Measurement of the speed of sound in air

Apparatus

1000 ml graduated cylinder, resonance tube, set of tuning forks in the frequency range 256 Hz to 512 Hz, vernier callipers, metre stick, stand (longest upright type), clamp and wooden block.

Procedure

• Clamp the tube so that the water in the graduated cylinder closes its lower end. The tube should be free to slide vertically through the clamp jaws. Take an approximate value of 300 m s⁻¹ for the speed of sound to obtain a rough estimate of the quarter wavelength resonance position.

• Strike the highest frequency (512 Hz) tuning fork on the wooden block, and hold it in a horizontal position just above the mouth of the tube (Fig. 1).

• Slide the tube slowly up/down until the note heard from the tube is at its loudest; resonance is now occurring.

• Tighten the clamp in this position and measure the length of the air column (from the water level to the top of the tube) with a metre stick.

• Clamp the tube (or its extension) so that the air column is 2 or 3 cm less than 3l₁ (Fig. 2).

• Obtain a second weaker resonance with the same tuning fork by again sliding the tube until the note heard is at its loudest, at the three-quarters wavelength resonance position.

• Clamp the tube in this position and measure with a metre stick, the air column length l₂ at this resonance.

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Measurement of the speed of sound in air

• Repeat this procedure to obtain the corresponding values of l₁ and l₂ for all the tuning forks in order of decreasing frequency.
• Record the measurements in a table.
• Calculate the wavelength using $λ = 2(l₂ - l₁)$ in each case.
• Calculate the speed of sound from $c = fλ$ for each of the tuning forks.
• Find the average value for the speed of sound.

Results

$f/Hz$	$l₁/m$	$l₂/m$	$λ/m$	$c/ms^{-1}$

The average value of the speed of sound in air =