$$\require{cancel}$$
But the up and down speed of a point on a transverse wave doesn't tell us how fast the wave moves from one place to the next. The wave speed, $$v$$, is how fast the wave travels and is determined by the properties of the medium in which the wave is moving. If the medium is uniform (does not change) then the wave speed will be constant. The speed of sound in dry air at $$20^{\circ}\text{C}$$ is $$344\text{ m/s}$$ but this speed can change if the temperature changes.
Speed of a point on the wave, speed of the wave, velocity of the wave, bulk modulus (compressibility), Young's modulus (stiffness), speed of electromagnetic waves, speed of sound in different media, linear waves, $$v=\lambda f$$, wave number, angular frequency, index of refraction.