 Shortening the string also reduces its mass, but does not alter the mass per unit length, and it is the latter ratio rather than the total mass which governs the frequency.The string vibrates in a standing wave whose speed of propagation is given by , where "T" is the tension and "m" is the mass per unit length; there is a node at either end of the vibrating length, and thus the vibrating length "l" is half a wavelength.Since the frequency of any wave is equal to the speed divided by the wavelength, we have frequency = .