The adjacent diagram shows three different modes of vibrations P, Q and R of the same string.

State the ratio of wavelengths of P and R.

Explanation

Frequency `f _(P) = 1. 5 f , ` frequency ` f _(x) = 0.5 f`
`lamda = (v)/(f)`
`therefore ` The ratio of wavelengt of P and R is given by,
`(lamda _(P))/( lamda _(R)) = ((v)/(f _(P)))/( ( v)/( f _(R))) = ( f _(R))/( f _(P)) = (0.5 f )/(1 .5 f) = (1)/(2) xx (2)/(3) = (1)/(3)`