(i) The equation of wave in a string fixed at both end is `y = 2 sin pi t cos pi x`. Find the phase difference between oscillations of two points located at `x = 0.4 m` and `x = 0.6 m`.
(ii) A string having length L is under tension with both the ends free to move. Standing wave is set in the string and the shape of the string at time `t = 0` is as shown in the figure. Both ends are at extreme. The string is back in the same shape after regular intervals of time equal to T and the maximum displacement of the free ends at any instant is A. Write the equation of the standing wave.

Answer

(i) `pi`
(ii) `y=A "cos" (pi x)/(L) "cos" (2pi)/T t`