A longitudinal wave spreads radially from a source with power 345 W. What is the intensity 40.0 meters away?
answer in W/m^2.
To find the intensity of a longitudinal wave, we can use the formula:
Intensity (I) = Power (P) / Area (A)
Given:
Power (P) = 345 W
To determine the Area (A), we need to use the formula for the surface area of a sphere:
Area (A) = 4πr^2
Where:
r is the radial distance from the source
Given:
r = 40.0 meters
Now, substituting the known values into the formulas:
Area (A) = 4π(40.0)^2
= 4π(1600)
= 6400π m^2
Intensity (I) = Power (P) / Area (A)
= 345 W / 6400π m^2
To simplify the answer, we can approximate π as 3.14:
Intensity (I) ≈ 345 W / (6400 * 3.14) m^2
≈ 0.017 W/m^2 (approximately)
Therefore, the intensity of the longitudinal wave 40.0 meters away from the source is approximately 0.017 W/m^2.