The relationship between energy, frequency, and wavelength is based on fundamental wave and quantum properties:

• Frequency (f) and wavelength (λ) are inversely related through the wave speed (v):

v=λ×fv=\lambda \times fv=λ×f

This means as frequency increases, wavelength decreases, and vice versa.

• Energy (E) of a photon or wave is directly proportional to frequency and inversely proportional to wavelength. The relation is:

E=h×f=h×vλE=h\times f=\frac{h\times v}{\lambda}E=h×f=λh×v​

where hhh is Planck's constant. So higher frequency means higher energy, and longer wavelength means lower energy.

Summary

• Frequency and wavelength have an inverse relationship.
• Energy is directly proportional to frequency.
• Energy is inversely proportional to wavelength.

Hence, with constant wave speed, increasing frequency shortens wavelength and raises energy, while decreasing frequency lengthens wavelength and lowers energy.