To calculate the sound level (in decibels, dB) at a given distance from a point source, we can use the inverse square law for sound propagation. The formula is as follows:
L = L₀ + 20 * log₁₀(d / d₀)
Where: L is the sound level at the given distance, L₀ is the reference sound level (usually 0 dB, which represents the threshold of human hearing), d is the distance from the source, d₀ is the reference distance (usually 1 meter).
In this case, the power output of the point source is given as 135 watts, but we need to convert it to the sound intensity level (in decibels) using the following formula:
Lᵢ = 10 * log₁₀(P / P₀)
Where: Lᵢ is the sound intensity level, P is the power output of the source, P₀ is the reference power (usually 1 picowatt).
We can now calculate the sound level at a distance of 10 meters using the given values:
Lᵢ = 10 * log₁₀(135 / 1) = 21.6 dB (rounded to one decimal place)
Now we can use this value as the reference sound level (L₀) in the inverse square law formula:
L = 21.6 + 20 * log₁₀(10 / 1) = 21.6 + 20 * log₁₀(10) = 21.6 + 20 * 1 = 41.6 dB
Therefore, the sound level at a distance of 10 meters from the point source emitting sound waves with a power output of 135 watts is approximately 41.6 dB.