Question

1. a water wave travels at a speed of 4m/s. an observer notices that the wave has a frequency of 20 cycles for every 17 seconds. calculate the frequency and the wavelength of the water waves.

Explanation:

Step1: Calculate the frequency

Frequency \( f=\frac{n}{t} \), where \( n = 20 \) cycles and \( t=17\ s \).
\( f=\frac{20}{17}\approx1.18\ Hz \)

Step2: Calculate the wavelength

The wave - speed formula is \( v = f\lambda \), where \( v = 4\ m/s \) and \( f=\frac{20}{17}\ Hz \).
We can solve for \( \lambda \) using \( \lambda=\frac{v}{f} \). Substitute \( v = 4\ m/s \) and \( f=\frac{20}{17}\ Hz \) into the formula:
\( \lambda=\frac{4}{\frac{20}{17}}=4\times\frac{17}{20}=\frac{17}{5} = 3.4\ m \)

Answer:

The frequency of the water wave is approximately \( 1.18\ Hz \) and the wavelength is \( 3.4\ m \)