If the speed of a wave decreases but the wavelength remains the same, what must be true of its frequency?

The frequency will decrease.

The frequency will fluctuate wildly.

The frequency will increase.

The frequency will stay the same.

The frequency increases.

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 v = λT v = λT. But the frequency is just the reciprocal of the period, so v=λf v=λf. Clearly, if v increases and the frequency stays the same, the wavelength must increase by an equivalent factor.