Here's an easy way to think about this. The wavelength is the distance from crest to crest, or trough to trough -- equivalently, it's the distance the wave travels in one period. This means that the speed of the wave is the wavelength divided by the period, or <span><span>v=<span>λT</span></span><span>v=<span>λT</span></span></span> . But the frequency is just the reciprocal of the period, so <span><span>v=λf</span><span>v=λf</span></span>. Clearly, if v increases and the frequency stays the same, the wavelength must increase by an equivalent factor.
