Respuesta :
Answer:
[tex]I=0.159\frac{W}{m^2}[/tex]
Explanation:
the formula to calculate the intensity, given the power:
[tex]I=\frac{P}{A}[/tex]
Where [tex]I[/tex] is intensity, and [tex]P[/tex] is the power that the wave carries in a given area [tex]A[/tex]. In this case:
[tex]P=8.00W[/tex], 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 [tex]2.00m[/tex]:
[tex]A=4\pi r^2[/tex]
replacing the radius value:
[tex]A=4\pi (2.00m)^2[/tex]
[tex]A=4\pi (4m^2)[/tex]
[tex]A=16\pi m^2[/tex]
[tex]A=16(3.1426)m^2[/tex]
[tex]A=50.266m^2[/tex]
So, now that we know the area we can calculate the intensity:
[tex]I=\frac{P}{A}[/tex]
[tex]I=\frac{8.00W}{50.266m^2}[/tex]
[tex]I=0.159\frac{W}{m^2}[/tex]
the sound intensity at the distance of 2.00m from the speaker is [tex]I=0.159\frac{W}{m^2}[/tex]
