The equation of a stationary wave is y = 2A s | vedclass

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(D) In the argument of the trigonometric functions,the dimensions must be dimensionless.For $\sin \left(\frac{2 \pi ct}{\lambda}\right)$,the term $\fr

Vedclass · Accepted Answer

The unit of $\frac{c}{\lambda}$ is same as that of $\frac{x}{\lambda}$

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(D) In the argument of the trigonometric functions,the dimensions must be dimensionless.For $\sin \left(\frac{2 \pi ct}{\lambda}ight)$,the term $\frac{ct}{\lambda}$ must be dimensionless,meaning $[ct] = [\lambda]$. Thus,the unit of $ct$ is the same as $\lambda$.For $\cos \left(\frac{2 \pi x}{\lambda}ight)$,the term $\frac{x}{\lambda}$ must be dimensionless,meaning $[x] = [\lambda]$. Thus,the unit of $x$ is the same as $\lambda$.Now,let us check the dimensions of the terms in option $C$:$\left[\frac{2 \pi c}{\lambda}ight] = \frac{[L T^{-1}]}{[L]} = [T^{-1}]$$\left[\frac{2 \pi x}{\lambda t}ight] = \frac{[L]}{[L][T]} = [T^{-1}]$Since both have dimensions of $[T^{-1}]$,option $C$ is correct.Now,let us check option $D$:$\left[\frac{c}{\lambda}ight] = [T^{-1}]$$\left[\frac{x}{\lambda}ight] = [M^0 L^0 T^0] = 1$ (dimensionless).Since $[T^{-1}] 
eq 1$,the statement in option $D$ is wrong.

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 statements is wrong?

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