Answer:
The sound level of the point source at a distance of 10 meters is approximately 110.294 decibels.
Explanation:
First, we calculate the intensity ([tex]I[/tex]), in watts per square meter, by the Inverse-Square Law:
[tex]I= \frac{\dot W}{4\pi\cdot r^{2}}[/tex] (1)
Where:
[tex]\dot W[/tex] - Power, in watts.
[tex]r[/tex] - Radius, in meters.
And the sound intenity level ([tex]L[/tex]), in decibels, is expressed by:
[tex]L = 10\cdot \log_{10} \frac{I}{I_{o}}[/tex] (2)
Where [tex]I_{o}[/tex] is the reference sound intensity, in watts per square meter.
If we know that [tex]\dot W = 135\,W[/tex], [tex]r = 10\,m[/tex] and [tex]I_{o} = 10^{-12}\,\frac{W}{m^{2}}[/tex], then we find that sound level at a distance of 10 meters is:
[tex]I= \frac{\dot W}{4\pi\cdot r^{2}}[/tex]
[tex]I = 0.107\,\frac{W}{m^{2}}[/tex]
[tex]L = 10\cdot \log_{10} \frac{I}{I_{o}}[/tex]
[tex]L \approx 110.294\,dB[/tex]
The sound level of the point source at a distance of 10 meters is approximately 110.294 decibels.
