A resonance tube can be used to measured the speed of sound in air. A tuning fork is held above the opening of the tube and struck, while the far end of the tube is lengthened or shortened. Resonances (loudnesses) are heard at a series of tube lengths, L, which are carefully measured.

resonance tube

The speed of sound in air is determined by measuring the distance between two consecutive resonances. A data set for a tuning fork with a frequency of 320 Hz are L1 = 25.8 cm; L2 = 78.4 cm; and L3 = 131.1 cm. Based on these data, what is the speed of sound in air?

Hint: the opening at the top is an antinode while the water surface is a node. Therefore, what fraction of a full wave is L1? What fractions are L2 and L3?