JEE Physics 2025 Question with Solution

Given: $y = \sin(20\pi x + 10\pi t)$

Find: The minimum distance between two points having the same oscillating speed.

For a point on the string, the oscillating speed is the time derivative of displacement:

Thus the oscillating speed depends on the cosine of the phase.

For two points at the same instant to have the same oscillating speed, we need equal values of

where

The nearest distinct points with equal cosine values occur for a phase difference of

or by symmetry. Using the phase relation for the nearest non-zero separation,

So,

Therefore, the minimum distance between two points having the same oscillating speed is $5.0 \, \text{cm}$.

The correct option is A.

The solution contains conflicting statements: one section marks Option C while another worked approach correctly derives $5 \, \text{cm}$ from the oscillating-speed condition. Since the worked derivation is the primary source, the defensible answer is taken as A.