Frequency of vibrations of a clamped metal rod

It's not necessary that the rod will vibrate with fundamental frequency but with any frequency satisfying the boundary condition so that $$e^{ikx}=e^{ik(x+l/2)}$$ $$Rightarrow k=frac{pi n}{l}Rightarrow boxed{lambda=frac{l}{2n}}$$ where $n$ is an integer.

You have represented a standing wave in the figure. A standing wave is created by superposition of traveling waves. The frequency of traveling waves will depend on the frequency of applied/driving force. To change the mode of vibration you can change the frequency of the driving force or change the tension in the rod.

You can observe it in this video. https://m.youtube.com/watch?v=-k2TuJfNQ9s