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 $\frac{2 \pi}{\lambda}(c t-x)$ is dimensionless.
Hence, $\frac{c t}{\lambda}$ is also dimensionless and unit of $c t$ 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 $x$.