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

Options

A. 2f
B. 3f
C. `f/4`
D. `f/3`

Answer

C

Explanation

Fundamental frequency of a vibrating string is expressed as
` f = ( 1 )/ ( 2 L ) sqrt (( T ) / ( mu ) ) = ( 1 ) /( LD) sqrt ((T ) /( pi rho ) ) `
Where , D = diameter of string
` rho ` = density of the material of string
As length L and radius are doubled, the new frequency
` f ' = ( 1 ) /( (2L ) ( 2D) ) sqrt ((T ) /(pi rho )) = ( 1 ) /( 4 ) f `