Question

A uniform plane wave travels through fresh water characterised by \(\varepsilon_r = 78\). Fresh water is non-magnetic and non-conducting. The wavelength of propagation in fresh water at an operating frequency of \(300~\text{MHz}\) is ________.

• A. 11.32 cm
• B. 22.68 cm
• C. 6.86 cm
• D. 32.86 cm

Hint:

Wavelength in a dielectric medium reduces by a factor of \(\sqrt{\varepsilon_r}\). Use this whenever \(\varepsilon_r\) is given.

Answer 1

The Correct Option is A

We use the formula for wavelength in a medium: \[ \lambda = \frac{c}{f\sqrt{\varepsilon_r}} \] Where: \(c = 3 \times 10^8\) m/s (speed of light) \(f = 300~\text{MHz} = 300 \times 10^6~\text{Hz}\) \(\varepsilon_r = 78\) Then: \[ \lambda = \frac{3 \times 10^8}{300 \times 10^6 \cdot \sqrt{78}} = \frac{1}{\sqrt{78}} \approx \frac{1}{8.83} \approx 0.1132~\text{m} = 11.32~\text{cm} \] Final Answer: 11.32 cm