We derived the wave equation by applying f=ma to an element of an oscillating string, yielding ∂2y/∂x2 = 1/v2 ⋅ ∂2y/∂t2. In order to get this result it was necessary to assume that the string in question was nearly horizontal, so that the angle formed by the tension vector and the horizontal axis satisfied the small angle approximation sinα=α. It follows that the equation applies only to waves of very small amplitude relative to wavelength. However, it is claimed, by my textbook for instance, that this equation is a general result that describes all wave phenomena. How can the derivation be generalized to waves with larger amplitudes if it requires the assumption that the string is nearly horizontal?