if the intensity of a mosquito's buzzing is 9.3 x 10^-8 W/m^2 at a distance of 0.21 m, how much sound power does that mosquito generate?
What is the area of a sphere of .21meters?
powertotal=Intensity*Area.
To calculate the sound power generated by the mosquito, we can use the formula:
Sound Power = Intensity x Surface Area
The surface area in this case is the area of a sphere, since sound waves radiate in all directions from the mosquito. The equation to calculate the surface area of a sphere is:
Surface Area = 4πr^2
Given:
Intensity = 9.3 x 10^-8 W/m^2
Distance (r) = 0.21 m
Step 1: Calculate the surface area of the sphere
To find the surface area, we substitute the given distance into the surface area formula:
Surface Area = 4π(0.21)^2
Step 2: Calculate the sound power
To calculate the sound power, we multiply the intensity by the surface area:
Sound Power = Intensity x Surface Area
Now, let's calculate the sound power generated by the mosquito:
Step 1:
Surface Area = 4π(0.21)^2
Surface Area = 4π(0.0441)
Surface Area = 0.5532π (approximately)
Step 2:
Sound Power = Intensity x Surface Area
Sound Power = 9.3 x 10^-8 W/m^2 * 0.5532π
Sound Power ≈ 5.167 x 10^-8 W
Therefore, the mosquito generates approximately 5.167 x 10^-8 watts of sound power.