At 25 m from a sound source, the intensity level is 55 dB. What's the level at distance of 56m? What's the level at distance of 273m?
56 m is 2.24 times as far away as 25m, so the sound power/area is less by a factor of 2.24^2 = 5.02
The dB level is down by 10 log(10)5.02 = 7.0 dB
To find the level of sound at different distances, we need to understand the relationship between distance and intensity level, which is governed by the inverse square law. According to the inverse square law, the intensity of sound decreases by a factor of 4 for every doubling of distance.
Let's calculate the intensity levels at different distances.
1. Level at a distance of 56m:
We know that the intensity level at 25m is 55 dB.
Using the inverse square law, we can calculate the reduction factor:
Reduction factor = (25m / 56m)^2 = 0.2497
To find the level at a distance of 56m, we multiply the reduction factor by the initial level:
Level at 56m = 55 dB - 10 * log10(0.2497) ≈ 49.86 dB
2. Level at a distance of 273m:
Again, we know the intensity level at 25m is 55 dB.
We calculate the reduction factor using the inverse square law:
Reduction factor = (25m / 273m)^2 = 0.0256
To find the level at a distance of 273m, we multiply the reduction factor by the initial level:
Level at 273m = 55 dB - 10 * log10(0.0256) ≈ 37.92 dB
Therefore, the level at a distance of 56m is approximately 49.86 dB, and the level at a distance of 273m is approximately 37.92 dB.