For a travelling wave, the phase difference between two points separated by a distance of 3 m at a given instant is 90^ . At a fixed point, the phase difference between two instants separated by a time interval of 0.01 s is 60^ . The velocity of the wave is ______ m s ⁻¹ .

Step-by-step solution

For a travelling wave, the spatial phase difference _x is related to the path difference x by: _x = 2 x Given _x = 90^ = 2 rad and x = 3 m : 2 = 2 (3) = 12 m The temporal phase difference _t at a fixed point over a time interval t is given by: _t = 2 T t Given _t = 60^ = 3 rad and t = 0.01 s : 3 = 2 T (0.01) T = 6 0.01 = 0.06 s The velocity of the wave is: v = T = 12 0.06 = 200 m s ⁻¹ Answer: 200