Given the length, tension and mass per unit length of a string, how is the frequency of the first harmonic found?

First, use the formula for wave speed in terms of tension and mass per unit length to find the wave speed c.

Then use the fact that on a string the length of the string is half a wavelength for the first harmonic. This is because in a string the ends are nodes as they are clamped, and N-A-N in any stationary wave=half wavelength. Then having found the wavelength use speed=frequency x wavelength to find the frequency. In AQA there is a formula for the frequency you can use in one go.