When a wave traverses a medium, the displacement of a particle located at x at a time t is given by y=a (b t-c x) , where a, b and c are constants of the wave, which of the following is a quantity with dimensions?

Step-by-step solution

Given, y=a (b t-c x) Comparing the given equation with general wave equation y=a ( 2 t T - 2 x ) we get b= 2 T , c= 2 (a) Dimensions o of aligned y a & = metre metre = [ L ] [ L ] & = Dimensionless aligned (b) aligned Dimensions of b t & = 2 T t= [ T ] [ T ] & = Dimensionless aligned (c) Dimensions of aligned c x & = 2 x= [ L ] [ L ] & = Dimensionless aligned (d) Dimensions of aligned b c & = 2 T / 2 & = / T= [ LT ⁻¹ ] aligned Thus, option (d) has dimensions.