In a resonance column tube (which acts as a closed organ pipe), the difference between two successive resonance lengths is equal to half the wavelength ($\lambda/2$). Given successive resonance lengths: $l_1 = 9.75 \text{ cm}$ $l_2 = 31.25 \text{ cm}$ $l_3 = 52.75 \text{ cm}$ We can find the wavelength $\lambda$: $\frac{\lambda}{2} = l_2 - l_1 = 31.25 \text{ cm} - 9.75 \text{ cm} = 21.5 \text{ cm}$ (Also verified by $l_3 - l_2 = 52.75 - 31.25 = 21.5 \text{ cm}$) $\lambda = 2 \times 21.5 \text{ cm} = 43.0 \text{ cm} = 0.43 \text{ m}$ Given the frequency of the tuning fork, $f = 800 \text{ Hz}$, the speed of sound $v$ is: $v = f\lambda = 800 \text{ Hz} \times 0.43 \text{ m} = 344 \text{ m/s}$