The distance between two consecutive points with phase difference of 45^ in a wave of frequency 300 Hz is 4.0 m . The velocity of the travelling wave is (in km / s )

Step-by-step solution

To determine the wave velocity , first find the wavelength from the given phase difference and the separation distance between the two points. The phase difference and path difference x are related by = 2 x . The phase difference is 45^ , equivalent to 4 radians. With x = 4.0 m, substitute into the equation: 4 = 2 4.0 Divide both sides by : 1 4 = 8 Solving for yields: = 32 m The wave velocity is given by v = f . With frequency f = 300 Hz: v = 300 32 = 9600 m/s Convert to km/s: v = 9.6 km/s The correct option is D .