Page 131 - Physics - XI

EXPERIMENT - 9

Aim

To study the relation between the length of a given wire and tension for constant frequency using sonometer.

Apparatus and Materials Required

A sonometer, a tuning fork, hanger of the given mass with slotted weights, rubber pad, paper rider, metre
scale, and two bridges

Principle/Theory
When a stretched wire is set in vibration, the frequency n of the fundamental note produced by it is given by

n = 1 T …(1)
2l m
where l is the length of the vibrating wire, T is the tension in the wire, and m is the mass per unit length of
the wire.

If frequency n and m are kept constant, then from (1) we have

T T = constant or
2
l
= constant, 2 l ∝ T or l ∝T,
l
i.e. if we plot a graph between l and T, the graph will be a straight line.
2
Procedure
1. Put the sonometer on a table and check that the pulley is frictionless, if not oil it. Stretch the wire by
placing suitable weights on the hanger.
2. Place two equal size sharp bridges below the wire, close to each other. Cut a small piece of paper into

V-shape, it is called a rider. Place the rider on the wire in the middle of the two bridges.
3. Set the given tuning fork into vibration by striking its prong gently against the rubber pad and place its
stem fi rmly on the sonometer board keeping the tuning fork vertical. Go on increasing the length of the
vibrating wire by adjusting the position of the two bridges till the paper rider start vibrating and fi nally
falls down. (Always keep the rider in the middle of the two bridges).

In this position, the frequency of the vibrating wire is exactly equal to the frequency of the tuning fork.
Measure the length of the wire while increasing.
4. Increase the distance between the bridges by 4 to 5 cm by moving them outward, so that the length of
the wire is increased. Repeat step 4 by decreasing the length of the wire till the paper rider falls down.

Note the distance between the two bridges with the help of a metre scale. This gives the resonant length
of the wire while decreasing.
5. Note the weights placed on the hanger.

6. Repeat steps 3, 4, and 5 at least six times by adding a load of 0.5 kg to the hanger each time using the
same tuning fork.
7. Note all the observations in the observation table.

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