A sound source of power 100 watts radiates sound uniformly in all directions. The intensity of the sound at a distance of 4.00 m is
Question
A sound source of power 100 watts radiates sound uniformly in all directions. The intensity of the sound at a distance of 4.00 m is
Solution
The intensity of a sound is given by the formula:
I = P / (4πr²)
where: I is the intensity, P is the power of the sound source, and r is the distance from the source.
Given that P = 100 watts and r = 4.00 m, we can substitute these values into the formula to find the intensity:
I = 100 W / (4π(4.00 m)²)
First, calculate the denominator:
4π(4.00 m)² = 4π(16.00 m²) = 201.06 m²
Then, divide the power by this value to find the intensity:
I = 100 W / 201.06 m² = 0.497 W/m²
So, the intensity of the sound at a distance of 4.00 m from the source is approximately 0.497 W/m².
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