# Do incoherent sources of waves mean that the frequency of the sources are different?

I studied that coherent sources of waves are those sources that maintain a constant phase difference between the two waves as time passed and incoherent sources are ones that don't. Does this imply that coherent sources are those sources which has same frequency and incoherent sources are those sources which have different frequency? Can we define incoherent sources as those sources whose frequencies are different?

• Your reasoning is correct. May 28 '21 at 12:45

No, If the two sources have a constant phase difference this doesn't imply that the waves have equal frequency, You actually need to additionally assume this.

The two sources are said to be coherent if their frequency and waveform are equivalent.

The sources which are not coherent are incoherent.

Edit: Note that, In general $$\mathbf{E}_1(\mathbf{r},t)=\mathbf{E}_{01}\cos(\mathbf{k}_1\cdot \mathbf{r}-\omega_1 t+\epsilon_1)$$ $$\mathbf{E}_2(\mathbf{r},t)=\mathbf{E}_{02}\cos(\mathbf{k}_2\cdot \mathbf{r}-\omega_2 t+\epsilon_1)$$ Thus the phase difference $$\delta =(\mathbf{k}_1\cdot \mathbf{r})-(\mathbf{k}_2\cdot \mathbf{r})+(\omega_1-\omega_2)t+\epsilon_1-\epsilon_2$$ Since at optical frequencies the fields oscillate at in excess of $$10^{14}$$ Hz, $$\epsilon_i(t)$$ are time dependent so For coherent sources one needs, $$\omega_1=\omega_2\ \ \ \ \ \ \ \epsilon_1-\epsilon_2=\text{constant}$$

• I guess that is why " temporal" and " spatial" coherence come from May 28 '21 at 13:26
• That's what refers to coherence, Coherence is a measure of the correlation between the waves or with itself. Naively, Between is what is said, temporal, and with itself is what refer to spatial. May 28 '21 at 13:30
• I see. What does it mean to be in coherence with itself? Does this involve a source that changes its frequency? Also, btw I've never heard of coherence relating to wavelength at all. May 28 '21 at 13:35
• @Sidarth You can ask a different question on this. The wavelength and frequency are related by $c=\lambda \nu$ so it doesn't matter. and I haven't talked about wavelength. May 28 '21 at 13:40
• We know that phase difference, $Δ\phi= (k_{2}-k_{1})(x_{2}-x_{1})-(ω_{2}-ω_{1})t$. For $Δ\phi$ to be constant, we have to obviously eliminate $t$ which is time because time will obviously keep changing which will lead to constantly changing $Δ\phi$. In order to eliminate $t$, $ω_{2}-ω_{1}= 0$ which implies $ω_{2}=ω_{1}$ which implies the frequency of both the waves must be equal. May 28 '21 at 13:41