Standing Waves and Harmonics

Question 1

Standing waves

Answer 1

When two waves meet and interfere with each other in a confined space, there is the potential for them to form a wave pattern that looks like it’s not moving

For this to happen, the reflected wave needs to interfere with the incident wave (the wave created by the source) at just the right place

When this happens, certain parts on the wave look like they are standing still. Because of this, we call these Standing waves

This can only happen at certain frequencies within a medium. We call these frequencies harmonic frequencies or just harmonics

Question 2

Nodes

Answer 2

Nodes are areas where no apparent displacement occurs - the particles of the medium appear to be standing still

Question 3

Antinodes

Answer 3

Antinodes are areas that oscillate between maximum positive and negative displacement. This is the opposite of a node, so we add the prefix Anti-.

Question 4

Harmonic #1

Answer 4

The first combination is known as the fundamental frequency or the first harmonic.

The first harmonic has 2 nodes (1 at each end) and 1 antinode (in the middle of the wave.

Question 5

Increasing Harmonics

Answer 5

we always increase harmonics by adding one node. We never add antinodes. They come along with the addition of a node

Question 6

L = (n/2) 𝞴

Answer 6

Where L is the length of the medium, n is the number of antinodes/the number of the harmonic, and 𝞴 is the wavelength
a wave with two fixed ends