A source of wave produces 20 crests and 20 troughs in 0.2 s The distance between a crest and the next trough is 50 cm. Find the wavelength, frequency and time period of the wave.

A source of wave produces $20$ crests and $20$ troughs in $0.2\mathit{ s}.$ The distance between a crest and the next trough is $50\mathit{ cm}$. 
Since the distance between a crest and next trough is $\frac{\lambda }{2}$ .
Therefore, $\frac{\lambda }{2}=50\mathit{ cm}$
$\lambda =100\mathit{ cm}= 1\mathit{ m}$

If there are 20 crests and 20 troughs in 0.2 seconds, it means that there are 20 complete waves in that time period.

To calculate the frequency (ν), we can use the formula:

ν = Number of Waves / Time Taken

ν = 20 / 0.2

ν = 100 Hz

Therefore, the frequency of the wave is 100 Hz, which means it completes 100 cycles or oscillations per second.

The time period (T) of the wave is the time it takes to complete one full cycle. It can be calculated as the reciprocal of the frequency:

T = 1 / ν

T = 1 / 100

T = 0.01 seconds

Hence the wavelength of the wave is $\mathit{ \lambda }=1\mathit{ m}$, the frequency of the wave, ν = 100 Hz and the time period of the wave T=0.01 s.