A wave traveling on a string at a speed of 10 m s^ -1 causes each...

The wavelength of the wave is given by $\lambda = vT$.

Substituting the given values, we get $\lambda = 10 \times 20 \times 10^{-3} = 0.2 \text{ m} = 20 \text{ cm}$.

The phase difference $\Delta \phi$ between two particles separated by a distance $\Delta x$ is $\Delta \phi = \dfrac{2\pi}{\lambda} \Delta x$.

For $\Delta x = 10 \text{ cm}$, the phase difference is $\Delta \phi = \dfrac{2\pi}{20} \times 10 = \pi$.

Since the phase difference is $\pi$, 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 $y_1 = 1.5 \text{ mm}$, the displacement of the second particle is $y_2 = -1.5 \text{ mm}$.