Question

The equation of the stationary wave is $ y=2A\sin \left( \frac{2\pi ct}{\lambda } \right)\cos \left( \frac{2\pi x}{\lambda } \right) $ Which of the following statements is wrong?

• A. The unit of $ ct $ is same as that of $ \lambda $
• B. The unit of $ x $ is same as that of $ \lambda $
• C. The unit of $ 2\pi c/\lambda $ is same as that of $ 2\pi x/\lambda t $
• D. The unit of $ c/\lambda $ is same as that of $ x/\lambda $

Answer 1

Answer: (D)

Here, $ (2\pi ct/\lambda ) $ as well $ (2\pi x/\lambda ) $ are dimensionless.
So, unit of $ ct $ is same as that of $ \lambda $ and unit of $ x $ is same as that of $ \lambda
$ Since, $ \left[ \frac{2\pi ct}{\lambda } \right]=\left[ \frac{2\pi x}{\lambda } \right]=[{{M}^{0}}{{L}^{0}}{{T}^{0}}] $
$ \therefore $ $ \frac{2\pi c}{\lambda }=\frac{2\pi x}{\lambda t} $
In the option , $ \frac{x}{\lambda } $ is unit less.
It is not the case with $ c/\lambda $ .