# Speed of a standing wave

Standing waves are the waves in which disturbances do not simply propagate forward or backward, but rather the material particles are moving up and down continuously, with the particles between two consecutive nodes in the same phase. But when we are talking about the harmonics of such a wave, we define the $$n^{th}$$ harmonic by- $$f_n=\dfrac{n}{2L} \sqrt{\dfrac{T}{\mu}}$$ The problem is, this formula is derived by assuming that the wave speed is $$v=f\lambda$$ or $$v=\sqrt{\dfrac{T}{\mu}}$$ But if the wave is actually standing, what does this speed actually mean? Does it mean twice the length of the string times the frequency of the individual particles performing harmonic oscillations? And if that is so, who is to say that it will be equal to $$\sqrt{T/\mu}$$?

• Could you provide more details about the system/equation that you are solving, how you arrive at harmonics, and why you think you need to know the speed. The question seems to lack the context. Sep 5, 2020 at 8:02