Spacing between two successive nodes in a standing wave on a string is `x`. If frequency of the standing wave is kept unchanged but tension in the string is doubled, then new sapcing between successive nodes will become:

Options

A. `x//sqrt(2)`
B. `sqrt(2)x`
C. `x//2`
D. 2x

Answer

B

Explanation

Spacing between successive nodes =`(lambda)/(2)` using `V = nlambda`
`lambdainfty Vinfty sqrt((T)/(mu))`
`(lambda')/(lambda) = sqrt(2T)/(sqrt(T))`
`lambda' = sqrt(2)lambda`
`(lambda')/(2) = sqrt(2). (lambda)/(2) = sqrt(2x)`