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 λ
• B. The unit of x is same as that of λ
• C. The unit of $2\pi c$/λ is same as that of $2\pi x$/λt
• D. The unit of c/λ is same as that of $x/\lambda$

Answer 1

Answer: (D)

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

Answer 2

Here, $\frac{2\pi ct}{\lambda}$ as well as $\frac{2\pi x}{\lambda}$ are dimensionless (angle) i.e. $\left\lbrack \frac{2\pi ct}{\lambda} \right\rbrack = \left\lbrack \frac{2\pi x}{\lambda} \right\rbrack = M^{0}L^{0}T^{0}$

So (i) unit of c t is same as that of λ (ii) unit of x is same as that of λ (iii) $\left\lbrack \frac{2\pi c}{\lambda} \right\rbrack = \left\lbrack \frac{2\pi x}{\lambda t} \right\rbrack$

and (iv) $\frac{x}{\lambda}$ is unit less. It is not the case with $\frac{c}{\lambda}.$