Question

An electromagnetic wave of frequency $2MHz$ propagates from vacuum to a non-magnetic medium of relative permittivity $9$. Then its wavelength

• A. Increases bv 100 m
• B. Increases by 50 m
• C. Decreases by 50 m
• D. Decreases by 100 m

Answer 1

Answer: (D)

In vacuum wavelength,
${\lambda }_0=\frac{c}{f_0}=\frac{3\times 10^8}{2\times 10^6}$
$=1.5\times 10^2=150m$
In medium, speed of wave is
$v=\frac{c}{\sqrt{{\epsilon }_r{\mu }_r}}\approx \frac{c}{\sqrt{{\epsilon }_r}}$
(as medium is non-magnetic)
$\therefore v=\frac{c}{\sqrt{9}}=\frac{c}{3}=1\times 10^{8}m{s}^{-1}$
Frequency remaining same, wavelength in medium is
$\lambda =\frac{v}{f_0}=\frac{10^8}{2\times 10^6}=50m$
$\therefore$ Wavelength decreases by $100m$.