Step 1: Identify the given information. 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. Step 2: Determine the wavelength ($\lambda$) from the graph. 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 $\lambda = 20 \, \text{cm}$. Step 3: Convert the wavelength to meters. Since $1 \, \text{m} = 100 \, \text{cm}$: $$\lambda = 20 \, \text{cm} = 20 \times 10^{-2} \, \text{m} = 0.20 \, \text{m}$$ Step 4: Calculate the velocity of the wave. The velocity of a wave ($v$) is given by the formula: $$v = \frac{\lambda}{T}$$ Substitute the values of $\lambda$ and $T$: $$v = \frac{0.20 \, \text{m}}{0.5 \, \text{s}}$$ $$v = 0.4 \, \text{m/s}$$ The velocity of the wave is $\boxed{\text{0.4 m/s}}$.