Wave Interference and Standing Waves
Describe the net disturbance that occurs when two or more wave pulses or waves overlap.
- Wave interference is the interaction of two or more wave pulses or waves.
- When two or more wave pulses or waves interact with each other, they travel through each other and overlap rather than bouncing off each other.
- When two or more wave pulses or waves overlap, the resulting displacement can be determined by adding the individual displacements. This is called superposition.
- Wave interference may be constructive or destructive.
- When the displacements of the superposed wave pulses or waves are in the same direction, the interaction is called constructive interference.
- When the displacements of the superposed wave pulses or waves are in opposite directions, the interaction is called destructive interference.
- Two or more traveling wave pulses or waves can interact in such a way as to produce amplitude variations in the resultant wave pulse or wave.
- Visual representations of wave pulses or waves are useful in determining the result of two interacting wave pulses or waves.
- Beats arise from the addition of two waves of slightly different frequency.
- Waves with different frequencies are sometimes in phase and sometimes out of phase at locations along the waves, causing periodic amplitude changes in the resultant wave.
- The beat frequency is the difference in the frequencies of the two waves. Relevant equation:
- Tuning forks are devices that are commonly used to demonstrate beat frequencies.
Describe the properties of a standing wave.
- Standing waves can result from interference between two waves that are confined to a region and traveling in opposite directions.
- Standing waves have nodes and antinodes. A node is a point on the standing wave where the amplitude is always zero. An antinode is a point on the standing wave where the amplitude is always at maximum.
- The possible wavelengths of a standing wave are determined by the size and boundary conditions of the region to which it is confined.
- Common regions where standing waves can form include pipes with open or closed ends, as well as strings with fixed or loose ends.
- A standing wave with the longest possible wavelength is called the fundamental or first harmonic. The second-longest wavelength is typically called the second harmonic, the third-longest wavelength is called the third harmonic, and so on. However, for a standing wave with a node at one end and an antinode at the other end, only odd harmonics can be established.
- Visual representations of standing waves are useful in determining the relationships between length of the region, wavelength, frequency, wave speed, and harmonic.