Verification of the relationship between the frequency of a stretched string and its vibrating length using the sonometer

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

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

If the graph of $l$ against $\frac{1}{f}$ is a straight line through the origin, the relation $l\propto\frac{1}{f}$ is verified.

1. Suspend an initial load of 2 kg from the wire that passes over the pulley fixed to the sonometer.
2. Arrange the bridges to have a small gap between them and place the paper rider on the middle of the wire between the bridges.
3. Select the tuning fork of highest frequency since it would give the shortest resonance length. Vibrate this tuning fork and hold it on the sonometer box.
4. Next increase the gap between the bridges until the rider gets thrown out of the wire. Measure the length $l$ of the wire between bridges and note down the value along with frequency $f$ of the fork.
5. Repeat the process by selecting the tuning forks in the descending order of frequencies and obtain about six sets of values of $f$ and relevant $l$ values.