A long taut string is connected to a harmonic oscillator of frequency `f` at one end. The oscillator oscillates with an amplitude `a_(0)` and delivers power `P_(0)` to the string. Due to dissipation of energy the amplitude of wave goes on decreasing with distance `x` from the oscillator given as `a = a_(0)e^( –kx)`. In what length of the string `(3/4)th` of the energy supplied by the oscillator gets dissipated?

Answer

`(ln 2)/(k)`