Q. Given that $y = A\sin{\left\lbrack \left( \frac{2\pi}{\lambda}(ct - x) \right) \right\rbrack,}$ where $y$ and $x$ are measured in metres. Which of the following statements is true
A) The unit of $\lambda^{- 1}$ is same as that of $\frac{2\pi}{\lambda}$
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
(a) Here, $\frac{ct}{\lambda}$ is dimensionless and unit of $ct$ is same as that of $x.$ Also unit of $\lambda$ 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.