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 v₂ be the original frequency. |400 - v₂| = 3 ⇒ v₂ = 397 Hz or 403 Hz . Increasing tension increases frequency. If v₂ = 397 , new v₂’ > 397 , beat = 400 - v₂’ < 3 , becomes 2 Hz, consistent ( v₂’ = 398 ). If v₂ = 403 , beat increases, contradicts. So, v₂ = 397 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L)