Root Mean Square Voltage Multiplied by \sqrt{}2: Explained

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Homework Statement

An AC generator produces a voltage of peak value V. The frequency of rotation of the coil of the generator is doubled. The r.m.s. value of the voltage produced is

Homework Equations

The answer is V multiplied by $$\sqrt{}2$$ but I don't understand why.

The Attempt at a Solution

I know that Vrms = Vo/$$\sqrt{}2$$so how does a division become a multiplication?

 

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Still looking at this. Does doubling the frequency mean V peak becomes 2 V peak?

In which case 2 V / $$\sqrt{}2$$ = V$$\sqrt{}2$$

Is that right?

 

[marmoset]

Initially the peak voltage is V. What does doubling the frequency of rotation do to the voltage produced? So what is the new peak voltage in terms of V? Then work out the rms value for this new peak voltage.

edit: I was too late. Yes, I think that is right : )

 

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Thank you!