The frequency of vibration of a stretched string depends upon its length , its mass per unit length and Tension in the string. Obtain dimensionally an expression for frequency .
Step-1: Given data
As per question the frequency of vibration depends on .
As is length so its dimension will be:
is mass per unit length so:
is a tension which is a form of force. so:
Step-2: Calculate the dimension of
As the dimension depends on .
So, let the dimension of be ; here K is a dimensional constant.
Actual dimension of =
Substituting the values in and equating.
Comparing LHS and RHS
and and
So the dimension of becomes
The possible expression of is