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. |392 - v₂| = 7 ⇒ v₂ = 385 Hz or 399 Hz . Increasing tension increases frequency. If v₂ = 385 , new v₂’ > 385 , beat = 392 - v₂’ < 7 , becomes 5 Hz ( v₂’ = 387 ), consistent. If v₂ = 399 , beat increases, contradicts. So, v₂ = 385 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L)