Activities

1. Check the trigonometry in the two expressions for the superposition of both oscillations.
2. Check that the angle between both phasors is φ = (ω₁ t + δ₁) -(ω₂ t + δ₂) = 2 ω t + 2 μ .
3. First, let us assume both frequencies are equal: ω₁ = ω₂. Can you write the full oscillation in the form of a single sinusoid? What will happen with the relative phase φ? Use the simulation to check your answers.
4. Now, let us assume both frequencies are different but very similar: ω₁ ≅ ω₂, so that ε is small. What will happen with the amplitude of the first term |2 A₂ cos(ε t + μ) |? What about the angle φ? Use the simulation to check your answers.
5. Can you now explain why beats are heard when two very similar frequencies are excited?
6. Which is the beat frequency, |ε| or |ω₁ - ω₂|? Why?