A Level Physics Practice Exam

If two points on a progressive wave are one-eighth of a wavelength apart and are 0.5 m apart, what is the minimum speed of the wave if the frequency is 10 Hz?

1. 20 m/s

2. 30 m/s

3. 40 m/s

4. 50 m/s

The correct answer is: 40 m/s

To determine the minimum speed of the wave, we can use the relationship between wave speed, frequency, and wavelength. The formula for wave speed is given by: \[ v = f \cdot \lambda \] where \(v\) is the wave speed, \(f\) is the frequency, and \(\lambda\) is the wavelength. Given that the frequency \(f\) is 10 Hz, we need to calculate the wavelength \(\lambda\). According to the information provided, the two points being one-eighth of a wavelength apart means that the distance between them (0.5 m) is equal to \(\frac{1}{8} \lambda\). We can express this as: \[ \frac{1}{8} \lambda = 0.5 \, \text{m} \] To find the full wavelength \(\lambda\), we multiply both sides by 8: \[ \lambda = 8 \times 0.5 \, \text{m} = 4 \, \text{m} \] Now that we have the wavelength, we can substitute the values for frequency and wavelength into the wave speed formula: \[ v = 10