Question

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

• 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 $\pi x/\lambda t$
• D. the unit of $\frac{ct}{\lambda }$ is same as that of $x\lambda$

Answer 1

Answer: (A), (B), (C)

the unit of ct is same as that of $\lambda$
the unit of $2\pi c/\lambda$ is same as that of $\pi x/\lambda t$
the unit of $x$ is same as that of $\lambda$

Since the quantity $\left(2\pi ct/\lambda \right)$ is the argument of the trignometric function, thus $\left(2\pi ct/\lambda \right)$ must be unit less. So, the unit of $ct$ is same as that of $\lambda$.

Similarly, unit of $x$ is same as that of $\lambda$.

Also, the quantities $\left(2\pi ct/\lambda \right)$ and $\left(\pi x/\lambda \right)$ are unitless. So we say that $\left(2\pi c/\lambda \right)$ has the same unit as that of $\left(\pi x/\lambda t\right)$

Unit of $\left(ct/\lambda \right)$ is equal to that of $x/\lambda$ but not equal to that of $\lambda x$.

Thus options A, B and C are correct.