$$\sigma = \frac{1}{\rho} \times \frac{1}{2\pi f \epsilon_0} \times \frac{c}{v}$$
Where:
- σ (S/m) is the conductivity of the medium
- ρ (kg/m3) is the density of the medium
- f (Hz) is the frequency of the wave passing through the medium
- ε0 (8.85 × 10−12 F/m) is the permittivity of vacuum
- c (3 × 108 m/s) is the speed of light in vacuum
- v (m/s) is the velocity of the wave passing through the medium
Given the velocity (v), wavelength (λ), and frequency (f) of the wave, you can calculate the conductivity (σ) of the medium using the following steps:
1- Calculate the wavelength (λ) using the formula:
λ = c / f
2- Rearrange the conductivity formula to solve for conductivity (σ):
σ = (ρ / 2π f ε0) × (c / v)
3- Substitute the values of v, λ, f, and c into the formula:
σ = (ρ / 2π f ε0) × (λ f)
4- Simplify the expression:
σ = ρ × λ × (10-7) S/m
By following these steps, you can calculate the conductivity (σ) of the medium using the provided information about velocity, wavelength, and frequency.
