In an experiment to determine the speed of sound in air a student measured the length / l of a column of air when it was vibrating at its fundamental frequency f - Leaving Cert Physics - Question 4 - 2022

The student held the vibrating tuning fork close to the mouth of the pipe while gradually adjusting the length of the column of air. They did this until the loudest sound was heard, which indicated that the fundamental frequency was resonating. The length was then measured from the closed end to the open end of the pipe.

To graph the relationship:

• Set up a Cartesian coordinate system with 1 / f on the y-axis and l on the x-axis.
• Plot the calculated values of 1 / f versus l:
  • For f = 256 Hz, 1/f = 0.0039
  • For f = 288 Hz, 1/f = 0.0035
  • For f = 320 Hz, 1/f = 0.0031
  • For f = 341 Hz, 1/f = 0.0029
  • For f = 384 Hz, 1/f = 0.0026
  • For f = 480 Hz, 1/f = 0.0021
• Draw the line of best fit, ensuring that it does not pass through the origin.

Using the slope of the line from the graph, we know that:

$\text{slope} = \frac{\Delta l}{\Delta (1/f)}$

Assuming the slope is calculated as k, we employ the relationship:

$v = slope \times c$

Where v = speed of sound in air. Given that the slope derived from the graph is approximately equal to 340 m/s, then we conclude the speed of sound in air is around 340 m/s.

The line of best fit does not go through the origin because there is an end correction term that accounts for the wave existing above the opening of the pipe. This is due to the fact that sound waves do not start exactly at the physical opening of the tube, but extend beyond it, thus introducing a discrepancy in the observed length of the air column versus the actual resonating length.