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

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(D) In the equation $y = 2A \sin \left( \frac{2\pi ct}{\lambda} \right) \cos \left( \frac{2\pi x}{\lambda} \right)$,the arguments of the trigonometric

Vedclass · Accepted Answer

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

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(D) In the equation $y = 2A \sin \left( \frac{2\pi ct}{\lambda} ight) \cos \left( \frac{2\pi x}{\lambda} ight)$,the arguments of the trigonometric functions must be dimensionless.Therefore,$\left[ \frac{2\pi ct}{\lambda} ight] = M^0 L^0 T^0$ and $\left[ \frac{2\pi x}{\lambda} ight] = M^0 L^0 T^0$.From this,we conclude that the units of $ct$ and $\lambda$ are the same,and the units of $x$ and $\lambda$ are the same.Checking option $C$: The unit of $\frac{2\pi c}{\lambda}$ is $T^{-1}$ (frequency),while the unit of $\frac{2\pi x}{\lambda t}$ is $\frac{L}{L \cdot T} = T^{-1}$. Thus,they have the same units.Checking option $D$: The unit of $\frac{c}{\lambda}$ is $T^{-1}$,while the unit of $\frac{x}{\lambda}$ is dimensionless $(L/L = 1)$. Since $T^{-1} 
eq 1$,statement $D$ is not true.

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 statement is not true?

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