If waves are traveling with the same speed, such as waves in a medium or electromagnetic waves in a vacuum, the relationship between wavelength, frequency, and speed is defined by the wave equation:
v = λf
where v represents the speed of the wave, λ is the wavelength, and f is the frequency.
If we rearrange the equation to solve for wavelength, we get:
λ = v / f
From this equation, we can observe that if the frequency (f) of the waves increases while the speed (v) remains constant, the wavelength (λ) must decrease.
In other words, as the frequency increases, the wavelength decreases proportionally, maintaining a constant speed. This relationship holds for various types of waves, including sound waves, electromagnetic waves, and any other waves that travel at a constant speed through a medium or space.