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Why would you need to divide wavelength by two to find out the distance between the two adjacent nodes?

Hi xueyang, good question. Wavelength is measured between equal parts of the wave. Adjacent nodes are not quite equal. Sure, they have the same displacement from equilibrium (zero, in other words), but the wave is moving in different directions at adjacent nodes, so in this respect adjacent nodes are not equal. Since they're not strictly equal, you can not measure wavelength as the distance between adjacent nodes, but it turns out that adjacent nodes are a half wavelength apart.