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`P_0`/2. At the point `x=l`. Angular frequency and amplitude are respectively:

Options

A. `omega_(0) and A_(0)//sqrt(2)`
B. `omega_(0)//sqrt(2) and A_(0)`
C. Less than `omega_(0)` and `A_(0)`
D. `omega_(0)//sqrt(2)` and `A_(0)//sqrt(2)`

Answer

A

Explanation

We have power of a wave is given as`P = (1)/(2)mu omega^(2)A^(2)v` 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 reduces to `A_(0)//sqrt(2)`