Reflection of Waves

What Reflection Is

When a progressive wave travelling through a medium reaches an interface separating two media, part of the wave energy comes back into the original medium and the wave changes its direction of travel. This is reflection of the wave from the interface. In terms of sound: reflection is the phenomenon in which the sound wave travelling from one medium to another comes back into the original medium with slightly different intensity and energy.

Reflection of a Transverse Wave

Example 1 — reflection from a rigid support (denser medium)

Take a long light string AB with the end B fixed to a rigid support. For the pulse travelling on it, the string is the rarer medium and the rigid support acts as the denser medium. Give a jerk to the free end A: a crest travels towards B.

As the crest moves along the string it pulls the particles of the string upwards. When it reaches the rigid support it tries to pull B upwards, but B cannot move; by Newton's third law an equal and opposite reaction is produced on the string, which is pulled downwards. So the crest returns as a trough, and a trough would return as a crest.

Because the particles at a crest and at a trough differ in phase by $\pi$ radian, there is a phase change of $\pi$ radian on reflection from a fixed end, that is from a denser medium.

Example 2 — reflection from a free end (rarer medium)

Attach the end B of the string to a ring that slides without friction on a vertical metal rod. Here the string is the denser medium and the freely moving end is the interface with a rarer medium. When the crest reaches B it pulls the ring upwards and the ring does move up; the wave is reflected back as a crest. There is no phase change on reflection from a rarer medium.

Example 3 — heavy string joined to a light string

Join a heavy string P and a light string Q at a point O; the heavy string is the denser medium. A crest sent along the heavy string towards O is reflected from the lighter string as a crest — reflection from a rarer medium keeps the phase. A crest sent along the light string towards the heavy string is reflected as a trough — reflection from a denser medium reverses the phase.

Reflection of a Longitudinal Wave

In a longitudinal wave a compression is a high pressure region and a rarefaction is a low pressure region.

From a denser medium

When a compression travelling in the rarer medium reaches the denser medium it tries to push the particles of that medium, but the energy of the particles of the rarer medium is not sufficient to compress the denser medium. By Newton's third law an equal and opposite reaction comes into play, and the particles of the rarer medium themselves get compressed. So a compression is reflected as a compression and a rarefaction as a rarefaction. There is no change of pressure phase on this reflection.

From a rarer medium

When a compression reaches a rarer medium from a denser medium it pushes the particles of the rarer medium; these get compressed and move forward, leaving a rarefaction behind. So a compression is reflected as a rarefaction and a rarefaction as a compression. Here the pressure phase is reversed, that is it changes by $\pi$ radian.

Diagram in Words

Draw the string as a horizontal line. Above it, an incident crest moving right towards a hatched rigid wall; below and to the left, the reflected pulse drawn as a trough moving left — that is the denser-medium case. For the rarer-medium case replace the wall by a small ring on a vertical rod and draw the reflected pulse as a crest. For the longitudinal cases, draw a row of dots crowded together for a compression and spread apart for a rarefaction, incident on the boundary, with the reflected pattern crowded (denser medium) or spread (rarer medium).

Standard Results