To determine the period of the wave, let's follow a step-by-step approach using the given information:
Step 1: Understand the given quantities
- Wave velocity (v) = 20 meters per second (ms^-1)
- Distance from a crest to the nearest trough (which is half the wavelength) = 20 meters (m)
Step 2: Determine the wavelength
We know that a complete wave cycle includes a crest and a trough. Therefore, the distance from a crest to the nearest trough represents half a wavelength. So, to find the full wavelength (λ), we need to double this distance.
Wavelength (λ) = 2 × Distance from crest to trough
Wavelength (λ) = 2 × 20 m
Wavelength (λ) = 40 m
Step 3: Calculate the period of the wave
The relationship between wave velocity (v), wavelength (λ), and period (T) is given by the formula:
\[ v = \frac{λ}{T} \]
This can be rearranged to solve for the period (T):
\[ T = \frac{λ}{v} \]
Step 4: Plug in the values and calculate the period
Using the values for wavelength and wave velocity:
\[ T = \frac{40 \text{ m}}{20 \text{ ms}^{-1}} \]
\[ T = \frac{40}{20} \]
\[ T = 2 \text{ seconds} \]
So, the period of the wave is 2 seconds.
