To calculate the intensity of the sound wave at a given distance from the source, we can use the inverse square law, which states that the intensity of a sound wave decreases as the square of the distance from the source increases.
The inverse square law formula for sound intensity is:
I = P / (4πr²)
Where: I is the sound intensity in watts per square meter (W/m²), P is the power emitted by the source in watts (W), and r is the distance from the source in meters (m).
In this case, the power emitted by the source is 0.500 W, and the distance from the source is 2 m. Plugging these values into the formula:
I = 0.500 W / (4π(2 m)²)
I ≈ 0.500 W / (16π m²)
I ≈ 0.500 / (16π) W/m²
I ≈ 0.00995 W/m² (approximately)
Therefore, at a distance of 2 meters from the source, the intensity of the sound wave is approximately 0.00995 watts per square meter (W/m²).