Question

Show the frequencies of the notes in the different clarinet registers that are fingered nearly the same are in the ratio of 1 : 3 : 5.

Answer 1

let L be the length and v be the speed of sound in air

λ₁ be the wavelength of first harmonic

λ₂ be the wave length of third harmonic

λ₃ be the wave length of fifth harmonic

now, λ₁ = 4 L

hence, frequency of first harmonic f₁ = v / λ₁ = v / 4L

now, λ₂ = 4L/3

frequency of third harmonic f₂ = v / λ₂ = v / (4L/3) = 3v / 4L

now, λ₃ = 4L/5

frequency of fifth harmonic f₃ = v / λ₃ = v / (4L/5) = 5v / 4L

hence, f₁ : f₂ : f₃ = v / 4L : 3v / 4L : 5v / 4L = 1 : 3 : 5