why wave factor for water is 10?

Hi everyone,

I have a very basic question. lets say we send 200MHz wave into water (150cm wavelength), somebody told me that i have to divide that wavelength by 10. is it the wave factor for water? why 10? where that 10 comes from? I ll appreciate all you answers, Thank you!:-D

Any elementary text in electromagnetics will assist you here. Basically "somebody" told you that the refractive index of water is 10. This likely stems from them believing that the real part of the permittivity of water is ~100. The refractive index is equal to the square root of the permittivity. Note, water is highly lossy at these frequencies (hence the high permittivity) therefore it is best to include the complex representation of the permittivity so that you get the correct relationships.

The real part of the refractive index is related to the propagation velocity of the EM wave as its fraction of the speed of light in a vacuum. Therefore, an EM wave will travel 1/10 as fast in water as it does in free space (using your numbers at 200MHz). Since this is the case and since V_light_in_medium=lambda/n*Freq (knowing that Frequency does not change in a medium) the effective wavelength must therefore decrease in order to maintain the equality. This seems to be the "wave factor" as you call it.

Have Fun

10 is a rough estimation, around 9 would be more exact. The value can be calculated from frequency and temperature dependant permittivity.
er' = 87.86 er'' = 1.82 (0°C, 200 MHz)
er' = 78.35 er'' = 0.76 (25°C, 200 MHz)

Thank you tallface65!very helpful.

---------- Post added at 20:34 ---------- Previous post was at 20:34 ----------

Thank you Fvm!it helped me a lot.