Question

An electromagnetic wave of frequency $2\, MHz$ 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,
$\lambda_{0}=\frac{c}{f_{0}}=\frac{3 \times 10^{8}}{2 \times 10^{6}}$
$=1.5 \times 10^{2}=150\, m$
In medium, speed of wave is
$v=\frac{c}{\sqrt{\varepsilon_{r} \mu_{r}}} \approx \frac{c}{\sqrt{\varepsilon_{r}}}$
(as medium is non-magnetic)
$\therefore v=\frac{c}{\sqrt{9}}=\frac{c}{3}=1 \times 10^{8}\, ms ^{-1}$
Frequency remaining same, wavelength in medium is
$\lambda=\frac{v}{f_{0}}=\frac{10^{8}}{2 \times 10^{6}}=50\, m$
$\therefore $ Wavelength decreases by $100\, m$.