Node spacing equation?

[maccha]

My textbook says that the equation for the distance between nodes of a standing wave is:

x=m(\lambda/2)

where m is an integer. What I'm confused about is wouldn't this mean that as m increases and produces the second, third, etc. harmonic, that the spacing between the nodes would become greater? I thought the wavelength got shorter as m increased.

[kuruman]

You are not thinking of it correctly. You will agree that the distance between any two adjacent nodes is λ/2. What about non-adjacent nodes? If there is one node between them, the distance will be 2(λ/2); if there are two nodes in-between, the distance will be 3(λ/2) and so on. Do you see now where the m belongs?

[maccha]

Oh that makes sense thanks so much!