A sine wave travels through a medium. At a specific instant, a particular particle exhibits zero displacement. The distance to the closest particle that also has zero displacement is

Step-by-step solution

The equation of a sine wave travelling through a medium can be represented as y = A (kx - t + ) . At a specific instant t , the displacement of a particle is zero when the phase is an integral multiple of . Let the position of the first particle be x₁ . For zero displacement, kx₁ - t + = n , where n is an integer. The closest particle that also has zero displacement will be at a position x₂ such that its phase differs by . Therefore, k(x₂ - x₁) = . Since the wave number k = 2 , we get: 2 x = x = 2 Thus, the distanc