Relativity Science Calculator - Relativistic Sinusoidal Wave Function

Relativistic Sinusoidal Wave Function

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture" - Bertrand Russell ( 1872 - 1970 )

§ Definitions:

(i).

angular_frequency.png

(ii).

phase_velocity.png

(iii).

wave_number.png

(iv).

wavelength.png

(v).

phase_cycle.png

§ Derivations:

(i). Therefore,

derivations.png

(ii). Relativistic sinusoidal wave function:

An observer in stationary S system would therefore view a sinusoidal wave form as  

sine_function.png

but another observer in relatively moving S' system would view the same sinusoidal wave form as follows: 

relativistic_sinusoidal.png