Two waves of frequencies 500 Hz and 504 Hz interfere to produce beats. How many beats are heard in 10 seconds?
**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. Beat frequency: vbₑₐt = v₁ - v₂ = 504 - 500 = 4 Hz . Beats in 10 s: 4 × 10 = 40 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 40, illustrating frequency-length-speed interdependence and quantization by boundaries.
Ref: NCERT > Physics Book > Waves > Beats Phenomenon
