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Aim(i) To study the relation between frequency and length of a given wire under constant tension using a sonometer.
(ii) To study the relation between the length of a given wire and tension for constant frequency using a sonometer.
Apparatus RequiredA sonometer
A wire of uniform cross-section
Weights (known masses)
Tuning fork
Meter scale
Screw gauge
Stopwatch
TheoryThe frequency of a vibrating wire is related to its length, tension, and mass per unit length. For a given wire under constant tension, the frequency is inversely proportional to the length of the wire. Similarly, for a given wire with constant frequency, the tension is directly proportional to the length of the wire. The frequency of a vibrating wire can be measured using a tuning fork. The length of the wire can be measured using a meter scale or screw gauge.
Prosedurei) To study the relation between frequency and length of a given wire under constant tension using a sonometer:
Fix the wire to the sonometer and adjust the tension to a constant value.
Strike the tuning fork and place it on the sonometer’s resonance box.
Adjust the position of the movable bridge to produce resonance in the wire.
Measure the distance between the two fixed bridges using a meter scale or screw gauge.
Repeat the experiment by varying the distance between the bridges and record the corresponding frequencies.
Plot a graph between frequency and length of the wire.
(ii) To study the relation between the length of a given wire and tension for constant frequency using a sonometer:
Fix the wire to the sonometer and adjust the distance between the bridges to produce resonance at a constant frequency.
Add weights to the wire to increase the tension.
Measure the distance between the bridges using a meter scale or screw gauge.
Measure the mass of the weights using a balance.
Repeat the experiment by varying the weight and record the corresponding lengths.
Plot a graph between length and tension of the wire.
Observation and Result(i) The frequency of a vibrating wire is inversely proportional to its length under constant tension. This relationship can be observed by plotting a graph between frequency and length of the wire. The graph should be a straight line passing through the origin. (ii) The tension in a wire is directly proportional to its length under constant frequency. This relationship can be observed by plotting a graph between length and tension of the wire. The graph should be a straight line passing through the origin. By measuring the slope of the graph, the mass per unit length of the wire can be calculated.