Question

Given that $y=A\sin \left[\left(\frac{2\pi }{\lambda }(ct-x)\right)\right],$ where $y$ and $x$ are measured in metre. Which of the following statements is true?

• A. The unit of $\lambda$ is same as that of $x$ and $A$
• B. The unit of $\lambda$ is same as that of $x$ but not of $A$
• C. The unit of $c$ is same as that of $\frac{2\pi }{\lambda }$
• D. The unit of $(ct-x)$ is same as that of $\frac{2\pi }{\lambda }$

Answer 1

Answer: (A)

Here $\frac{2\pi }{\lambda }(ct-x)$ is dimensionless.
Hence, $\frac{ct}{\lambda }$ is also dimensionless and unit of $ct$ is same as that of $x$. Therefore, unit of $\lambda$ is same as that of $x$. Also unit of $y$ is same as that of $A$, which is also the unit of $x$.