Wirth was born in Žlutice (German: Luditz) in western Bohemia. As Joseph Joachim's assistant at the Hochschule für Musik (Berlin), he taught violin and viola. August Wilhelmj said he was the best violin teacher of his generation. His students included Albert Stoessel and Edmund Severn.
Wirth played viola in the famous string quartet of its time, the Joachim Quartet. Wirth died in Berlin.
His son Joseph Wirth married Julia Wirth née Stockhausen (1886–1964), daughter of the singer and voice teacher Julius Stockhausen.
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