Wave Motion

The wave equation is given as , where: - is the amplitude, - is the wavelength, - is the period, and - is the position. The maximum particle velocity is given by , where is the angular frequency. The wave velocity is , where is the wave number. Given that the maximum particle velocity is equal to four times the wave velocity, we have the equation: Substituting and , we get: Simplifying, we find: Since , substituting this value: Solving for , we get: Thus, the correct answer is .