The correct answer is (b) λ /2
Explanation:
In a sine wave, the particles on the string vibrate in simple harmonic motion. The particles having equal displacements from the mean position will have equal speed. So at any instant, there may be up to four particles having the same displacement in a wavelength. But in the next instant, the displacements of the particles do not remain the same. Out of the four particles, a pair of particles will have some displacement while another pair will have some other displacement. And the distance between the particles of the pair will be λ/2. In fact, the particles on a string having separation λ/2 will have always the same displacements and the same speed.
In this diagram particles A, B and C, D have always the same displacements and the same speed.
