To find the frequency of the waves, we can use the wave speed equation, which relates the speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) of the wave:
\[ v = f \cdot \lambda \]
Where:
- \(v\) is the speed of the wave (4.0 m/s)
- \(f\) is the frequency (which we are trying to find)
- \(\lambda\) is the wavelength (2.5 m)
Rearranging the equation to solve for frequency:
\[ f = \frac{v}{\lambda} \]
Now, substituting in the values:
\[ f = \frac{4.0 , \text{m/s}}{2.5 , \text{m}} = 1.6 , \text{Hz} \]
So, the frequency of the waves is 1.6 Hz.
Next, to find the time it takes for one wave to pass under the buoy, we can use the relationship between frequency and the period (\(T\)) of the wave:
\[ T = \frac{1}{f} \]
Substituting the frequency we just calculated:
\[ T = \frac{1}{1.6 , \text{Hz}} \approx 0.625 , \text{s} \]
Thus, it takes approximately 0.625 seconds for one wave to pass under the buoy.