The lengths of the two pipes open at both ends are L and (L + L₁) . If they are sounded together, the beat frequency will be ( v = velocity of sound in air)

Step-by-step solution

The fundamental frequency of a pipe open at both ends of length L is given by f₁ = v 2L . The fundamental frequency of a pipe open at both ends of length L + L₁ is given by f₂ = v 2(L + L₁) . The beat frequency is the difference between the two frequencies: f_B = f₁ - f₂ f_B = v 2L - v 2(L + L₁) f_B = v 2 ( 1 L - 1 L + L₁ ) f_B = v 2 ( L + L₁ - L L(L + L₁) ) f_B = vL₁ 2L(L + L₁) Answer: vL₁ 2L(L+L₁)