Practice question

**Beats arise** when two waves of slightly different frequencies f₁ and f₂ superpose, producing amplitude modulation at beat frequency f_beat = |f₁ - f₂| (Hz). Intensity waxes and wanes periodically, number of beats in interval Δt equals f_beat·Δt, loudness variation audible when f_beat < 10 Hz. Let v₂ be the original frequency. |256 - v₂| = 5 ⇒ v₂ = 251 Hz or 261 Hz . Decreasing tension decreases frequency. If v₂ = 261 , new v₂’ < 261 , beat = 261 - 256 = 5 or decreases, so v₂’ = 253 , beat = 256 - 253 = 3 , consistent. Thus, v₂