IB Physics Phase of a wave

An important term applied to an oscillating particle and a wave is phase. Below is a tutorial sheet on phase.

  1. Two points on a progressive wave are in phase if they have the same displacement and velocity. True or false?
  2. Two points on a progressive wave are in phase if the distance between the points is a whole number of wavelengths. T or F?
  3. P and Q are two points on a progressive wave. The gradients of the tangents to the wave at P and Q have the same value. Are P and Q in phase?
  4. What is the phase difference between two points on a progressive wave of wavelength 8.0 cm that are 3.0 cm apart?
  5. The displacement from the equilibrium caused by a progressive wave is given by the equation y = 2sin(2x - t). What is the phase difference when t = 1 between points on the wave at x = 3 and x = 1?
  6. X and Y are two points on a standing wave. X is at a distance 𝜆/4 from a node and Y a distance 𝜆/3 from this same node, both points being to the right of the node. Are X and Y in phase?
  7. R and S are two points on a standing wave. The gradients of the tangents to the wave at R and S are different. Could R and S be in phase?
  8. What is the phase difference between two points on a standing wave of wavelength 6.0 cm that are 2.0 cm apart?
  9. The displacement from the equilibrium caused by a standing wave is given by the equation y = 2sin(3x)cos(2t). What is the phase difference when t = 1 between points on the wave at x = 4 and x = 1?