IB Physics Phase of a wave

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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?

IB Physics What causes the resistance of a wire?

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What causes the electrical resistance of a conductor? Some explanations from textbooks are given below:

Tipler and Mosca, Physics for Scientists and Engineers page 840 (6th edition)

When an electric field is applied, the field exerts a force -eE on each free electron giving it a change in velocity in the direction opposite the field. However any additional kinetic energy acquired is quickly dissipated by collisions with the lattice ions in the wire.

Serway and Jewett, Physics for Scientists and Engineers with Modern Physics page 779 (eighth edition)

The excess energy acquired by the electrons in the electric field is transferred to the atoms of the conductor when the electrons and atoms collide. The energy transferred to the atoms increases their vibrational energy which causes the temperature of the conductor to increase.

Serway, Physics for Scientists and Engineers with Modern Physics, page 784 (fourth edition)

According to quantum mechanics, electrons have wave like properties. If an array of atoms is regularly spaced, (that is periodic), the wave-like character of the electrons makes it possible for them to move freely through the conductor and a collision with an atom is unlikely. Electron waves are scattered only if the atomic arrangement is irregular (not periodic) as a result of, for example, structural defects or impurities. At high temperatures, the resistivity is dominated by scattering caused by collisions between the electrons and the atoms in the conductor, which are continually displaced as a result of thermal agitation. The thermal motion of the atoms causes the structure to be irregular (compared with an atomic array at rest), thereby reducing the electron’s mean free path.