A wave travelling on a string is y = sin(20πx + 10πt), with x and t in SI units. The minimum distance between two points having the same oscillating speed is:
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Question

A wave travelling on a string is y = sin(20πx + 10πt), with x and t in SI units. The minimum distance between two points having the same oscillating speed is:

G1 Physics · Accepted Answer

The wave number is k = 20π rad/m. Hence wavelength is λ = 2π/k = 2π/(20π) = 0.10 m = 10 cm. For two points in the same sinusoidal wave, the minimum non-zero spatial separation for equal oscillation-speed magnitude is λ/2. Therefore, Δ x m i n x_min x m ​ in = 10/2 = 5 cm. Correct option: A.