The distance between two successive crests of a water wave is 0.25m. If a particle on the surface of the water makes four complete vertical oscillations in ...

Answer Details

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.