The given information:
- The wave produces 20 crests and 20 troughs in 0.2 seconds.
- The distance between a crest and the next trough is 50cm.

Calculating the wavelength:
To calculate the wavelength, we need to find the distance between two consecutive crests or troughs. Since the wave produces 20 crests and 20 troughs in 0.2 seconds, we can say that it completes one full cycle in 0.2 seconds.

Time period:
The time period of a wave is the time it takes to complete one full cycle. In this case, the wave completes one full cycle in 0.2 seconds, so the time period is 0.2 seconds.

Frequency:
The frequency of a wave is the number of cycles it completes in one second. It is the reciprocal of the time period. Therefore, the frequency can be calculated as 1 divided by the time period.

Calculations:
1. Wavelength: Since the wave completes one full cycle in 0.2 seconds and produces 20 crests and 20 troughs, the total distance covered by the wave in 0.2 seconds is equal to 20 wavelengths.
- Total distance covered by the wave = 20 wavelengths
- Distance covered in 0.2 seconds = Speed of the wave × Time
- Speed of the wave = Distance ÷ Time
- Distance covered in 0.2 seconds = 50cm × 20 = 1000cm
- Wavelength = Distance covered in 0.2 seconds ÷ 20 = 1000cm ÷ 20 = 50cm

2. Time period: Given as 0.2 seconds.

3. Frequency: Frequency = 1 ÷ Time period = 1 ÷ 0.2 seconds = 5 Hz (Hertz)

Summary:
- The wavelength of the wave is 50cm.
- The time period of the wave is 0.2 seconds.
- The frequency of the wave is 5 Hz.

By following the given rules, the information has been broken down into headings and key points, making it visually appealing and easy to understand.