Waves

INERNATIONAL BACCALAUREATE SUBSIDIARY LEVEL

WAVES SUMMARY

4.1 Travelling wave characteristics

A medium is a material through which a wave passes.

When a wave passes, each part of the medium moves away from its normal position and then returns. This is called an oscillation.

Oscillations within the medium are slight movements either side of the normal position. The wave motion is the disturbance that passes through the medium.

A wave pulse causes the medium to have one oscillation. A continuous travelling wave causes the medium to keep oscillating. Waves transfer energy without transporting matter because each part of the medium oscillates on the spot.

A transverse pulse causes the spring to move at right angles to the direction of motion of the pulse.

A longitudinal pulse causes the spring to move parallel to the direction of motion of the pulse.

The direction of propagation is at right angles to the wavefront.

The displacement at a point is how much the medium has been displaced from its normal position. Displacements are given + or - signs depending on the direction of the displacement.

Amplitude is the largest distance from the normal position that the medium is displaced.

The wavelength l of a wave is the distance from one point to the next corresponding point.

The period T of a wave is the time in seconds that it takes one wavelength to pass by. In this time the medium will complete one oscillation.

The frequency f of the wave is the number of wavelengths that pass each second.

Frequency and period are reciprocals. T = 1/f.

The speed of a wave is equal to its frequency times its wavelength.

A displacement/position graph shows the displacement of the different sections of a medium.

A displacement/time graph shows the displacement of one point of a medium as time elapses.

The speed of the particles of a medium is a maximum when their displacement is zero.

The speed of the particles of a medium is zero where the medium has maximum displacement.

For a longitudinal wave, the medium has a high pressure called a compression where particles are closer than normal.

For a longitudinal wave, the medium has a low pressure called a rarefaction where particles are further apart than normal.

The particles around a compression move in the same direction as the wave.

The particles around a rarefaction move in the opposite direction to the wave.

The particles near a compression and rarefaction have small displacements.

The particles where the pressure is normal, have large displacements.

4.2 Wave Properties

For a transverse wave, the phase of a wave is the side of the normal position that the displacement occurs.

The speed of a pulse depends on the tension in the spring and the mass of the spring per metre.

The greater the tension the faster the pulse.

The greater the mass per metre the slower the pulse.

Transmitted pulses always have the same phase as the incident pulse.

Transverse pulses reverse their phase when reflecting from a fixed end.

Transverse pulses keep the same phase when reflecting from a free end.

When a transverse pulse moves towards a heavier spring the partial reflection has the reverse phase.

When a transverse pulse moves towards a lighter spring, the partial reflection has the same phase.

Huygens principle - every point on a wavefront is a source of secondary circular waves.

When a wave meets a boundary the angle of incidence is the angle between the direction of propagation and the normal.

When a wave reflects off a barrier the angle of incidence is equal to the angle of reflection.

When