A wave moving with constant speed on a uniform string passes the point `x=0` with amplitude `A_0`, angular frequency `omega_0` and average rate of energy transfer `P_0`. As the wave travels down the string it gradually loses energy and at the point `x=l`, the average rate of energy transfer becomes half. At the point `x=l`. Angular frequency and amplitude are respectively:

Options

A. `omega_(0)` and` (A_(0))/(sqrt2)`
B. `(omega_0)/(sqrt2)` and `A_0`
C. less than `omega_(0)` and `A_(0)`
D. `(omega_0)/(sqrt2)` and `(A_0)/(sqrt2)`

Answer

A

Explanation

`P=(1)/(2)muomega^2A^2V` and `v=sqrt((T)/(mu))` will not change as both T and `mu` are constant. `omega` will also not change as it is property of the source only that is causing the wave motion. Hence to make power half the amplitude Becomes `(A_0)/(sqrt2)`