What happens to the wavelength of a wave on a string when the frequency is doubled (tension remains the same)?

When the frequency of a wave on a string is doubled, the wavelength decreases. This relationship is described by the wave equation ( v = f \lambda ), where ( v ) is the wave speed, ( f ) is the frequency, and ( \lambda ) is the wavelength. Since the tension remains constant, the wave speed also remains constant, so if the frequency increases, the wavelength must decrease in order to maintain the same wave speed. Specifically, if the frequency is doubled, the wavelength is halved.