Answer :
Answer:
130.2dB
Explanation:
The formula for determining the intensity of a wave is expressed as
[tex]I=\frac{P}{A}\\[/tex]
Where P is the power in watts, and A is the area of the sphere formed by the wave
Data given
Power,P=3.65*10^5W
distance,d=52.7
Hence since the distance represent the radius, we can determine the area of the sphere formed
[tex]A=4\pi r^{2}\\A=4\pi *52.7^{2}\\A=34900.45m^2[/tex]
The intensity can be computed as
[tex]I=\frac{3.65*10^5}{34900.45}\\ I=10.46W/m^2[/tex]
we can convert to decibel
[tex]I=10log\frac{10.46}{10^{-12}} \\I=130.2dB[/tex]
Answer:
10.46W/m²
Explanation:
The intensity (I) of a sound is related to the power (P) radiated by the sound within an area (A) as follows;
I = [tex]\frac{P}{A}[/tex] ----------------(i)
But;
A = 4[tex]\pi[/tex] r²
Where;
r is the specified distance covered by the sound.
Substitute A = 4 [tex]\pi[/tex] r² into equation (i) to get;
I = [tex]\frac{P}{4\pi r^{2} }[/tex] ------------------------(ii)
From the question;
P = acoustic power = 3.65 x 10⁵W
r = 52.7m
To calculate the intensity of the sound, take [tex]\pi[/tex] = 3.142 and substitute other values into equation (ii) as follows;
I = [tex]\frac{3.65*10^5}{4*3.142*52.7^2}[/tex]
I = [tex]\frac{3.65*10^5}{34904.98}[/tex]
I = 10.46W/m²
Therefore, the intensity of the sound at that distance is 10.46W/m²