Question: I know that when I am playing one string on the guitar, it creates a standing wave which causes the entire body vibrates in its frequency and therefore create sound waves. But, what about two strings?

Do the two waves cause the same body to vibrate in some kind of a sum of the two frequencies? How come you get the sound of both from the same body?

Answer: 
The first image shows a string oscillating at its fundamental frequency $f$.

The second image shows a string oscillating at $2f$.

The third image shows a string (or the wooden soundbox of a guitar or the air in and around a guitar) oscillating at both frequencies at the same time.

[![enter image description here](https://i.stack.imgur.com/Il1VA.gif)](https://i.stack.imgur.com/Il1VA.gif)

[![enter image description here](https://i.stack.imgur.com/REE9k.gif)](https://i.stack.imgur.com/REE9k.gif)
[![enter image description here](https://i.stack.imgur.com/zma4o.gif)](https://i.stack.imgur.com/zma4o.gif)

Finally, here is a graph showing the height of a point a short way along the last string, as a function of time. Notice that it vibrates with an overall period of $2\pi$, but within each period there is also a faster oscillation with period $\pi$.
[![enter image description here](https://i.stack.imgur.com/oVPU1.png)](https://i.stack.imgur.com/oVPU1.png)
The body of the guitar will vibrate at both frequencies at the same time.

This is because the body of the guitar is approximately a [linear system](https://en.wikipedia.org/wiki/Linear_system) so the vibration at each frequency is independent of each other.

This is also the case for air, which is why we can hear multiple things at the same time.