10 log (I/I₀)
Log (I/I₀) = 10
(I/I₀) = 10¹⁰
I = I₀ × 10¹⁰ = 10⁻¹² × 10¹⁰
= 10⁻² W/m²
In this case, the sound intensity varies inversely as the square of the distance of the sound.
= I ∝ (1/d²)
0.01 = k/1
k = 0.01 W
Then, at d = 20 m, we solve for I
I = 0.01/20²
= 2.5 × 10⁻⁵ W/m²
Since 4 people mowing their lawns at the same time, I will be:
= 4 × 2.5 × 10⁻⁵ = 10⁻⁴ W/m⁻²
The sound intensity level in decibelswill be:
[D] = 10 log (I/I₀)
[D] = 10 log (10⁻⁴/10⁻¹²)
[D] = 10 log (10⁸) = 10 × 8 = 80dB
In conclusion, the lowest detectable intensity is 80dB.
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