Arun
Last Activity: 5 Years ago
Closed organ pipe:If the air is blown lightly at the open end of the closed organ pipe, then the air column vibrates in the fundamental mode. There is a node at the closed end and an antinode at the open end. If l is the length of the tube,l = λ1/4 or λ1 = 4l …... (1)If n1 is the fundamental frequency of the vibrations and v is the velocity of sound in air, thenn1 = v/λ1 = v/4l …... (2)If air is blown strongly at the open end, frequencies higher than fundamental frequency can be produced. They are called overtones. Fig.b & Fig.c shows the mode of vibration with two or more nodes and antinodes.l = 3λ3/4 or λ3 = 4l/3 …... (3)Thus, n3 = v/λ3 = 3v/4l = 3n1 …... (4)This is the first overtone or third harmonic.Similarly, n5 = 5v/4l = 5n1 …... (5)This is called as second overtone or fifth harmonic.Therefore the frequency of pth overtone is (2p + 1) n1 where n1 is the fundamental frequency. In a closed pipe, only odd harmonics are produced
