Stationary waves
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State the principle of superposition.
When two or more waves overlap in a region, the resultant displacement at any point is the vector sum of the displacements of the individual waves at that point.
Describe how stationary waves are formed.
Stationary waves are formed when two progressive waves, travelling in opposite directions, with the same frequency and amplitude, superpose. Interference results in points of maximum displacement (antinodes) and zero displacement (nodes).
What is the distance between two adjacent nodes (or antinodes) in a stationary wave?
The distance between two adjacent nodes (or antinodes) is half the wavelength (λ/2) of the wave.
Explain how a stationary wave can be produced using microwaves.
Microwaves are directed at a metal plate, causing reflection. The incident and reflected waves, having the same frequency and amplitude, superpose to form a stationary wave. A microwave detector can be used to locate nodes and antinodes.
Describe an experiment to demonstrate stationary waves using a stretched string.
A string is attached to a vibration generator at one end and passes over a pulley with a hanging mass at the other. By adjusting the frequency of the vibration generator, standing waves are created when an integer number of half-wavelengths fit along the string. The frequency at which resonance occurs is noted.
Explain how you can determine the wavelength of a stationary wave from the positions of its nodes.
Measure the distance between several nodes, then divide by the number of internodal distances to find the average internodal distance. Since the distance between adjacent nodes is λ/2, multiply the internodal distance by 2 to find the wavelength λ.
What is the difference between a node and an antinode in a stationary wave?
A node is a point on a stationary wave where the displacement is always zero (destructive interference). An antinode is a point on a stationary wave where the displacement has maximum amplitude (constructive interference).
How are stationary waves in air columns formed?
Stationary waves can form in air columns (
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