Question

The equation of the stationary wave is
$y=2Asin\left(\frac{2\pi ct}{\lambda }\right)cos\left(\frac{2\pi x}{\lambda }\right)$
Which of the following statements is wrong?

• A. The unit of ct is same as that of $\lambda$.
• B. The unit of x. is same as that of $\lambda$
• C. The unit of ct is same as that of $x$
• D. The unit of ct, $\lambda$ and $x$ are same

Answer 1

The correct option is D The unit of ct, $\lambda$ and $x$ are same

$y=2A\sin \left(\frac{2\Pi t}{\lambda }\right)\cos \left(\frac{2\Pi x}{\lambda }\right)$

Arguments of $sin$ and $cos$ are unit less.

$\Rightarrow \frac{Ct}{\lambda },\frac{x}{\lambda }$ have dimension $M^0{L}^0{T}^0$.

$\Rightarrow$ $Ct,x$ and $\lambda$ have same dimensions.