# Investigation of the variation of fundamental frequency of a stretched string with length

Every object has a natural frequency of vibration. If kinetic energy is applied to an object at a rate that matches its natural frequency, resonance occurs and the object vibrates. In this experiment a small current, produced by a signal generator, causes the sonometer wire (must be a conductor) to move up and down due to interaction with the magnetic field of a U-shaped magnet. When the frequency of the a.c. current matches the fundamental frequency of the wire, resonance occurs causing noticeable vibration of the wire. In this simulation only the fundamental frequency is found, no harmonics.

Procedure:
1. Press the "Signal ON" button.

2. Adjust the frequency of the signal current using the right hand slider at the bottom.

3. When maximum vibration occurs, press the "Signal OFF" button.

4. Press "Get ruler" to measure the length of the wire.

5. Record the length of the wire (m) and the frequency.

6. Using the left hand slider move the bridge a little to the right. The magnet stays midway between the bridges.

7. Repeat steps 1 to 6 until you have at least six sets of length and frequency readings.

Graph: On graph paper, draw a graph of frequency against 1 / length (x-axis). Start both axes at zero.
A straight line graph through the origin shows that frequency is proportional to 1 / length (i.e. frequency is inversely proportional to length).

Precautions:
• To avoid parallax errors, ensure that your eye is directly above the ruler when measuring the length of the wire.
• Ensure that the tension remains constant throughout as the bridges are moved.
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