A uniform string is vibrating with a fundamental frequency 'f. The new frequency, if radius and length both are doubled would be……..

A uniform string is vibrating with a fundamental frequency 'f. The new

1.	A uniform string is vibrating with a fundamental frequency 'f. The new frequency, if radius and length both are doubled would be……..
Answer» 2f 3f `F/4` `f/3` Solution :Linear density of MASS for a given string, `mu = (M)/(L) = (V RHO )/(L) =( AL rho )/(L ) = A rho = jpi r ^(2) rho ` Now fundamental frequency is, `f - (1)/(2L ) SQRT((T)/(mu)) = (1)/(2L ) sqrt ((T)/( pi r ^(2) rho ))` ` therefore f = (1)/(2Lr ) sqrt ((T)/(pi rho )) implies f prop (1)/(Lr )` `therefore (f _(1))/( f.) = (L.r.)/(Lr) implies (f)/(f.) = ((2L) (2r))/( Lr ) implies f._(1) = (f)/(4)`