The equation of a wave travelling on a string is y = sin[20πx +… | JEE Main 2025 (7 Apr, Shift 2)

Q32JEE Main 2025 · 7 APR · SHIFT 2Easy

Progressive Wave Equation

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is:

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Answer: (d)

$k = 20\pi\text{ m}^{-1} \Rightarrow \lambda = \frac{2\pi}{k} = 0.1\text{ m} = 10\text{ cm}$
Particle speed $\propto |\cos(20\pi x + 10\pi t)|$ , which repeats when the phase changes by $\pi$ .
Phase difference $\pi$ corresponds to $\Delta x = \frac{\lambda}{2} = 5\text{ cm}$
So the answer is (d) 5.0 cm.

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