A transverse wave is described by the equation y = y 0 s i n 2 π f t - x λ .The maximum particle velocity is equal to four times the wave velocity if

Question

A transverse wave is described by the equation y = y 0 s i n 2 π f t - x λ .The maximum particle velocity is equal to four times the wave velocity if, λ = π y 0 4, λ = 2 π y 0, λ = π y 0, λ = π y 0 2

MARKS App · Accepted Answer

d y d t = y 0 cos ⁡ 2 π f t - x λ × 2 π f ∴ maximum particle velocity = d y d t m a x = 2 π f y 0 × 1 Wave velocity = f λ As 2 π f y 0 = 4 f λ , ∴ λ = 2 π y 0 4 = π y 0 2

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