The Equation of a wave is given by : y=r Sin 2/T[x/v-k] where the symbols have their usual meanings,what are - Physics - Units And Measurements

Question

The Equation of a wave is given by : y=r Sin 2/T[x/v-k] where
the symbols have their usual meanings,what are the dimensions of x
and k?

Jyoti Pant · Accepted Answer

Given,
y=r sin 2T[xv-k]or y=r sin [2xTv-2kT]  In the equation, sin [2xTv-2kT ] is dimenionless quantity and [2xTv-2kT] represents the angle which is also dimensionless
Therefore, 2xTv and 2kT both are dimensionless
xTv=[M0L0T0]x[T] [LT-1]=[M0L0T0]x=[M0L0T0] [T] [LT-1]=[M0L1T0] and kT=[M0L0T0]or [k]=[M0L0T0] [T]=[M0L0T1]

The Equation of a wave is given by : y=r Sin 2/T[x/v-k] where the symbols have their usual meanings,what are the dimensions of x and k?