2-4 Standing Waves
Look at the following stimulation: Formation of Standing Waves
The blue wave is moving to the right while the green wave is moving to the left. What happens when the two waves meet?
By now, you should know that interference occurs when the two waves meet. This causes the waves to superimpose one another to form a new wave pattern. This is show in black on the stimulation.
This particular pattern is known as a standing wave.
When does a standing wave occur?
A standing wave occurs when there is a collision between two waves of identical frequency traveling in opposite directions. Due to their equal frequencies the waves will cancel each other out causing perfect equilibrium.
Look at the stimulation here: Standing Wave in Motion
It starts with a blue and red wave of equal frequencies moving in opposite directions. The black line represents the resultant wave. We can see that the resultant wave moves in perfect equilibrium motion. The high and low points (we call these the peaks and troughs) are trading positions in a perfect pattern.
Would this still occur if the independent waves had different frequencies?
No. According to the theory of superposition, when waves collide the resultant wave is the sum of the component waves. The perfect equilibrium that exists in standing waves only occurs because the wave's simultaneous frequencies and opposite direction "cancels out" each other when adding the sums together.
For example, when you add 5 and -5 together you get 0. This is what is happening with a standing wave because the number (frequency) is the same while the direction is opposite (hence why one number is positive and the other negative). This results in a perfect equilibrium, represented by the 0.
Parts of the Standing Wave
Nodes- part of the standing wave where the wave appears to be standing still. It is said that no displacement occurs here. When looking at the wave at the node it would appear to be a straight line that is not moving.
Antinodes- part of the standing wave where the maximum displacement occurs. When looking at the antinode it will appear to be a typical wave in periodic motion. It will be clear to see the peaks (high points) and troughs (low points) of the wave.
This can be seen here: Nodes and Antinodes
Practice Problems:
1. Suppose that there was a ride at an amusement park that was titled "The Standing Wave". Which location - node or antinode - on the ride would give the greatest thrill?
2. A standing wave is formed when ____
(a) wave refracts due to changes in the properties of the medium.
(b) a wave reflects off a canyon wall and is heard shortly after it is formed.
(c) red, orange, and yellow wavelengths bend around suspended atmospheric particles.
(d) two identical waves moving different directions along the same medium interfere.
3. The number of nodes in the standing wave shown in the following link is ____. Question 3 Link
(a) 6
(b) 7
(c) 8
(d) 14
4. 4. The number of antinodes in the standing wave shown in the following link is ____. Question 4 Link
(a) 6
(b) 7
(c) 8
(d) 14
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