Question

A portable audio speaker has a power output of 8.00 W. If the speaker emits sound equally in all directions, what is the sound intensity at a distance of 2.00 m from the speaker? Express you

Answer 1

`I=0.159(W)/(m^2)`

Step-by-step explanation:

the formula to calculate the intensity, given the power:

`I=(P)/(A)`

Where
`I` is intensity, and
`P` is the power that the wave carries in a given area
`A`. In this case:

`P=8.00W`, and the area since the speaker emits the sound equally in all directions is the area of a surface of a sphere with a radius of
`2.00m`:

`A=4\pi r^2`

replacing the radius value:

`A=4\pi (2.00m)^2`

`A=4\pi (4m^2)`

`A=16\pi m^2`

`A=16(3.1426)m^2`

`A=50.266m^2`

So, now that we know the area we can calculate the intensity:

`I=(P)/(A)`

`I=(8.00W)/(50.266m^2)`

`I=0.159(W)/(m^2)`

the sound intensity at the distance of 2.00m from the speaker is
`I=0.159(W)/(m^2)`