Measurement of the speed of sound in air

A column of air in a tube, closed at one end, has a natural frequency of vibration at a particular length. If a vibrating tuning fork is placed over the tube and the length of the column of air is altered, it is possible to find the length that resonates with the tuning fork. At this point a loud sound is heard. In it's fundamental mode of vibration the length of the air column is approximately equal to one quarter of a wavelength. By measuring the length of the air column (l) and the diameter of the tube (d) it is possible to calculate the speed of sound in air (c) using the formula: c = 4f ( l + 0.3d), where f is the frequency of the tuning fork.

Note: In this simulation I have not included sound, so the position of resonance is found from the shape of the wave (1/4 wave).
Procedure:
  1. Press the "Strike Fork" button.
  2. Adjust the height of the inner tube, by dragging with the mouse, until resonance occurs. You will recognise resonance (at 1/4 wavelength) when the wave pattern produces a curved V shape. If you have not found resonance before the fork stops vibrating you can press "Strike Fork" again.
  3. At resonance, when the fork has stopped vibrating, press the "Get Ruler" button. Record the distance (l) from the top of the water to the top of the tube
  4. Press "New Fork". Record the frequency f
  5. Repeat steps 1 to 3 until you have got a resonant length for each tuning fork.
Note: For the last two forks (480 Hz and 512 Hz) it is possible to rise the tube sufficiently to find resonance at 3/4 wavelength position also. For these the distance between the two resonance positions is 1/2 wavelength. Multiply by 2 and multiply by the frequency to find the speed of sound

 

Frequency (Hz)
Length, l (m)
speed: c = 4f( l +0.3d )
     

Analysis: Calculate the average value of the speed of sound from the right hand column of the table.

It is also possible to calculate an average value by graphing l (y-axis) against 1/f. Since l = (c/4)(1/f) - 0.3d the value of c is calculated by finding the slope (c/4) of the graph and multiplying it by 4.

Precautions:

  • Ensure that your eye is level with the top of the tube when measuring the length to avoid parallax error
  • Repeat your efforts to find the loudest resonance position for each tuning fork. Take the average of the attempts