Two open organ pipes of lengths 50 ~cm and 51 ~cm are totally immersed in a medium. They are found to give 40 beats in 10 ~s when each is sounding at its fundamental note. The speed of sound in this medium is

Step-by-step solution

We know that, fundamental frequency aligned f₀ & = v 2 l Beat & =f₁-f₂ 40 10 & = v 2 l₁ - v 2 l₂ 4= v 2 ( 1 l₁ - 1 l₂ ) 4 & = v 2 ( 1 50 - 1 51 ) 1 10⁻² 8 10⁻² & =v ( 51-50 50 51 ) 8 10⁻² & = v 2550 v & =2550 8 10⁻² & =204 ~ms ⁻¹ aligned