The equation of a standing wave in a string is given by y = 5 sinleft(frac{pi x}{3}right) cos(40pi t), where x and y are in centimeters and t is in s…

Comparing the spatial part of the equation with the standard standing wave equation $y = A \sin(kx) \cos(\omega t)$, we find $k = \frac{\pi}{3}$. The wavelength $\lambda$ is given by $k = \frac{2\pi}{\lambda}$, so $\frac{\pi}{3} = \frac{2\pi}{\lambda} \implies \lambda = 6\text{ cm}$. The distance between two consecutive nodes is $\frac{\lambda}{2} = \frac{6}{2} = 3\text{ cm}$.