This is an interesting question that often gets asked, and something I have been conscious of whilst working with different teams and projects. Do you need to have someone as a dedicated Scrum Master?
The origin of this question lies in the nature of how many projects do not have enough work for a dedicated Scrum Manager, simply because there isn't enough work full-time. There are two paths teams can take as Max Wenzin suggests in the blog post Dedicated ScrumMaster or Not, some of which as we will come to realize is in fact not viable.
Scrum Master can work on multiple projects
This is not ideal, and something I don't suggest, but some teams decide to utilize the SM in multiple projects and teams, in order to make greater use of his or her time. The SM would not feel like he or she fits in either team completely, will muck up your intuition because your mindset will be split between both projects.
As both projects would normally work concurrently, it is virtually impossible to be omni-present, and you will eventually miss out on key conversations that will hamper your management of the project, as Max identified correctly. The other path is to play a primary/secondary role in one project.
The primary/secondary role for a Scrum Master is a solution to bring enough workload. This involves the primary role being a SM, and the secondary role involving some other aspect that contributes to the project. Ideally, if a SM is technically-proficient, he/she could code or work on specific components, or work on the UI/design, or even Customer Development/Validation.
However as the author of Dedicated ScrumMaster or Not points out, this is a secondary role and when the SM needs to put his or her Scrum Manager hat on, that takes precedence over any other secondary work.
The author and I agree on the fact that not all Agile projects and teams work according to the book, and common-sense should prevail, allowing you to work as an effecting SM whilst not impeding your effectiveness by spreading yourself too thin or not committing enough to a specific project.