The equation of a stationary wave along a stretched string is given by $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$. Here $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is: (in $cm$)

The pattern of standing waves formed on a stretched string at two instants of time is shown in the figure. The velocity of the two waves superimposing to form stationary waves is $360 \ m/s$ and their frequencies are $256 \ Hz$.
$(a)$ Calculate the time at which the second curve is plotted.
$(b)$ Mark nodes and antinodes on the curve.
$(c)$ Calculate the distance between $A^{\prime}$ and $C^{\prime}$.

Length of a string tied to two rigid supports is $40 \ cm$. The maximum wavelength (in $cm$) of a stationary wave produced on it is ... $cm$.

The equation of a stationary wave is given by $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin (200 \pi t) \text{ cm}$. What is the distance between two consecutive nodes in cm?

The equation of a stationary wave is given by $y = 5 \cos \left( \frac{\pi x}{3} \right) \sin (40 \pi t) \text{ cm}$. What is the distance between two consecutive nodes in $\text{cm}$?

When a stationary wave is formed,what is its frequency?