Question

If the equation of the stationary wave is $y=2asin\left(\frac{2\pi ct}{\lambda }\right)cos\left(\frac{2\pi x}{\lambda }\right)$, then which of the following statements is incorrect?

• 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, $\frac{2\pi ct}{\lambda }$ as well as $\frac{2\pi x}{\lambda }$ are dimensionless
($\because$ angle), i.e., $\left[\frac{2\pi ct}{\lambda }\right]=\left[\frac{2\pi x}{\lambda }\right]=\left[M^0{L}^0{T}^0\right]$
So, $(1)$ unit of $ct$ is same as that of $\lambda$
$(2)$ unit of $x$ is same as that of $\lambda$
$(3)$ $\left[\frac{2\pi c}{\lambda }\right]=\left[\frac{2\pi x}{\lambda t}\right]$
$(4)$ $\frac{x}{\lambda }$ is unit less. It is not the case with $\frac{c}{\lambda }$.