At a fixed sound frequency, two successive resonant lengths of an air column closed at one end differ by half a wavelength. Subtract the shorter length from the longer length, then double that difference to find the wavelength.
The closed end is a displacement node and the open end is approximately a displacement antinode. The next resonant pattern fits one more half wavelength while keeping the same types of endpoints.
- Check that the two resonances are successive and have the same frequency.
- Double the difference between the lengths to find the wavelength.
- Multiply wavelength by frequency if the question asks for wave speed.
Worked example | Read two resonant lengths
A 500 Hz source gives successive resonances when the air column is 16.1 cm and 50.5 cm long. The length difference is 34.4 cm, so the wavelength is 68.8 cm, or 0.688 m.
The speed is fλ = 500 × 0.688 = 344 m/s. The 34.4 cm gap is the extra half wavelength that fits into the longer column.
Why use the difference between the lengths?
In the ideal model the first two resonances have effective lengths λ/4 and 3λ/4. Their difference is λ/2. In a real tube the displacement antinode is slightly beyond the open end. If the same end correction applies to both readings, it cancels in the subtraction.
The spacing method also works for any pair of successive resonances in this setup. You only need to know that there is no missed resonance between the two readings.
What if one resonance was missed?
Three consecutive resonance lengths are 12 cm, 38 cm and 64 cm. Find the wavelength using only the first and third lengths.
Answer. The 52 cm difference spans two half-wavelength steps. So the wavelength is 52 cm. Doubling the gap would incorrectly treat the readings as successive.
Frequently asked questions
Is the open end a displacement node?
It is approximately a displacement antinode. Keep the distinction between pressure and displacement clear when labelling nodes.
Can I compare resonant lengths at different frequencies this way?
Use two lengths measured at the same frequency. A frequency change can change the wavelength and therefore the spacing between resonances.
Official information
SEAB, 2027 GCE A-Level H2 Physics syllabus (9478), Superposition, stationary waves in air columns. Syllabus checked 11 November 2026. The examples are original.