Optics question - carrier waves

[jaejoon89]

I am trying to understand what exactly the envelope is and why does the irradiance have twice its frequency?

In class my teacher showed that when you sum individual waves, you get the carrier wave. Then my teacher showed something called an envelope, which looks a lot like an oscillating sine wave with lambda = 2pi/k. I guess the envelope shows how the amplitude of the carrier wave oscillates, but what is it exactly? And why does the irradiance have 2x its frequency?

 

[turin]

I guess the envelope shows how the amplitude of the carrier wave oscillates, ...

Yes.

... but what is it exactly?

It is not physical, nor even necessarilly well-defined. It approaches well-defined as f_AM/f_carrier → 0, where f_AM is the amplitude modulation frequency, and f_carrier is the carrier frequency.

... why does the irradiance have 2x its frequency?

I think we need more information to help you understand this. It seems like there is some special condition that you are neglecting to mention ...