"Too Taut" String = Higher Frequency???

[justadream]

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TPR SW #362

"A violin string, known to be too taut, is being tuned with a tuning fork that is producing an accurate pitch of E (equal to 330 Hz). When the string and the fork are sounded together, beats of frequency 3 Hz are heard. What is the period of vibration of the violin string"?

The answer is clearly either 1/333 or 1/327 since T = 1/f.

TPR says the answer is 1/333 because being "too taut" means the frequency is "too high".

How does TPR know this (which equation/concept is this from)?

 

[DrknoSDN]

Too taut means higher than normal tension. Tension is the restoring force for the vibration of the string so it will vibrate more quickly (less time) or at the higher frequency.