Question

If a vibrating string is made shorter (i.e., by holding your finger on it), what effect does this have on the frequency of vibration and on the pitch? 1. both decrease. 2. no effect 3. both increase. 4. the frequency decreases; the pitch decreases. 5. the frequency increases; the pitch decreases.

Answer 1

The correct answer is "3. Both increase"

In fact, the frequency of a vibrating string is given by
$f= \frac{1}{2L} \sqrt{ \frac{T}{\mu} }$
where L is the length of hte string, T the tension and $\mu$ the linear mass density. 
We can see that string is made shorter, L decreases, so the frequency f increases. And since the pitch has the same behaviour of the frequency, it increases as well.