I want you to act as a web developer and please write some code for me to create a fixed header for the website.

I want you to act as a web developer and please write some code for me to create a fixed header for the website.
The initial state background is semi-transparent or solid color.
When a user scrolls down the page (not just when the mouse cursor hovers), a subtle bottom shadow (box-shadow) should be added to the header to enhance visual hierarchy and distinguish it from the content area.