Question

In a closed pipe the first, second and third harmonic frequencies are in the ratio :

• A. 1:2:3
• B. 1:3:5
• C. 1:4:8
• D. 1:2:4

Answer 1

Answer:

B. 1:3:5

Physics Principles of Closed Pipes

• A closed pipe (or closed organ pipe) is an air column that is closed at one end and open at the other.

• In a closed pipe, the air molecules at the closed end are at a node (displacement node), while those at the open end are at an antinode.

• The fundamental frequency (first harmonic) is given by f₁ = v / 4L, where v is the speed of sound and L is the length of the pipe.

• Because of the boundary conditions, only odd harmonics can be produced in a closed pipe.

• The frequencies generated are:

  • First harmonic (Fundamental frequency): f₁

  • Third harmonic (First overtone): 3f₁

  • Fifth harmonic (Second overtone): 5f₁

• Therefore, the ratio of the first, second, and third harmonics produced by a closed pipe is 1:3:5.