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

1. Hold the Tuning Fork: The vibrating tuning fork is held over the open end of the air column.
2. Increase Length of Column: Gradually increase the length of the air column starting from zero until the first resonance is observed.
3. Identify Loudest Sound: The first position of resonance is reached when the loudest sound is heard from the column.

To calculate the speed of sound, use the formula:

$v = 4f(L + 0.34)$

Where:

• $v$ is the speed of sound,
• $f$ is the frequency (512 Hz), and
• $L$ is the length of the air column (16.2 cm = 0.162 m).

Substituting in the values:

$v = 4 \times 512 \times (0.162 + 0.34)$

Calculating gives: $v = 4 \times 512 \times 0.502 = 1026.048 \text{ m/s}$

Hence, the speed of sound in air is approximately $338.8 ext{ m/s}$.

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

1. Wave Adjustment: The diameter influences how sound waves resonate within the tube and the accuracy of the measurement.
2. Error Correction: It allows for adjustments in calculations to account for end correction, where wave ends partially extend beyond the end of the tube.
3. Proportionality: Sound wave behavior in tubes can vary based on diameter, affecting the speed calculations.

1. Find Distance Between First Two Positions: Measure the length of the column of air for the first two positions of resonance denoted as $L_1$ and $L_2$.
2. Double the Distance: The wavelength ($\lambda$) can be found using the formula: $\lambda = 2(L_2 - L_1)$
3. Calculate Speed: Then, use the speed of sound formula: $v = \frac{\lambda}{T}$, where T is frequency. Substituting gives: $v = \frac{2(L_2 - L_1) imes f}{f}$, ultimately helping to determine the speed of sound in air.