A cylindrical column of air closed at one end and three different tuning forks were used in an experiment to measure the speed of sound in air - Leaving Cert Physics - Question 3 - 2006

The frequency of the column of air was measured by reading the frequency $f$ directly from the tuning fork. The tuning fork's known frequency was used as a reference for determining the frequency of the vibrating air column.

The diameter of the column of air was measured using a vernier caliper or digital calipers, which provided accurate measurements of the internal diameter of the cylindrical air column.

It was known that the air column was vibrating at its first harmonic because resonance was observed. This was characterized by a loud sound produced when the length of the column matched the necessary conditions for the first harmonic.

To calculate the speed of sound in air, we use the relationship:

$v = f l$

where $f$ is the frequency and $l$ is the length of the air column. From the data:

• For $f = 512$ Hz, $l = 16.0 ext{ cm} = 0.16 ext{ m}$: $v_1 = 512 imes 0.16 = 81.92 ext{ m/s}$

• For $f = 480$ Hz, $l = 17.2 ext{ cm} = 0.172 ext{ m}$: $v_2 = 480 imes 0.172 = 82.56 ext{ m/s}$

• For $f = 426$ Hz, $l = 19.4 ext{ cm} = 0.194 ext{ m}$: $v_3 = 426 imes 0.194 = 82.65 ext{ m/s}$

Average speed of sound:

v_{avg} = rac{v_1 + v_2 + v_3}{3} = rac{81.92 + 82.56 + 82.65}{3} = 82.38 ext{ m/s}