Standing Waves and Harmonics

Question 1

What are standing waves?

Answer 1

In a string with different waves, the reflection wave with the same resonant frequency superimposes with another wave with matching frequency. This causes resonance to occur and they interfere to form a standing wave pattern (Since it doesnt appear to be moving.

Question 2

What are nodes?

Answer 2

Nodes are a point in the superposition where they destructively interfere creating a zero energy point in the wave.

Question 3

What are antinodes?

Answer 3

Antinodes are points where complete interference occurs, the string oscillates with maximum amplitude.

Question 4

Fundamental Frequency? ƒ0

Answer 4

Is the standing wave with 1 antinode and 2 nodes. It is the simplest standing wave.

Question 5

Second Harmonic? (First overtone)
ƒ2

Answer 5

Is the first overtone of the fundamental frequency and is a standing wave with 2 antinodes and 3 nodes.

Question 6

What are harmonics?

Answer 6

Waves that are a integer multiple of the fundamental frequency.

Question 7

Harmonic series:

Answer 7

Forms when combining the overtones/harmonics and the fundamental frequencies together.

Question 8

How to calculate wavelength of standing waves?

Answer 8

λ = 2ℓ/n
ℓ = Length of string
n = Number of antinodes/Harmonic Number

Question 9

How to calculate frequency of a standing wave?

Answer 9

ƒ = nƒ0 = nv/2ℓ
v = Velocity of speed in string
n = Number of antinodes/Harmonic number