In an experiment to determine the speed of sound in air a student determined the lengths l of a narrow column of air when it was vibrating at different fundamental frequencies f - Leaving Cert Physics - Question 3 - 2020

The student used a vibrating tuning fork placed over the air column. To find the correct length for a specific frequency, the student would change the length of the air column until the first loud sound was heard, indicating resonance. This adjustment made it possible to find the precise length corresponding to that frequency.

The student started with a small length of the air column and gradually increased it until the first loud sound was heard. By focusing on the first resonant frequency instead of higher harmonics, the student ensured that only the fundamental frequency was being excited.

First, calculate the values of 1/f for each frequency:

Plot these values on a graph with 1/f on the x-axis and l on the y-axis. Make sure to label the axes clearly.

The slope (m) of the graph can be calculated using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Select two points, for example, (0.002, 17) and (0.004, 34), to find the slope:

$m = \frac{34 - 17}{0.004 - 0.002} = \frac{17}{0.002} = 8500\, \text{cm}^2/s$

From the relationship between the speed of sound (v), the frequency (f), and the wavelength (λ), we use:

$v = f \times \lambda$

Given the values obtained and the calculated slope, the speed of sound can be derived. Assuming you find an appropriate value of m proportional to the speed of sound, for example, let’s take m = 85, then:

$v = 340 \text{ m/s}$

This indicates that the speed of sound in air is approximately 340 m/s.