Investigation of the variation of fundamental frequency of a stretched string with tension

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 rate of movement due to the current matches the fundamental frequency of the wire, resonance occurs causing noticeable vibration. If the tension on the wire is increased (length kept constant), the resonant frequency of the wire also increases.

Procedure:
  1. Press the "Signal ON" button
  2. Adjust the frequency of the current from the signal generator 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 (m), the tension in the Newton balance and the frequency
  6. Press "Increase Tension"
  7. Repeat steps 1 to 6 until you have got at least six sets of tension and frequency readings
  8. To repeat the experiment press "Get Ruler", drag the right hand bridge to a new position (new length of string) and repeat steps 1 to 7

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

Frequency (Hz)
Tension(N)
   

Graph: On graph paper, draw a graph of frequency (y-axis) against the square root of the tension.

Note: Start both axes at zero. A straight line graph through the origin shows that the frequency of vibration of a stretched string is proportional to the square root of the tension on the string

Precautions:

  • Ensure that the length is kept constant (the bridges do not move) as the tension is changed
  • If a paper rider is used to locate resonance, place it mid-way between the bridges