Derive expression for beat frequency.

(i) Explain the formation of beat.

When two notes of slightly different frequencies but similar amplitudes are sounded together, they superpose producing a note whose intensity increases and reduces periodically. This phenomenon is called beats.

(ii) Derive expression for beat frequency.

Consider two notes of frequencies f₁ and f₂ sounded together. Suppose the wave of frequency f₁ makes one cycle more than that of f₂ in time T₀.

In time T, the number of waves of f₁ is f₁T

The number of waves of f₂ is f₂T

Therefore f₁T – f₂T = 1

f₁– f₂ = 1/T

but 1/T =f

f₁ –f₂ = f, the beat frequency

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