Problem with logo on transparanet background?

I have a tansparent background on my header and my logo has white text in it.. so it looks great when the home page is first loaded. However, when I scroll down, the header shrinks and the background turns to white… but then my logo can’t be seen properly. I might be missing something, but for this type of effect shouldn’t it require two different logos? In other words one logo for a white background and another logo for a dark backround? Please let me know how I can ensure that my logo is visible at all times. Many thanks!