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. hint: frequency can be solved by dividing the cycles and time

Explanation:

Step1: Calculate the frequency

Frequency \( f=\frac{\text{number of cycles}}{\text{time}} \). Given number of cycles \( = 20 \) and time \( t = 17\space s \).
\( f=\frac{20}{17}\space Hz\approx1.18\space Hz \)

Step2: Calculate the wavelength

The formula for the speed of a wave is \( v = f\lambda \), where \( v = 4\space m/s \) and \( f=\frac{20}{17}\space Hz \). Rearranging for \( \lambda \), we get \( \lambda=\frac{v}{f} \).
Substitute \( v = 4\space m/s \) and \( f=\frac{20}{17}\space Hz \) into the formula:
\( \lambda=\frac{4}{\frac{20}{17}}=\frac{4\times17}{20}=\frac{68}{20} = 3.4\space m \)

Answer:

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