Determination of the frequency of a tuning fork using the sonometer

If $f$ is the resonance frequency, $l$ the resonance length, $T$ the tension and $m$ the mass of a unit length of the sonometer wire,

$$f=\frac{1}{2~l}\sqrt{\frac{T}{m}}$$

If $M$ is the mass hang from the sonometer wire, $T=Mg$,

$$f=\frac{1}{2~l}\sqrt{\frac{Mg}{m}}$$ $$l^{2}=(\frac{g}{4f^{2}m})M$$

Gradient of the graph of $l^{2}$ against $M = \frac{g}{4f^{2}m}$

$$f=(\frac{g}{4~m(gradient)})^{\frac{1}{2}}$$

1. Suspend an initial load of 0.5 kg from the sonometer wire that passes over the pulley.
2. Arrange the bridges to have a small gap between them and place the light paper rider in the middle of the wire over the bridges.
3. Vibrate the given tuning fork and place it on the sonometer. Pull the two bridges apart to increase the gap until the rider is instantly thrown out of the wire.
4. Obtain the fundamental resonance situation in this manner and note down the value $M$ of the suspended mass and also the length $l$ of the sonometer wire between the bridges.
5. Increasing the value of $M$ by 0.5 kg each time and repeating the experiment obtain about six more relevant values of $l$.
6. In order to determine the value of $m$ (the mass per unit length of the wire) measure the length of the piece of sonometer wire by the metre ruler and its mass by the three beam balance.