question_answer

In the equation \[y=A\sin \left( \omega t-kx \right)\], obtain the dimensional formula of \[\omega \] and k. Given x is distance and r is time.

Answer:

                The given equation is \[y=A\sin \left( \omega t-kx \right)\] The argument of a trigonometrical function, i.e., angle is dimensionless i.e.,       \[\omega t=\theta \] \[\omega =\frac{\theta }{t}=\frac{1}{T}={{T}^{-1}}=\left[ {{M}^{0}}{{L}^{0}}{{T}^{-1}} \right]\] Also,     \[k\,x=\theta \] \[k\,=\frac{\theta }{x}=\frac{1}{L}={{L}^{-1}}=\left[ {{M}^{0}}{{L}^{-1}}{{T}^{0}} \right]\]