# Clarification on Phase wave derivation in De Broglie's paper

De Broglie's paper refers to his theorem

A periodic phenomenon is seen by a stationary observer to exhibit the frequency $$ν_1=h^{-1}m_0c^2\sqrt{1-\beta^2}$$ that appears constantly in phase with a wave having frequency $$ν=h^{-1}m_0c^2/\sqrt{1-\beta^2}$$ propagating in the same direction with velocity $$V=c/\beta$$.

where,

• $$\beta$$=Velocity of periodic matter/ speed of light

• $$m_0$$=proper mass

• $$c$$=velocity of light

• $$ν_1$$=refers to frequency of the periodic oscillation as seen by the fixed observer

• $$ν$$= refers to frequency obtained by equating E=hν=m$$c^2$$

De Broglie also provides a proof for this theorem. He calculates the phase of the two waves($$ν_1$$ and $$ν$$) and shows that the two waves maintain equal phase for any given distance x travelled by the waves.

He calculates phase of $$ν_1$$ at time t by calculating $$ν_1\cdot t$$. He then goes on to calculate phase of $$ν$$ by calculating $$ν\cdot(t-\frac{\beta \cdot x}{c})$$.I have a question here. Can someone explain how does the factor $$(t-\frac{\beta \cdot x}{c})$$ comes into play for calculating phase of $$ν$$

Another question, What does $$ν$$ frequency obtained through energy relation (hν) indicates. Is it a hypothetical frequency that has no relation to real world?

The full de broglie paper can be downloaded from http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf . I am referring to Chapter 1 'The Phase Wave' derivation.

• Are you saying that the first relation is for a fixed observer and a fixed source? What is the observer fixed relative to? – ggcg May 8 '19 at 20:39
• @ggcg as I understand there is some periodic oscillation of a moving particle. If an observer watches the moving particle from a fixed reference, he sees the frequency to be lesser. – Karthick S May 9 '19 at 2:32