There are 2 train companies operating 2 routes - IC56, RS4. The cheapest train costs $37 and is 2h 36min.
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There are 3 ways to travel from Hanover to Wilhelmshaven. 4 buses, 4 trains and 1 by car are possible between the two areas. The by car from Hanover to Wilhelmshaven is the cheapest. The train operated by DB running from Hanover to Westerstede-Ocholt is the fastest. The train operated by running from Hanover to Nordenham is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!