A point sound is located in the perpendicular to the plane of a ring drawn through the centre `O` of the ring. The distance between the point `O` and the source is `l = 1.00 m`, the radius of the ring is `R = 0.50 m`. If the mean energy flow rate across the area encloseed by the ring is (in `muW`). Find `(x_(0))/(5)`. Given, at point `O` the energy intensity of sound is equal to `I_(0) = 30 muW//m^(2)` and assuming the damping of the waves is negligible.

Answer

4

Explanation

Assume a spherical surface of radious a passing through the ring. The waves passing through ring also pass through sphere.
area of `ds = 2pia sintheta ad theta`
`ds = 2pia^(2) sintheta d theta`
`s = 2pia^(2)overset(alpha)underset(0)(int)sinthetad theta`
`s = 2pi a^(2)[-cosalpha + cos 0]`
`s = 2pi a^(2)[1-cosalpha)`
`"Energy" = ("power")/(4pia^(2))s = ("power")/(2)(1-cosalpha)`
`I_(0) = ("power")/(4pil^(2)) rArr "Energy" = (4pil^(2)I_(0))/(2)(1-cosalpha)=2pil^(2)I_(0) (1-(l)/(sqrt(l^(2) + 0.5)^(2))) approx 20muw`