Concept:
Rochelle salt is a double salt. It contains sodium, potassium, and tartrate ions.
Step 1: Chemical name.
Rochelle salt is chemically known as sodium potassium tartrate.
Step 2: Formula.
Its chemical formula is commonly represented as:
\[
KNaC_4H_4O_6 \cdot 4H_2O
\]
Step 3: Why option (B) is correct.
The name sodium potassium tartrate directly matches the composition of Rochelle salt.
Step 4: Checking other options.
Sodium potassium chloride, potassium sodium sulphate, and sodium potassium carbonate are not Rochelle salt.
Step 5: Final answer.
Therefore, Rochelle salt is chemically sodium potassium tartrate.
\[
\boxed{\text{Sodium potassium tartrate}}
\]