Question

The equation of the 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 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 $2\pi c/\lambda$ is same as that of $2\pi x/\lambda t$
• D. The unit of $c/\lambda$ is same as that of $x/\lambda$

Answer 1

Answer: (D)

The unit of $c/\lambda$ is same as that of $x/\lambda$

$2\pi \frac{ct}{\lambda }$ is dimension less $2\pi \frac{x}{\lambda }$ is dimension less
$t\to$ second $x\to m$
$c\to m.s^{-1}$ $\lambda \to m$
$\lambda \to m$
Obviously 4) is wrong.