A string of length `'l'` is fixed at both ends. It is vibrating in its `3^(rd)` overtone with maximum ampltiude `'a'`. The amplitude at a distance `(l)/(3)` from one end is `= sqrt(p)(a)/(2)`. Find `p`.

Answer

3

Explanation

For third overtone `(4lambda)/(2) = l rArr 2lambda = l rArr lambda = (l)/(2)`
As `x = 0` is a node , `:. A_(s. omega) = A sin "(2pi)/('lambda) xx = a sin ((2pi)/((lambda)/(2))(1)/(3)) = a(sqrt(3))/(2)`