Question

𝑦 = 𝐴 sin(𝜔𝑡 − 𝑘𝑥) Represent the equation of a wave. What are the dimensions of ω and k? 𝑡 𝑎𝑛𝑑 𝑥 are time and position.

Answer 1

Dear student

$$\begin{gathered} y=A\sin (\omega t-kx) \\ dimensionof \\ \omega t=M^0{L}^0{T}^0 \\ \omega =\frac{M^0{L}^0{T}^0}{T}=\left[M^0{L}^0{T}^{-1}\right] \\ dimensionof \\ kx=M^0{L}^0{T}^0 \\ k=\frac{M^0{L}^0{T}^0}{L}=\left[M^0{L}^{-}{T}^0\right] \\ Regards \end{gathered}$$