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AC Sonometer Experiment with Readings (Class 12)

 

FREQUENCY OF AC MAINS EXPERIMENT WITH READINGS (CLASS 12)

Aim:

 

To determine the frequency of ac main using a sonometer.

 

Apparatus:

 

Sonometer, a step down transformer (230 V – 6 V or 230 V – 9 V), horse-shoe magnet (or two powerful bar magnets), weight hanger, slotted weights, screw gauge, rheostat etc.

 

Principle:

 

If l is the length of the sonometer wire vibrating in resonance with the frequency n of the ac main, then,

Where M is the mass suspended at the end of the sonometer wire and mis the linear density of the sonometer wire.

 

Procedure:

 

The low voltage side (secondary) of the transformer is connected, through a rheostat R, across the sonometer wire. The bridge C is now placed closer to the bridge B. A horse-shoe magnet is mounted mid-way between B and C with the poles of the magnet on either side of the sonometer wire so as to produce a magnetic field perpendicular to the wire. (Instead of a horse shoe magnet, two powerful bar magnets can be clamped on either side of the sonometer wire with unlike poles facing each other). The wire can vibrate freely without touching the poles. The rheostat may be adjusted to reduce the current through the wire in order to prevent overheating.

 

A suitable mass M (say 20 g) is suspended from the free end of the sonometer wire. A light paper rider is placed on the wire between the bridges C and B. The primary of the transformer is connected to the ac main and the main supply is switched on. Since the current flows through the wire perpendicular to the magnetic field, the wire experiences a force. Since the current is alternating, the wire vibrates. The movable bridge C is adjusted until the vibrations of the wire BC show a maximum amplitude, indicating that resonance has been obtained. Now the paper rider will be thrown off. (The magnet is moved as the bridge is moved so that it is at the mid-way between the bridges B and C). The resonating length l of the wire between the bridges B and C is measured. Then (M/l2) is calculated. The experiment is repeated for different values of the load M and the average value of (M/ l2) is determined.

 

The radius r of the wire is measured by a screw gauge. The linear density in of the wire is calculated by the equation, m = πr2d; where d is the density of the material of the wire. The frequency n of the ac main is calculated using the equation,

Observations and Readings


Trial

Tension

Resonating length

Frequency (n)

1 (cm)

2 (cm)

Mean (l)

1

14.7

52.9

47.2

50.05

100

2

19.6

50.5

48

49.25

105

3

24.5

55.5

51.3

55.5

97

 

n = 100.66

Frequency = n/2 = 50.33 Hz


Calculations


Weight Suspended, T = 1.5 kg, 2 kg, 2.5 kg

Length of Sonometer wire = 1 m

Mass of wire, m = 1.5 x 10-4 kg

M = m/l = 1.5 x 10-4 kg/m

 

Result:

 

The frequency of the ac main = 50.33 Hz.

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