Mathematical Tripos Dynamics and Relativity 2022

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Below are my answers to the 2022 Mathematical Tripos Part 1A Dynamics and Relativity questions examined on 08 June 2022.

  1. 3C (a) The vector equation of the plane is ͢r = ͢x0 + 𝜇 ͢E + λ ͢v . The motion is in a plane containing the initial point (x0) and is perpendicular to the magnetic field since the initial velocity has no component in the direction of B. The parameters 𝜇 and λ depend on m, q, t, E and B. These are identified in part (b). The scalar equation of the plane is ͢r · ͢B = ͢x0 · ͢B , since ͢E and ͢v are both perpendicular to ͢B.
  2. 3C (b)...answer to come

IB Physics Nodes and antinodes

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A tutorial sheet on nodes and antinodes is given below.

  1. Is a node always at a rarefaction in a standing wave in a pipe containing air?
  2. Is the pressure always a minimum at a node in the standing wave pattern in a pipe containing air?
  3. In a sound wave are the displacement and pressure variations 90 degrees out of phase?
  4. The open end of a pipe containing air is a displacement antinode and a pressure node. True or false?
  5. When a tuning fork is struck and held above a vertical pipe containing water only odd harmonics can form as the water is drained from the pipe. True or false?
  6. The length of the air column above the water level in a vertical pipe is 120 cm. Near the open end a loudspeaker can produce sound waves having a frequency ranging from 10 to 5000 Hz. (a) Find the lowest frequency that can produce resonance in the air column (b) How many different frequencies of the loudspeaker will produce resonance. Neglect the end correction. Take the speed of sound as 343 m/s.