C

To identify the false statement, we first analyze the units of the variables in the given stationary wave equation:
$$y = 2A ext{sin}\left(\frac{2\pi ct}{\lambda}\right) \cos\left(\frac{2\pi x}{\lambda}\right)$$

• The amplitude \(A\) has units of displacement (meters).
• The time period is related to frequency, which has units of Hz (or s^-1).
• The wavelengths have units of meters.
• The wave number provided by \(\frac{2\pi}{\lambda}\) has units of m^-1.
• The angular frequency is given by \(\frac{2\pi f}{1}\), with units of radians per second.

By evaluating these relationships, we can see that the unit of the term corresponding to the wave number and the product of \(ct\) has a mismatch, confirming the incorrect nature of Option C, where it equates different units that are not compatible.
Therefore, the correct answer is Option C.