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Small amplitude standing waves of wavelength $λ$ occur on a string with tension, T, mass per unit length $μ$ and length L. One end of the string is fixed and the other end is attached to a ring of mass M that slides on a frictionless rod, as shown in the figure above. When gravity is neglected, which of the following conditions correctly determines the wavelength?

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$\frac{μ}{M} = \frac{2 π}{λ} \tan (\frac{2 π L}{λ})$

$λ = \frac{2 L}{n}, n = 1, 2, 3..........$

$λ = \frac{2 L}{(n + \frac{1}{2})}, n = 1, 2, 3.......$

$\frac{μ}{M} = \frac{2 π}{λ} \cot (\frac{2 π L}{λ})$

answer is B.

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Detailed Solution

Consider the case for $M \to 0$ and $M \to \infty$

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