For mechanical wave : e.g. wave on a string propagate in x direction (displacement in y direction)
y(t)=A \sin (kx-\omega t)
So vy(t)=\frac{dy(t)}{dt}=-A\omega \cos(kx-\omega t)
The kinetic energy  per unit length K=\frac{1}{2}m v^2=\frac{1}{2} \rho dx A^2\omega^2 \cos^2(kx-\omega t) where \rho is the mass per unit length
So the energy of the wave proportional to amplitude A^2 and frequency f^2, where \omega=2\pi f.

However, the wave speed is determined by the wave media (string) v=\sqrt{\frac{T}{\rho}}
The frequency of the wave is determined by source. And the wavelength \lambda =v/f
If you did not change the frequency of the wave source, putting more energy means increase the amplitude of the wave.
Actually, it is also possible to change the frequency of the wave source, however, more power is required to generate wave with the same amplitude.

E=hc/\lambda is the relation for light. It means that the power of light is proportional to the frequency (assume electric field is the same).
Light source determined the frequency of the generated light.