If you say that something is unsound in some way, you mean that it is damaging in that way or to the thing mentioned. The project is environmentally unsound A diet extremely low in calories can also be a diet that is nutritionally unsound. sound
If a conclusion or method is unsound, it is based on ideas that are wrong. The thinking is good-hearted, but muddled and fundamentally unsound The national tests were educationally unsound. sound