The problem states that the period of the wave is T = 0.5 s.

The problem states that the period of the wave is $T = 0.5 \, \text{s}$.
The graph shows displacement versus what appears to be distance, despite being labeled as a "displacement-time graph". For a wave velocity calculation, we need both period (or frequency) and wavelength. Given the x-axis labels (10, 20, 30, etc.) and the y-axis in cm, it is standard practice to interpret the x-axis as distance in cm to extract the wavelength.

A complete wave cycle (one wavelength) is the distance over which the wave's shape repeats. From the graph, one full wave cycle starts at 0, goes up to a crest, down through the equilibrium to a trough, and back to the equilibrium position. This cycle completes at the x-axis value of 20.
Therefore, the wavelength $\lambda = 20 \, \text{cm}$.

Since $1 \, \text{m} = 100 \, \text{cm}$:

The velocity of a wave ($v$) is given by the formula:

Substitute the values of $\lambda$ and $T$:

The velocity of the wave is $\text{0.4 m/s}$.