The velocity (v) of transverse waves on a string may depend upon (1) length (l) of string, (2) tension T - Physics - Units And Measurements

Question

The velocity (v) of transverse waves on a string may depend upon
(1) length (l) of string, (2) tension T in the string and (3) mass
per unit length (m) of the string Derive the formula
dimensionally

Neha Gupta · Accepted Answer

Velocity is given by:v = klaTbmc[M0LT-1] = [L]a[MLT-2]b[M]c[L]c[M0LT-1] = [Mb+cLa+b-cT-2b]b+c = 0a+b-c =1-2b =-1we getb= 12c = -12a =0thereforev = kTm

The velocity (v) of transverse waves on a string may depend upon (1) length (l) of string, (2) tension T in the string and (3) mass per unit length (m) of the string. Derive the formula dimensionally.