An Electromagnetic Wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ε = 4.0. Them

Wavelength is halved and frequency remains unchanged

In vacuum, $ε_0 = 1$

In medium,$ε = 4$

So, refractive index $ \mu = \sqrt{ε/ε_0} = \sqrt{4/1} = 2 $

wavelength $λ' = \frac{λ}{\mu}=\frac{λ}{2}$

and wave velocity $ v = \frac{c}{\mu}=\frac{c}{2}$

Hence, it is clear that wavelength and velocity will become half but frequency remains uncharged when the wave is passing through any medium.