Two waves of frequencies 465 Hz and 470 Hz interfere. How many beats are heard in 12 seconds?
**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. Beat frequency: vbₑₐt = 470 - 465 = 5 Hz . Beats in 12 s: 5 × 12 = 60 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 60, illustrating frequency-length-speed interdependence and quantization by boundaries.
Ref: NCERT > Physics Book > Waves > Beats Phenomenon
