An open organ pipe of length ' l ' is sounded together with another open organ pipe of length (l+l₁ ) in their fundamental modes. Speed of sound in air is ' V '. The beat frequency heard will be ( l₁ l )

Step-by-step solution

For a pipe open at both ends, f = V 2 l f ₁= V 2 l ; f ₂= V 2 (l+l₁ ) beat frequency, f _ b = f ₁- f ₂= V 2 l - V 2 (l+l₁ ) f _ b = V [ 2 (l+l₁ )-2 l 4 l (l+l₁ ) ]= V 2 l₁ 4 l (l+l₁ ) f _ b = V l₁ 2 l (l+l₁ ) Since l₁ l, l₁ in the denominator can be taken as zero. f _ b = V l₁ 2 l^2