the velocity V of transverse wave in a stretched wire depends on tension F in the wire and its mass per unit length M stablished the formula for velocity of transverse wave with the help of dimensions
v = kla Tb mc
[ M0 L T-1 ] = [ L ]a [ M L T-2 ]b [M] c \ [ L ]c
[ M0 L T-1 ] = [ Mb+c La+b-c T -2b ]
b+c = 0
a+b-c = 1
-2b = -1 we get
b = 1\2
c = -1\2
a = 0 therefore v = k whole root of T \ m
[ M0 L T-1 ] = [ L ]a [ M L T-2 ]b [M] c \ [ L ]c
[ M0 L T-1 ] = [ Mb+c La+b-c T -2b ]
b+c = 0
a+b-c = 1
-2b = -1 we get
b = 1\2
c = -1\2
a = 0 therefore v = k whole root of T \ m
