A wave traveling on a string at a speed of 10 m s ⁻¹ causes each particle of the string to oscillate with a time period of 20 ms . If a particle has a displacement of 1.5 mm at a specific instant, determine the displacement of a particle located 10 cm away at that identical instant.

Step-by-step solution

The wavelength of the wave is given by = vT . Substituting the given values, we get = 10 20 10⁻³ = 0.2 m = 20 cm . The phase difference between two particles separated by a distance x is = 2 x . For x = 10 cm , the phase difference is = 2 20 10 = . Since the phase difference is , the two particles are exactly out of phase. Therefore, their displacements at any instant are equal in magnitude and opposite in sign. Given the displacement of the first particle is y₁ = 1.5 mm , the displacement of the second particle is