A certain string on a piano is tuned to produce middle C (f = 261.63 Hz) by care

Question

A certain string on a piano is tuned to produce middle C (f = 261.63 Hz) by carefully adjusting the tension in the string. For a fixed wavelength, what is the frequency when this tension is doubled? The answer is 370 Hz equation I saw in a previous equation was f1= sq.2 f2.... they said that f2 was 261.63. That does not make sense, because the beginning freq. is 261.63 so that would equal f1 not f2. f2 would be what happens to the freq. once is doubled. Help in understanding as to why it is like this.

Explanation / Answer

if we double the tension the frequency becomes sqrt(2) times the original frequency

hence

f2 = 261.63 * sqrt(2) = 370 Hz

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