To find the period of the wave, we need to first determine the frequency using the wave speed and wavelength.
The formula for wave speed (\(v\)) is:
\[ v = f \times \lambda \]
where:
- \(v\) is the wave speed,
- \(f\) is the frequency,
- \(\lambda\) is the wavelength.
We know that:
- \(v = 2 , \text{m/s}\)
- \(\lambda = 0.4 , \text{m}\)
Now we can solve for frequency (\(f\)):
\[ f = \frac{v}{\lambda} = \frac{2 , \text{m/s}}{0.4 , \text{m}} = 5 , \text{Hz} \]
Next, we can find the period (\(T\)) of the wave, which is related to frequency by the formula:
\[ T = \frac{1}{f} \]
Substituting the frequency we calculated:
\[ T = \frac{1}{5 , \text{Hz}} = 0.2 , \text{seconds} \]
Therefore, the period of the wave is \( \textbf{0.2 seconds} \).