Question

What is the relationship between the wavelength of a wave and it's energy?

Answer 1

Answer:

In general, the energy of a wave is inversely proportional to its wavelength.

Explanation:

Start with the simple proportional relationship: Energy of a wave is directly proportional to the wave's frequency. In quantum physics, the constant of proportionality is the Planck's constant $\hslash = 6.626 \cdot 10^{-34} J s$. Symbolically, for a photon (elementary unit of electromagnetic waves)

$E = \hslash \cdot f$

Frequency f, on the other hand, is inversely proportional to the wavelength $\lambda$. The constant here is the propagation speed v:

$f = \frac{v}{\lambda}$

and so combining both relationships, we get the following relationship between the energy and the wavelength:

$E = \hslash \cdot f = \frac{\hslash v}{\lambda}$

In classical physics, energy is jointly proportional to the square of the amplitude and to its frequency. Again, this implies an inversely proportional relationship to its wavelength.

In summary, the energy of a wave is inversely proportional to its wavelength.