# Thought for the day…

• I wanted to make an underwater 433 MHz aerial
• The aerial is normally either 1 wavelength, 1/2 wavelength or 1/4 wavelength.

Unfortunately the speed of light (radio is a kind of light) is also really important. It slows down by something called the “refractive index”. A vacuum has a refractive index of 1.0000000; air at 1 ATM,20 C is 1.000277 The “optimum” aerial length in metres is (Speed of light in m/s)/(Frequency in Hz or “waves per second”) so “metres/s” / “waves/s” = “metres * waves”. To get the length, we make waves = 1, 0.5, 0.25 depending on the fraction of a wavelength we want (sorry but this is needed when we talk about signal strength in air and water)…

So “in a vacuum” we get: Speed of light is 299’792’458 m/s, pod is 433 MHz which is 433’000’000 waves/s (does anyone know the real pod frequency?): 299’792’458/433’000’000 = 0.692361335 metre.waves which gives 69.24cm; 34.62cm; 17.31cm

In “air” we get: Speed of light is 299’709’438 m/s which makes the aerial 0.692169603 metre.waves or 69.22cm; 34.61cm; 17.30cm

Who cares?

In “water” at 20 C the refractive index is 1.330 and this matters because: Speed of light is 225’407’863 m/s which makes our aerial becomes 0.520572432 meter.waves or 52.06cm; 26.03cm; 13.01cm

• So I made a 26cm aerial and it works under water