The adjective 'sound' here means 'safe' or 'reliable'. As an adjective it can also mean 'in good condition'. The foundations were sound. It's also British English slang to mean 'very good' or excellent. 'The new song by Oasis is sound (as a pound).' It can also mean severe. 'Manchester United took a sound beating at the weekend.' [They lost heavily]

The meaning of "sound" here is "healthy/stable/solid".