Final answer:
The mathematical relationship between frequency and wavelength is an inverse one, described by the equation c = fλ. As frequency increases, wavelength decreases, and this relationship is crucial for understanding the energy of waves.
Step-by-step explanation:
The mathematical relationship between frequency (f) and wavelength (λ) is an inverse relationship. This means that as the wavelength of a wave increases, its frequency decreases, and vice versa. The equation that represents this relationship is c = fλ, where c is the speed of light in a vacuum (approximately 3 x 108 meters per second). When you solve this equation for frequency, you get f = c / λ, again showing the inverse relationship between the two variables.
For example, if the frequency of a wave is doubled, the wavelength is halved, assuming the speed of the wave remains constant. This is consistent with the concept that higher frequency waves have more energy, as established by Planck's formula, E = hf, where E is energy, h is Planck's constant, and f is frequency.