Reflection and Transmission

(a) Circular water waves are reflected from a boundary on the left. PSSC Physics.

Sound waves can echo back from a cliff, and light waves are reflected from the surface of a pond. We use the word reflection, normally applied only to light waves in ordinary speech, to describe any such case of a wave rebounding from a barrier. Figure (a) shows a circular water wave being reflected from a straight wall. In this chapter, we will concentrate mainly on reflection of waves that move in one dimension, as in figure (b).

Wave reflection does not surprise us. After all, a material object such as a rubber ball would bounce back in the same way. But waves are not objects, and there are some surprises in store.

First, only part of the wave is usually reflected. Looking out through a window, we see light waves that passed through it, but a person standing outside would also be able to see her reflection in the glass. A light wave that strikes the glass is partly reflected and partly transmitted (passed) by the glass. The energy of the original wave is split between the two. This is different from the behavior of the rubber ball, which must go one way or the other, not both.

Second, consider what you see if you are swimming underwater and you look up at the surface. You see your own reflection. This is utterly counterintuitive, since we would expect the light waves to burst forth to freedom in the wide-open air. A material projectile shot up toward the surface would never rebound from the water-air boundary!

(b) A wave on a coil spring, initially traveling to the left, is reflected from the fixed end. PSSC Physics.

What is it about the difference between two media that causes waves to be partly reflected at the boundary between them? Is it their density? Their chemical composition? Ultimately all that matters is the speed of the wave in the two media. A wave is partially reflected and partially transmitted at the boundary between media in which it has different speeds. For example, the speed of light waves in window glass is about 30% less than in air, which explains why windows always make reflections. Figures (c) and (d) show examples of wave pulses being reflected at the boundary between two coil springs of different weights, in which the wave speed is different.

Reflections such as (a) and (b), where a wave encounters a massive fixed object, can usually be understood on the same basis as cases like (c) and (d) later in his section, where two media meet. Example (b), for instance, is like a more extreme version of example (c). If the heavy coil spring in (c) was made heavier and heavier, it would end up acting like the fixed wall to which the light spring in (b) has been attached.

Self-Check A	In figure (b), the reflected pulse is upside-down, but its depth is just as big as the original pulse's height. How does the energy of the reflected pulse compare with that of the original?
Answer	The energy of a wave is usually proportional to the square of the amplitude. Squaring a negative number gives a positive result, so the energy is the same.
Self-Check B	Sonar is a method for ships and submarines to detect each other by producing sound waves and listening for echoes. What properties would an underwater object have to have in order to be invisible to sonar?
Answer	A substance is invisible to sonar if the speed of sound waves in it is the same as in water. Reflections occur only at boundaries between media in which the wave speed is different.

Fish have internal ears.

Whale songs traveling long distances.

Long-distance radio communication.

The use of the word "reflection" naturally brings to mind the creation of an image by a mirror, but this might be confusing, because we do not normally refer to "reflection" when we look at surfaces that are not shiny. Nevertheless, reflection is how we see the surfaces of all objects, not just polished ones. When we look at a sidewalk, for example, we are actually seeing the reflecting of the sun from the concrete. The reason we don't see an image of the sun at our feet is simply that the rough surface blurs the image so drastically.

Inverted and uninverted reflections

Notice how the pulse reflected back to the right in example (c) comes back upside-down, whereas the one reflected back to the left in (d) returns in its original upright form. This is true for other waves as well. In general, there are two possible types of reflections, a reflection back into a faster medium and a reflection back into a slower medium. One type will always be an inverting reflection and one noninverting.

(c) A wave in the lighter spring, where the wave speed is greater, travels to the left and is then partly reflected and partly transmitted at the boundary with the heavier coil spring, which has a lower wave PSSC Physics.	(d) A wave moving to the right in the heavier spring is partly reflected at the boundary with the lighter spring. The reflection is uninverted. PSSC Physics.

It's important to realize that when we discuss inverted and uninverted reflections on a string, we are talking about whether the wave is flipped across the direction of motion (i.e. upside-down in these drawings). The reflected pulse will always be reversed front to back, as shown in figures (e) and (f ). This is because it is traveling in the other direction. The leading edge of the pulse is what gets reflected first, so it is still ahead when it starts back to the left - it's just that "ahead" is now in the opposite direction.

(e) An uninverted reflection. The reflected pulse is reversed front to back, but is not upside-down.	(f) An inverted reflection. The reflected pulse is reversed both front to back and top to bottom.