During propagation of a wave from one medium to another, the frequency remains constant and wavelength changes.

$\mathrm{\mu }=\sqrt{\frac{\mathrm{\epsilon }}{{\mathrm{\epsilon }}_0}}=\sqrt{4}=2$

Since  $\mathrm{\mu }\propto \frac{1}{\mathrm{\lambda }}$

$\therefore$Wavelength is halved
Hence option (wavelength is halved and frequency remains unchanged) holds good.