To find the wavelength of the wave, we need to understand the relationship between the cut-off wavelength, guided wavelength, and the wavelength of the wave.

1. Cut-off Wavelength:
The cut-off wavelength is the minimum wavelength at which a wave can propagate in a particular medium or waveguide. It is determined by the physical dimensions and characteristics of the waveguide. Waves with a wavelength shorter than the cut-off wavelength will not be able to propagate.

2. Guided Wavelength:
The guided wavelength is the wavelength of a wave that is propagated through a waveguide. It is the actual wavelength of the wave within the waveguide and is determined by the cut-off wavelength and the properties of the waveguide.

3. Relationship between Cut-off Wavelength, Guided Wavelength, and Wavelength of the Wave:
The relationship between the cut-off wavelength, guided wavelength, and the wavelength of the wave can be expressed as follows:

λ_guided = λ_wave / √(1 - (λ_wave / λ_cutoff)^2)

Where:
λ_guided = guided wavelength
λ_wave = wavelength of the wave
λ_cutoff = cut-off wavelength

To find the wavelength of the wave, we can rearrange the equation as follows:

λ_wave = λ_guided * √(1 - (λ_wave / λ_cutoff)^2)

Now, let's substitute the given values into the equation:

λ_cutoff = 0.5 units
λ_guided = 2 units

λ_wave = 2 * √(1 - (λ_wave / 0.5)^2)

Simplifying the equation:

(λ_wave / 0.5)^2 = 1 - (λ_wave / 0.5)^2

2 * (λ_wave / 0.5)^2 = 1

(λ_wave / 0.5)^2 = 1/2

Taking the square root of both sides:

λ_wave / 0.5 = √(1/2)

λ_wave = 0.5 * √(1/2)
λ_wave = 0.5 * (√2 / 2)
λ_wave = 0.5 * 0.7071
λ_wave ≈ 0.3535 units

Therefore, the correct answer is option 'A' - 0.48 units.