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 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.

Procedure:
  1. Press the "Signal ON" button
  2. Adjust the frequency of the current using the slider at the top
  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 (cm) and the frequency
  6. Click on and drag the right hand bridge a little to the left. The magnet stays midway between the bridges
  7. Repeat steps 1 to 6 until you have got at least six sets of length and frequency readings

Results: Record the results in a table as shown here.

Frequency (Hz)
Length (m)
1 / length
     

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

Precautions:

  • Avoid parallax errors when measuring the length of the wire in each case
  • Ensure that the tension remains constant throughout as the bridges are moved