An electromagnetic wave of frequency \(5\, GHz ,\) is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are \(2 .\) Its velocity in this medium is \(\times 10^{7}\, m / s\)

\(=5 \times 10^{9} Hz\)

Relative permittivity, \(\epsilon_{ r }=2\)

and Relative permeability, \(\mu_{ r }=2\)

Since speed of light in a medium is given by,

\(v =\frac{1}{\sqrt{\mu \in}}=\frac{1}{\sqrt{\mu_{ s } \mu_{0} \cdot \epsilon_{ s } \epsilon_{0}}}\)

\(v =\frac{1}{\sqrt{\mu_{ s } \epsilon_{ x }}} \frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}=\frac{ C }{\sqrt{\mu_{ s } \epsilon_{ r }}}\)

Where \(C\) is speed of light is vacuum.

\(\therefore v =\frac{3 \times 10^{8}}{\sqrt{4}}=\frac{30 \times 10^{7}}{2} m / s\)

\(=15 \times 10^{7} m / s\)

\(\therefore\) Ans. is \(15\)