A source emits sound uniformly in all directions. There are no reflections of the sound. At a distance of 12 m from the source, the intensity of the sound is 1.7 × 10-3 W/m2. What is the total sound power P emitted by the source?
Would I do 1.7e^-3 (12) ?
To find the total sound power emitted by the source, you need to use the formula for intensity:
Intensity = Power / Area
At a given distance of 12 m from the source, the intensity of the sound is given as 1.7 × 10^-3 W/m^2.
We can rearrange the formula to calculate the power:
Power = Intensity x Area
Since the sound is emitted uniformly in all directions, the sound energy spreads out over the surface area of a sphere. The surface area of a sphere is given by:
Area = 4πr^2
Where r is the distance from the source.
Plugging in the values:
Area = 4π(12)^2
= 4π(144)
= 576π
Now, let's calculate the power:
Power = 1.7 × 10^-3 W/m^2 x 576π
Use a calculator to calculate the right hand side of the equation and you will get the value for power emitted by the source.
To find the total sound power emitted by the source, you can use the formula:
Power (P) = Intensity (I) × Surface Area (A)
The intensity of the sound is given as 1.7 × 10^(-3) W/m^2, and we know that the sound is emitted uniformly in all directions. Therefore, the sound energy is spread out over the surface of a sphere.
The surface area of a sphere is given by the formula:
A = 4πr^2
where r is the distance from the source.
In this case, the distance from the source is 12 m, so the surface area is:
A = 4π(12^2)
A = 4π(144)
A = 576π
Substituting the values into the formula for power:
P = I × A
P = (1.7 × 10^(-3)) × (576π)
P ≈ 3.086 × 10^(-3) π W
So, the total sound power emitted by the source is approximately 3.086 × 10^(-3) π W.
Sound is reduced by distance squared.
I= 4PI(12)^2*1.7E-3 watts