An experiment requires sound intensity 0.942 W/m2 at the distance of 2.7 m in any direction from a speaker.
What total sound power is required? Answer in units of W.
To find the total sound power required, we need to first calculate the surface area of the sphere at a distance of 2.7 m from the speaker. This is because sound energy spreads out uniformly in all directions, forming a spherical wave.
The formula to calculate the surface area of a sphere is given by:
Surface Area = 4πr²
where r is the radius of the sphere, equal to the distance from the speaker to the point where the sound intensity is measured. In this case, r = 2.7 m.
First, let's calculate the surface area:
Surface Area = 4π(2.7)²
Surface Area = 4π(7.29)
Surface Area ≈ 91.14 m²
Now, using the equation for sound intensity (I) in terms of sound power (W) and surface area (A):
I = W / A
We can rearrange the equation to solve for sound power:
W = I * A
Given that the sound intensity (I) is 0.942 W/m², and the surface area (A) is 91.14 m², we can substitute these values into the equation:
W = 0.942 * 91.14
W ≈ 85.86 W
Thus, the total sound power required is approximately 85.86 W.