A tuning fork emits sound waves into the air. If the temperature of...

The frequency of a sound wave depends only on the source (the tuning fork) and remains constant regardless of the temperature of the medium.

Since the frequency $f$ is constant, the time period $T = \dfrac{1}{f}$ also remains constant.

The speed of sound in a gas is directly proportional to the square root of its absolute temperature, $v \propto \sqrt{T}$. As the temperature of the air rises, the speed of sound $v$ increases.

From the wave relation $v = f \lambda$, since the speed $v$ increases and the frequency $f$ remains constant, the wavelength $\lambda$ must increase.

Therefore, the wavelength of the sound wave changes.