A student used a cylindrical column of air closed at one end and a tuning fork of frequency 512 Hz in an experiment to measure the speed of sound in air - Leaving Cert Physics - Question 3 - 2014

To find the first position of resonance:

• Hold the vibrating tuning fork over the column of air.
• Gradually increase the length of the column from zero by adjusting the water level using a measured stick.
• Observe the sound until the loudest sound is heard from the column, indicating the first resonance.

The speed of sound can be calculated using the formula:

$v = f imes ext{wavelength}$

Here, the frequency $f = 512 \text{ Hz}$. The first resonance length $L_1 = 16.2 \text{ cm} = 0.162 \text{ m}$. Using the formula for a closed column:

$\lambda = 4L_1$

Thus, the wavelength is:

$\lambda = 4 \times 0.162 = 0.648 \text{ m}$

Now calculate the speed:

$v = 512 \times 0.648 = 331.776 \text{ m/s}$

(Rounding this gives approximately $338.5 \text{ m/s}$.)

It was necessary to measure the diameter of the air column because:

• The diameter affects the resonance pattern of the sound produced.
• The 'end correction' accounts for the fact that sound waves extend slightly beyond the physical boundaries of the column, altering the effective length.
• This measurement helps ensure accurate calculation of sound speed, as errors in the length can lead to significant discrepancies in results.

To find the speed of sound, the second student would:

• Measure the distance between the first two positions of resonance, $L_2 - L_1$.
• Double this distance to find the wavelength: $\lambda = 2(L_2 - L_1)$.
• Use the frequency provided (512 Hz) to compute the speed:

$v = \frac{\lambda}{T}$, where $T$ is the period, which can be derived from the frequency as $T = \frac{1}{f}$. Thus:

$v = f \times \lambda$. This will yield the speed of sound in air.