3 Transverse waves have a speed of \( 0,5 \mathrm{~m} \cdot \mathrm{~s}^{-1} \) and a wavelength of 25 mm . a) Calculate the frequency of the waves. b) What is the period of the waves?

To find the frequency of the waves, we can use the wave equation: \[ v = f \lambda \] Where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength. We have \( v = 0.5 \, \text{m/s} \) and \( \lambda = 25 \, \text{mm} = 0.025 \, \text{m} \). Rearranging the equation for frequency gives: \[ f = \frac{v}{\lambda} = \frac{0.5 \, \text{m/s}}{0.025 \, \text{m}} = 20 \, \text{Hz} \] To determine the period of the waves, we can use the relationship between period \( T \) and frequency \( f \): \[ T = \frac{1}{f} \] With \( f = 20 \, \text{Hz} \), we find: \[ T = \frac{1}{20 \, \text{Hz}} = 0.05 \, \text{s} \] So the frequency of the waves is 20 Hz and the period is 0.05 seconds.