Question

a violin string vibrates at 196 Hz. what frequency will it vibrate with if it is fingered at one quarter of its length.

Answer 1

if the wavelength of the string unfingered is λ, what will it be in the scenario you describe?

Use the answer to that question together with the fact that
(wavelength) x (frequency) = speed, which is a constant
λf=v

Answer 2

theres only 1 number given to us in this question, how do you find speed when all we have is frequency ?