Objectives:

• To understand and observe stationary (standing) waves using microwaves, stretched  strings and air columns
• To observe and interpret graphical representations of a stationary wave
• To distinguish similarities and differences between stationary and progressive waves
• To understand what nodes and antinodes are and where they exist

Progressive and stationary waves

There are waves that are progressive and some that are stationary. The progressive waves are the ones that start from a source and travel outwards, transferring energy as they do so. Stationary waves are defined as a wave that does not travel forward and therefore does not transfer energy, instead it stores it.

Standing waves, also known as stationary waves, are a combination of two waves moving in opposite directions to one another each having the same amplitude and frequency. The phenomenon is the result of interference – that is, when waves are superimposed, their energies are either added together or cancelled out. They do not transfer energy.

Using a long rope and fixing it on one end and move the other end up and down you are creating a transverse wave that then reflects on the fixed side and come back. If you adjust the frequency of the shaking, you should be able to achieve a stable pattern where there are some points where the rope appears to be stationary. These points are called nodes. Other points (they should be in between two of these nodes) are called antinodes and they are where the maximum displacement occurs.

Using a vibration generator instead of… well a human, a more consistent wave can be produced. The following is an example of the type of setup that would be suitable:

By adjusting the frequency a standing wave like the following can be produced. By decreasing the frequency, fewer ‘loops’ will be formed (or none at all) and similarly if the frequency is increased the number of ‘loops’ could increase.

Nodes and antinodes

When standing waves are formed due to certain frequencies and lengths of the string, the loops are formed – as shown to the left. A node is a point that remains stationary. Take the middle image with two loops to the left, if you were to pinch the centre position labelled $N$, the rest of the wave would continue to vibrate.

The opposite poisition to this is the antinode which is the point at the waves maximum displacement from the equilibrium position. There is always an antinode at the midpoint between two adjacent nodes. The energy is actually stored within the loops shown – so there is no energy at a node (as it is stationary) and there is maximum energy at the antinodes (this should make sense as it is these points that are vibrating up and down at the greatest average speed).

Standing waves in microwaves

When you heat up food in your microwave, they use the same concept to heat up your food. In fact, the antinodes have loads of energy so the microwave generates standing microwaves and the dish in the microwave rotates so that the antinodes can heat up the food uniformly. If you take the dish off and put some marshmallows in the microwave uniformly spread around, you will notice that some points in the marshmallows will be more melted than some others.

Page co-written by Luca Quinci – Thank you!