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# Reflection of Mechanical Waves

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Reflection of Mechanical Waves

When mechanical waves strike a barrier, at least part of the energy of the waves will be reflected back into the media from which they came. You experience this every single day, when you look in the mirror and see your own reflection.

### Reflection of Mechanical Waves

When a wave strikes an obstacle or comes to the end of the medium it is traveling in, some portion of the wave is reflected back into the original medium. It reflects back at an equal angle that it came in. These angles are called the angle of incidence and the angle of reflection . The normal line, the incident and reflected rays, and the angles of incidence and reflection are all shown in the diagram sketched above. The law of reflection states that the angle of incidence equals the angle of reflection. These rules of reflection apply in the cases of water waves bouncing off the side of a pool, sound waves echoing off a distant cliff, or wave pulses traveling down a rope or a slinky.

Consider the change that would occur with a light rope joined to a heavier rope.  When a wave pulse travels down the rope and encounters the media change, a reflection will occur. Look at the image below. In the top sketch, we see a lightweight (black) rope attached to a heavier rope (red).  There is a wave pulse traveling down the rope from left to right. When the wave pulse encounters the barrier (the change in rope weight), part of the wave moves into the new medium and part of the wave is reflected back into the old medium.

As you can see in the bottom half of the diagram, the transmitted portion of the wave continues into the new medium right side up. The transmitted wave is somewhat diminished because some of the energy of the wave was reflected and also because the rope to be lifted is heavier. The reflected wave is also diminished because some of the energy was transmitted through the barrier. The reflected wave is also inverted (upside down). This is a general rule for mechanical waves passing from a less dense medium into a more dense medium, that is, the reflected wave will be inverted.

The situation changes when the wave is passing from a more dense medium into a less dense medium.  As you can see in the sketch below, when a wave pulse moving in denser medium encounters a media interface to a medium of less density, the reflected wave is upright rather than inverted.

It is also possible for a mechanical wave to encounter an impenetrable barrier, that is, a barrier which does not allow any transmission at all.  In such a case, the complete wave pulse will be reflected and the reflected wave will be inverted.

#### Summary

• When a wave strikes an obstacle or comes to the end of the medium it is traveling in, some part of the wave is reflected back into the original medium.
• The law of reflection states that the angle of incidence equals the angle of reflection.
• The general rule, for mechanical waves passing from a less dense medium into a more dense medium, the reflected wave will be inverted.
• When a wave pulse moving in denser medium encounters a media interface to a medium of lesser density, the reflected wave is upright rather than inverted.
• When a mechanical wave encounters an impenetrable barrier, the complete wave pulse will be reflected and the reflected wave will be inverted.

#### Practice

The following video shows a wave machine in action. Use this video to answer the questions that follow.

1. What happens to the wave when it is reflected from an open end?
2. What happens to the wave when it is reflected from a fixed end?

#### Review

1. Draw a diagram showing a surface with a normal line.  On the diagram, show a wave ray striking the surface with an angle of incidence of $60^\circ$ .  Draw the reflection ray on the diagram and label the angle of reflection.
2. Light strikes a mirror’s surface at  $30^\circ$ to the normal.  What will the angle of reflection be?
3. If the angle between the incident ray and the reflected ray is $90^\circ$ , what is the angle of incidence?
4. When a water wave is reflected from a concrete wall, will the reflected wave be inverted or upright?
5. If you tie a heavy spring to a light spring and send a wave pulse down the heavy spring, some of the wave will be reflected when the wave passes into the lighter spring.  Will the reflected pulse be upright or inverted?