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Q.

The equation of a stationary wave in a string is $y = 4 \sin (6.28 x) \cos (200 π t) m$ where x is in m. The smallest possible length in cm is

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answer is 50.

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Detailed Solution

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\begin{matrix} y = 4 \sin (6.28 x) \cos (200 π t) \\ y = 2 A \sin (k x) \cos (200 π t) \end{matrix}

Comparing,

k = \frac{2 π}{λ} = 6.28

λ = 1 m = 100 cm

Smallest possible length, i.e. string vibrates in one loop.

L = \frac{λ}{2} = 50 cm

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