A Level Physics Practice Exam

What is the phase difference between two points 25 mm apart on a progressive wave with a speed of 20 m/s and a frequency of 100 Hz?

1. π/2 radians

2. π/4 radians

3. π/3 radians

4. π/8 radians

The correct answer is: π/4 radians

To determine the phase difference between two points on a progressive wave, we first need to assess key parameters of the wave, namely its wavelength and the distance between the two points in question. The wave speed (v) is given as 20 m/s, and the frequency (f) is 100 Hz. The relationship between wave speed, frequency, and wavelength (λ) is given by the equation: \[ v = f \times \lambda \] By rearranging this equation, we can find the wavelength: \[ \lambda = \frac{v}{f} = \frac{20 \, \text{m/s}}{100 \, \text{Hz}} = 0.2 \, \text{m} \] Next, we need to find the phase difference between two points that are a distance of 25 mm (or 0.025 m) apart. The phase (φ) of a wave is related to the distance (d) from a reference point by the equation: \[ \phi = \frac{2\pi d}{\lambda} \] Substituting the known values: \[ \phi = \frac{2\pi (0.025 \, \text{m})}{