Reflection of waves

A travelling wave may encounter a boundary between two media of different properties. If the boundary does not allow the wave to pass through, the wave bounces back to the medium in which it was propagating before striking the boundary. This phenomenon is referred to as reflection. For example, a wave travelling through a string which is fixed at one end will reflected upon reaching the fixed end of the string. In this case, the fixed end of the string acts as the boundary.

Consider the situation where a string is fixed to a rigid wall at its right end. This end is called a fixed end. When a wave is allowed to propagate through the string, the wave reaches the fixed end, and gets reflected. The reflected wave will be inverted as shown in Figure 1.10 (a). In this case, the amplitudes of both the incident and reflected waves are the same.

If the right end of the string is tied to a ring, which can slide up and down on a rod without any friction, the end is termed as a free end. In this case, when the wave arrives at the free end, the ring moves up and down. The motion of the free end results into a reflected wave which is not inverted. The reflected wave will have the same speed and wavelength as the incident wave. However, the reflected wave will have a smaller amplitude as shown in Figure 1.10 (b). The decrease in amplitude indicates that the wave lost some of its energy at the boundary.

Figure 1.10: Reflection of waves at fixed and free ends of a string

When a wave encounters a boundary that allows it to pass through, part of the wave will be reflected and part will be transmitted into the new medium. Consider two ropes of different thicknesses tied together end-to-end and suppose that, a transverse wave is produced in the thinner rope. When the wave reaches the boundary between the two ropes, it will split into an inverted reflected wave and an upright transmitted wave. The reflected wave will have the same speed and wavelenth as the incident wave. The transmitted wave will have a lower speed and a shorter wavelength than the incident wave. Each wave will have an amplitude less than that of the incident wave since the energy of the incident wave is split into the two waves. See Figure 1.11.

Figure 1.11: Reflection of a wave travelling from a less dense medium to a denser medium

If the new medium has a lower density, the reflected wave will not be inverted, as illustrated in Figure 1.12. It will have the same speed and wavelength as the incident wave. The transmitted wave will have a higher speed and longer wavelength. According to the principle of conservation of energy, when the wave breaks up into a reflected wave and a transmitted wave at the boundary, the sum of the energies of these two waves must be equal to the energy of the incident wave. Because the reflected wave contains only part of the energy of the incident wave, its amplitude must be smaller. Reflection and other behaviours of waves may be demonstrated using water waves. This is done using a ripple tank.

Figure 1.12: Reflection of a wave travelling from a denser medium to a less dense medium

Ripple tank

A ripple tank is an example of an instrument used to demonstrate the behaviour of waves. The structure of a ripple tank is shown in Figure 1.13. It consists of a power supply used to run an electric motor. When the motor runs it makes the oscillating paddle attached to an elastic band to vibrate on the water surface. The vibration of the paddle generates parallel water waves (ripples). The oscillating paddle is used to transform mechanical energy generated by the motor to ripples in a shallow tank of water. A bulb/lamp shines light through the water and a shadow of the wave pattern is produced on a sheet of paper or glass placed under the tank. The paper or glass act as viewing screen. All behaviours of waves can be demonstrated with the aid of a ripple tank.

Figure 1.13: Ripple tank

Reflection of water waves can be observed by placing various obstacles in the tray of the ripple tank. The depth of the water can also be varied by laying glass plates of different thicknesses in the tray. This allows the observation of waves travelling from one medium to another.

Reflection involves a change in the direction of waves when they fall on a barrier.

The direction in which a wave is travelling is represented by an arrow. The arrow is called a ray and is drawn perpendicular to the wavefronts. Upon reaching the barrier placed within the water, water waves bounce off the barrier and head in a different direction. Regardless of the angle at which the wavefronts approach the barrier, the waves will always be reflected in such a way that the angle of incidence at the barrier with respect to the normal is equal to the angle at which the waves are reflected off the barrier (Figure 1.16). This is in accordance to the laws of reflection which states that:

1. Upon reflection from a straight barrier, the angle of the reflected ray, r is equal to the angle of incident ray, i with tespect to the normal, N (a line that is perpendicular to the surface at the point of contact). That is, i = r.
2. The incident line of propagation, the normal line and the reflected line of prapagation all lie in the same plane.

Figure 1.16: Reflection of water waves

When, a straight water wave strikes a curved barrier, the principles of reflection still apply, but the pattern becomes more complex. Consider a rubber tube having the shape of a parabola placed within the water. Upon reflection on the parabolic barrier, the water wave will change direction and head towards a point known as the focal point. This is the point at which the wave energy concentrates. After passing through the focal point, the waves spread out as shown in Figure 1.17. This is also the case when circular water waves strike a staight or an outward curved (convex) barrier.

Note that the parabolic barrier focusses the water waves exactly at half the distance from the centre of curvature.

Figure 1.17: Reflection of linear waves from curved barriers (a) concave barrier (b) convex barrier

Applications of reflection of waves

Reflection of waves is used in various human activities. Some of the applications of wave reflections are hereby described.

1. Reflection of light waves is used in designing mirrors. Light waves bounce upon striking a silvery surface of glass.
2. Sonar (sound navigation and ranging) systems rely on the reflection of sound waves to measure the distance and speed of underwater objects.
3. The reflection of sound is what makes a hearing aid operate. Sound waves are reflected into a smaller region in a hearing aid, which directs the sound to the ear.
4. The soundboard is built upon sound reflection. Here, sound waves are uniformly reflected in an auditorium. This aids in the enhancement of sound quality.
5. The working of a stethoscope is based on the reflection of sound. In the stethoscope, the sound of a patient’s heartbeat reaches a doctor’s ear by multiple reflections of sound.