Show the frequencies of the notes in the different clarinet registers that are fingered nearly the...
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.
Homework Answers
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
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