Harmonics
Main Concept
Standing waves are waves that remain in a constant position but have a changing amplitude. They can result from the interference of waves traveling in different directions through a medium. A random stress applied to the object will produce many different waves, but only those waves with certain wavelengths will persist as standing waves.
The corresponding frequencies are called the natural frequencies of the object.
The fundamental frequency is the lowest frequency in which a standing wave pattern can form in a one dimensional medium.
Higher harmonics are multiples of the fundamental frequency.
The equations below govern the standing waves created in three different types of pipes filled with air.
Length of pipe
Wavelength
Frequencies
Closed-Closed pipe
L = n2⋅λ
λ = 2⋅Ln
f = n ⋅v2⋅L
where
n = Harmonic (positive integer)
L = Length of the pipe (m)
v = Speed of sound in air (m/s)
Open-Open Pipes
f= n ⋅v2⋅L
Closed-Open Pipes
L = n4⋅λ
λ = 4⋅Ln
f = n ⋅ v4⋅L
n = Harmonic (odd positive integer)
harmonic=
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