What is the smallest frequency at which the string can be moved to produce any standing wave?

v/2l the first harmonic of the wave.

Explanation:

Since the first harmonic of standing wave is produced when the wavelength is double of the string length, so that crest and trough of the wave falls over one another to form a standing wave.

As v=fλ and λ=2L (L being the length of the string)

so, f=v/2L

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