Question

The equation of a stationary wave is
$y=2A\sin \left(\frac{2\pi ct}{\lambda }\right)\cos \left(\frac{2\pi x}{\lambda }\right)$ ,Which of the following is correct?

• A. Unit of $ct$ is same as that of $\lambda$
• B. Unit of $x$ is same as that of $\lambda$
• C. Unit of $\frac{2\pi c}{\lambda }$ is same as that of $\frac{2\pi x}{\lambda t}$
• D. Unit of $\frac{c}{\lambda }$ is same as that of $\frac{x}{\lambda t}$

Answer 1

The correct option is A Unit of $ct$ is same as that of $\lambda$

$y=2Asin\left(\frac{2\pi ct}{\lambda }\right)cos\left(\frac{2\pi x}{\lambda }\right)$

Unit of $ct=\frac{m}{s}\times s=m......\left(1\right)$

Unit of $\lambda =m...\left(2\right)$

From the above equations it is shown that tha units of $ct$ and $\lambda$ are same.