Q. Given that $:y = A\sin\left\lbrack \left( \frac{2\pi}{\lambda} \right)\ (ct - x) \right\rbrack$ 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 $\frac{2\pi}{\lambda}$
Explanation
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 $x.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.