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How to Determine the Wavelength of a Standing Wave

Most waves that you are familiar with are likely propagating waves, such as those seen at the beach. A propagating wave moves through the medium, such as water, but standing waves appear to be still. When two waves propagate in opposite directions at a specific frequency, called the harmonic frequency, in a bounded medium, constructive interference causes them to appear to be standing still. You can observe a standing wave by plucking the string of a guitar. A standing wave is not really a wave, but a pattern formed from two or more waves undergoing interference. You can easily create a standing wave and determine its wavelength in a few steps.

Things You'll Need

Metal coil toy or rope
Tape measure
2 Assistants

Instructions

- 1
  Hold one end of a length of rope or coil toy in your hand. Give the other end to your assistant and stretch it between the two of you. Be sure to leave some slack in order to make the wave.
- 2
  Move your hand up and down once quickly and a wave is generated. The assistant should hold his end of the rope still. This creates a fixed boundary which helps to create a standing wave. At first you should see the wave propagate down the rope toward your assistant. Note that when the wave returns, it is upside down, or inverted. As it moves away from you, the wave is called an incident crest, and as it returns inverted it is called a reflected trough.
- 3
  Repeat Step 2 and create a wave. This time, create another wave at the exact moment the first wave reaches your assistant. In theory, the two waves should meet in the middle of the rope and the crest and trough will cancel each other out, creating a node. In other words, a node is where there is no displacement from center. However, this requires exact timing, so it is unlikely you will succeed in creating a single standing wave in this manner.
- 4
  Move your hand repeatedly up and down to create a series of waves. Your partner continues to hold his end of the rope still. Experiment with the frequency in which you create the waves. When the driving frequency, that is the frequency that you are moving your hand up and down, meets the natural frequency of the rope, you will create a standing wave. This is called resonance. To be able to measure the wavelength, you must vibrate the rope so you can see at least one node.
- 5
  Measure the wavelength. As you continue to vibrate the rope at the resonance frequency, a third assistant measures the length of the rope from the your assistant's hand to the node in the middle of the rope. A wavelength is the distance from node to node, from crest to crest, or trough to trough. In this example, it is easiest to measure from node to node. Note that your assistant's still hand creates a node.
- 6
  Measure the frequency by counting the number of times your hand completes an up and down cycle per minute.

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