Question

When two frequencies are added together, the beat frequency and the average frequency are an octave apart?

Answer 1

Very clever !

One of the original frequencies is 0.6 times the other.

Then (A-B) = (1/4) (A+B)

Answer 2

One of the frequency is double of the lower frequency.

Beat frequency is defined as the difference in frequency produced by two waves.

• Let the frequency of the first wave = F₁
• Let the frequency of the second wave = F₂

The beat frequency, F = F₂ - F₁

The average of the two frequencies is calculated as follows;

$F_{avg} = \frac{F_1 + F_2}{2}$

When the beat frequency and the average frequency are an octave apart;

$(F_2 - F_1 ) - (\frac{F_1 + F_2}{2} ) = 2F_0\\\\\frac{F_2 + F_2}{2} = 2F_0\\\\2F_2 = 4F_0\\\\F_2 = 2F_0$

Thus, we can conclude that one of the frequency is double of the lower frequency.

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