Q149 / 200 · JIPMER 2008 · Physics

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

  • Correct answer
    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 $(c t-x)$ is same as that of $\frac{2 \pi}{\lambda}$

Solution

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 $x$.

Hence, the correct answer is option: 'A'.

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