2-3 Superposition of Waves
What is superposition?
Superposition is the term which describes what happens when one wave is superimposed (sits on top of) another wave.
As we recalled in Unit 1, the two waves are said to be going through interference when the collision occurs. The resulting sound from the overlapping waves is a combination of the two separate waves.
Watch the following link showing two sound waves going through superposition: Superposition of Waves
As you can see, one wave is traveling to the right while one wave is traveling to the left. At the point of superposition, the displacement is equivalent to the algebraic sum of the individual waves. The waves then continue to travel along their original direction of motion as if the collision never occurred.
When does superposition occur in music?
By now you should be asking yourself, "when does superposition occur in music?"
The answer is "always". Whenever we hear a musical interval we are hearing two waves going through superposition.
Can we determine what pitch will be produced when waves collide?
Yes! The frequencies of the two individual waves will affect the pitch of the wave produced.
For example:
When f1 = f2 unison is heard
When f2 = 2f an octave is heard
When f2 = 3/2 f1 a fifth is heard
Are there different type of interference that occurs?
Yes,there is some variety in the type of interference that may occur when waves collides. These include:
Constructive Interference- when the waves combine together to form a larger oscillation.
Destructive Interference- when the waves possess opposing displacements which cancel each out, resulting in a small oscillation.
These are shown in the visual below:
Practice Problems:
1. The traces below show beats that occur when two different pairs of waves are added. For which of the two is the difference in frequency of the original waves greater?
(a) Pair 1
(b) Pair 2
(c) The frequency difference was the same for both pairs of waves.
(d) Need more information.
- REDIRECT The Physics of Music