The frequency of vibration of a string depends of on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimensionally the relation for frequency.

The frequency of vibration of a string depends of on, (i) tension in t

1.	The frequency of vibration of a string depends of on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimensionally the relation for frequency.
Answer» SOLUTION :`npropI^(a)T^(B)m^(c),[I]=M^(0)L^(1)T^(0)` `[T]=M^(1)L^(1)T^(-2)` (force) `[M]=M^(1)L^(-1)T^(0)` `[M^(0)L^(0)T^(-1)]=[M^(0)L^(1)T^(0)]^(a)[M^(1)L^(1)T^(-2)]^(b)[M^(1)L^(-1)T^(0)]^(c)` `b + c = 0` `a + b – c = 0` `-2b=-1impliesb=(1)/(2)` `c=-(1)/(2)a=1` `nprop(1)/(l)sqrt((T)/(m))`