<p>If frequency doubles what is the wave's speed? I get tricked up because books keep saying it's the medium that determines the waves speed. Not the frequency</p>
<p>If the frequency doubles then the wavelength reduces by a factor of 2, but the wave’s speed is constant (this constant depends on the medium).</p>
<p>The relation between frequency f and phase speed c is L = c/f, where L is the wavelength. If you consider a propagation of light, the frequency of the light wave is constant in a vacuum and a medium because it determines the energy. The medium affects the speed of a wave and the wavelength. Every transparent medium is characterized by refractive index n (for example, for distilled water n = 1.33 and for glass it is about 1.5, different values for different types of glasses). It shows in how many times light speed decreases during propagation inside given medium: n = c/v, where v is the real speed of light in the medium. Since frequency is always constant, the wavelength is changed. So, if the frequency doubles, the wave speed remains the same. </p>
<p>Note that if one says about group speed which determines the speed of the energy transfer, it can be affected by the frequency and is dependent on the inner properties of a given medium. This dependency is described by the so-called dispersion law for a given medium and answer cannot be given in a general case.</p>