One end of a taut string of length 3m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms–1. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible wave from(s) of these stationary waves is(are)

Engineering

Physics

Standing Wave on String

Question

One end of a taut string of length 3m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms^–1. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible wave from(s) of these stationary waves is(are)

$y (t) = A sin \frac{5 πx}{2} \cos 250 πt$

$y (t) = A sin \frac{πx}{6} \cos \frac{50 πt}{3}$

$y (t) = A sin \frac{5 πx}{6} \cos \frac{250 πt}{3}$

$y (t) = A sin \frac{πx}{3} \cos \frac{100 πt}{3}$

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$(2p - 1) \frac{λ}{4} = 3$ $∴ λ = \frac{12}{2 p - 1}$

$c = fλ \Rightarrow 100 = f \frac{(12)}{2 p - 1}$

$∴ f = (2p - 1) \frac{100}{12}$

$k = \frac{2 π}{λ} = \frac{π}{6} (2p - 1)$

$ω = 2 π f = \frac{50 π (2 p - 1)}{3}$