When two sound waves interfere destructively, the phase difference between them is typically 180 degrees or π radians. Destructive interference occurs when the crests of one wave align with the troughs of the other wave, resulting in a cancellation or reduction of the overall amplitude.
In the case of sound waves, the amplitude represents the variation in air pressure. When two sound waves with equal amplitudes interfere destructively, the regions of high pressure (compression) in one wave align with the regions of low pressure (rarefaction) in the other wave, and vice versa. This alignment of opposite phases leads to a decrease in the net amplitude of the combined waves.
To be more precise, if we consider two sound waves with equal amplitudes, their mathematical representation can be given as:
Wave 1: A sin(ωt + ϕ₁) Wave 2: A sin(ωt + ϕ₂)
Here, A represents the amplitude, ω is the angular frequency, t is time, and ϕ₁ and ϕ₂ are the phase angles of the two waves, respectively.
For destructive interference, the phase difference between the waves should be 180 degrees or π radians. Mathematically, this condition can be expressed as:
ϕ₁ - ϕ₂ = π
This means that the phase angle of one wave is exactly half a cycle (or π radians) ahead or behind the phase angle of the other wave. As a result, the crests of one wave align with the troughs of the other wave, leading to destructive interference and a reduction in the overall amplitude.