Practice question

**Superposition of nearly equal frequencies** creates resultant y = 2A cos(Δω·t/2) sin(ω_avg·t), envelope frequency Δf/2, beat frequency Δf. Total beats heard in Δt is f_beat·Δt, explaining counting over seconds. Let original frequency of second string = v₂ . |256 - v₂| = 4 ⇒ v₂ = 252 Hz or 260 Hz . Tension increase raises frequency. If v₂ = 252 , new v₂ > 252 , beat = 256 - v₂’ < 4 , contradicts. If v₂ = 260 , new v₂ > 260 , beat = v₂’ - 256 = 6 ⇒ v₂’ = 262 Hz , consistent. So, v₂ = 260 Hz .