Class 12 Physics practical reading To find the frequency of the a.c. mains with a sonometer.

Aim 

To find the frequency of the a.c. mains with a sonometer.

Apparatus Required

 Sonometer with non-magnetic wire, a horse-shoe magnet, a step down transformer (220 - 6V), screw gauge, weights and hanger.

Theory

A current carrying conductor placed in a magnetic field experiences a force. If the conductor carries alternating current, the direction of the force gets reversed after every half cycle and the wire oscillate with frequency of a. c. 

For a wire of length 'I' and mass per unit length 'm' under a tension T, the frequency of the vibration of the wire is given by 

       v= (1/2l) ×√(T/m)

Procedure

1. Set up the apparatus as shown in Fig.

Setup for finding frequency of A.C. mains by sonometer

2. Place the horse - shoe magnet in the middle of the wedges. [In the labs, where electromagnet is used instead of a horse-shoe magnet, the electromagnet should be adjusted a little above the sonometer wire so that one of its poles lies close to the middle of the somometer wire.] 

3. Suspend a suitable weight, say 1 kg, from the hanger and switch on the a.c supply.

4. Adjust the position of the wooden edges A and B so that wire begins to vibrate with a large amplitude. The wire r dus case resonates with a.c supply. Ensure that the wire vibrates in a single loop. To test the resonance, keep a Paper rider on the wire and adjust until it flies off. The horse-shoe magnet should be adjusted so that it is in the middle of the wedges. 

5. Measure the resonating length PQ by adjusting position of wedges initially when the distance between them is increasing. Also repeat the process when the distance is decreasing. Increase the load by half kg each time and repeat steps 4 and 5 to get the resonating length. Record at least five

6. different observations for different values of suspended weight. 

7. Take a suitable length (say 1m) of the wire. Find its mass using a sensitive physical balance.

Observation & Calculations

Precautions

1. The wire should be of uniform thickness and there should be no kinks in the wire. 

2. The horse-shoe magnet should be placed in the middle of the wedges.

3. The tension should not be too large so that the wire is not stretched beyond its elastic limit. 

4. Weight of the hanger should also be taken into account. 

5. The sonometer wire should be non-magnetic. 

6. The magnet should not touch the wire. 

7. The wedges should have sharp edges.

Sources of Errors

1. The wire is not of uniform cross-sectional area and there are kinks in it. 

2. To presence of friction at the pulley so that the actual tension is different from the applied tension.