Calculate the wavelength of a wave with a speed of \( 10 \mathrm{~m} \cdot \mathrm{~s}^{-1} \) and a frequency of 20 Hz .

To calculate the wavelength (\( \lambda \)) of a wave when you know its speed (\( v \)) and frequency (\( f \)), you can use the following fundamental wave equation: \[ v = \lambda \times f \] Where: - \( v \) is the speed of the wave (in meters per second, m/s) - \( \lambda \) is the wavelength (in meters, m) - \( f \) is the frequency (in hertz, Hz) **Given:** - Speed, \( v = 10 \, \text{m/s} \) - Frequency, \( f = 20 \, \text{Hz} \) **Step-by-Step Calculation:** 1. **Rearrange the equation to solve for wavelength (\( \lambda \)):** \[ \lambda = \frac{v}{f} \] 2. **Plug in the known values:** \[ \lambda = \frac{10 \, \text{m/s}}{20 \, \text{Hz}} \] 3. **Calculate the wavelength:** \[ \lambda = 0.5 \, \text{meters} \] **Conclusion:** The wavelength of the wave is **0.5 meters**.