To calculate the speed of the wave, we need to understand some fundamental wave properties: **wavelength**, **frequency**, and **wave speed**.
1. **Wavelength (\( \lambda \))**: The wavelength is the distance between two successive crests of a wave. In this case, the wavelength is given as **0.25 meters**.
2. **Frequency (\( f \))**: Frequency is the number of complete oscillations or cycles that occur per second. It is given that a particle on the surface of the water makes **four complete vertical oscillations in one second**. So, the frequency is **4 Hz (hertz)**.
3. **Wave Speed (\( v \))**: The speed of a wave is calculated using the formula:
\( v = f \times \lambda \)
Where:
\( v \) is the wave speed,
\( f \) is the frequency, and
\( \lambda \) is the wavelength.
Substitute the given values into the formula:
\( v = 4 \text{ Hz} \times 0.25 \text{ m} \)
\( v = 1 \text{ m/s} \)
Therefore, the **speed of the wave** is 1 m/s.