What is the Approximation for Retarded Time?

[noamriemer]

Hello again!
Facing some problems (my exam is taking place tomorrow... help is needed. Many thanks in advance!)

I need to find an approximation for a retarded time. I don't understand how. This is what my lecturer wrote: $sin(\varphi-\omega t)=exp(i\varphi'-i\omega(t-r/c)-i\omega(r'cos\theta cos\theta'+r'sin\theta sin\theta'cos(\varphi-\varphi'))/c$


Could you please explain how ?
Thank you!

 

[yungman]

I think you copy incorrect. You are assuming harmonic wave in you case where it is a sinusoidal wave. Usually it is represented by cosine wave:

$$cos ( \beta z -\omega t -\phi) = cos ( \omega t -\beta z +\phi) = \Re e[e^{j\omega t}e^{-j\beta z}e^{j\phi}]$$

The way you look at this is the peak of the cosine function is at $\omega t - \beta z +\phi = 0$. Let's first assume $\phi= 0$ to simplify the problem. So if z is positive, then t has to be positive to get $\omega t - \beta z = 0$. In words, if you start at z=0, it takes $\omega t = \beta z$ for the wave at z=0 to reach z. So this is the retard time function.

 

[noamriemer]

Thank you...