Write down the equation of a progressive wave that superimposes the above to form a stationary wave and determine the equation of the resultant stationary wave and state the amplitude.

From $y_1 = 20 \sin \left(300\pi t - \frac{\pi x}{15}\right)$, we have $A = 20$, $\omega = 300\pi$, and $k = \frac{\pi}{15}$.

The equation for the progressive wave traveling in the opposite direction is:

The equation of the progressive wave is $\boxed{y_2 = 20 \sin \left(300\pi t + \frac{\pi x}{15}\right)}$.

Let $A = 300\pi t + \frac{\pi x}{15}$ and $B = 300\pi t - \frac{\pi x}{15}$.

The amplitude of the stationary wave is given by the term multiplying $\sin(300\pi t)$, which is $40 \cos\left(\frac{\pi x}{15}\right)$. The maximum amplitude occurs when $\cos\left(\frac{\pi x}{15}\right) = \pm 1$.
The maximum amplitude of the stationary wave is 40 cm.
The equation of the resultant stationary wave is $\boxed{y = 40 \cos\left(\frac{\pi x}{15}\right) \sin\left(300\pi t\right)}$.
The maximum amplitude of the stationary wave is $\boxed{40 \text{ cm}}$.

The wave number $k = \frac{2\pi}{\lambda}$. From the given equation, $k = \frac{\pi}{15}$ rad/cm.

The wavelength of the stationary wave is $\boxed{30 \text{ cm}}$.

From the given wave equation, $k = \frac{\pi}{15}$ rad/cm.
The separation $\Delta x = 2.5$ cm.

The phase difference is $\boxed{\frac{\pi}{6} \text{ radians}}$.