Error method never bring exact result but some time it saves a lot of time
So what you basically did is you knew the formula relating frequency and tension
By knowing change in tension you calculated change in frequency
So can this (error method ) be applied anywhere where we want to know change in a particular quantity when we have the relation the relates the unknown change with the changes given in the question
Yes error method can be applied anywhere when there is not a very large change is mentioned but since it a approximation method , it never bring exact result . So be careful while applying in numerical based question and when option are very close to each other.