Question

If a wave traveling through air decreases its wavelength by half, describe what happens to the wave speed and frequency.

Answer 1

The frequency, the speed and the wavelength of a wave are related by the following equation:
$f= \frac{v}{\lambda}$ (1)
where
f is the frequency
$\lambda$ is the wavelength
v is the wave speed

The speed of the wave does depend only on the properties of the medium, so since the wave is still traveling in air, the medium has not changed and therefore the speed remains the same. We see instead from eq.(1) that the frequency is inversely proportional to the wavelength, so if the wavelength is decreased by half, we see that the frequency will double.