The relationship between wavelength and frequency is given by the wave equation:
c = λν
where c is the speed of light, λ is the wavelength, and ν is the frequency.
When the frequency is doubled, the wavelength is halved, assuming the speed of light remains constant. This relationship holds true for any type of wave, not just electromagnetic waves.
So, if the frequency is doubled, the wavelength is divided by two.
If the frequency is then tripled, we can apply the same relationship. Starting from the doubled frequency, if we triple it, the wavelength will be divided by three.
To summarize:
- When the frequency is doubled, the wavelength is halved.
- When the frequency is tripled (starting from the doubled frequency), the wavelength is divided by three.
It's worth noting that this relationship holds true for waves with a constant speed, such as electromagnetic waves in a vacuum. In different media, the speed of the wave might change, which can affect the relationship between wavelength and frequency.