A closed organ pipe of length ' L ' and an open organ pipe contain gases of densities ₁ and ₂ respectively. The compressibility of gases are equal in both the pipes. If the frequencies of their first overtones are same, then the length of the open organ pipe is

Step-by-step solution

For closed organ pipe, Ist overtone =3 rd harmonic f=f₂=3 f₁= 3 v 4 L = 3 4 L p ₁ For open organ pipe, Ist overtone =2 nd harmonics f=f₂=2 f₁= 2 v 2 L^ = v L^ = 1 L^ p ₂ As B is same. So pressure ( ) is also same for both gas For same sound frequency aligned & 3 4 L p ₁ = 1 L^ p ₂ & L^ = 4 L 3 ₁ ₂ aligned