Vibrations of air
column in pipes
instruments like flute, clarinet etc. are based on the principle of vibrations
of air columns. Due to the superposition of the incident wave and the reflected
wave, longitudinal stationary waves are formed in the pipe.
pipes are musical instruments which are used to produce musical sound by
blowing air into the pipe. Organ pipes are two types
(i) closed organ pipes, closed at one end
(ii) open organ pipe, open
at both ends.
Closed organ pipe : If the air is blown lightly at the open end of
the closed organ pipe, then the air column vibrates (Fig. a) 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
n1 is the fundamental frequency of the vibrations and v is the
velocity of sound in air, then
= v / λ1 = v/4l
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.
λ3/4 or λ3=4l/3
= v/ λ3=3v/4l=3n1
is the first overtone or third harmonic.
is called as second overtone or fifth harmonic.
the frequency of pth overtone is (2p + 1) n1 where n1 is the
fundamental frequency. In a closed pipe only odd harmonics are produced. The
frequencies of harmonics are in the ratio of 1 : 3 : 5.....
(ii) Open organ pipe -
When air is blown into the open organ pipe, the air column vibrates in the
fundamental mode Fig. a. Antinodes are formed at the ends and a node is formed
in the middle of the pipe. If l is the length of the pipe, then
λ1= n1 2 l
the next mode of vibration additional nodes and antinodes are formed as shown
in Fig. b and Fig. c.
l = λ2
or v = n2λ2 = n2 . l
∴ n2 =(v/l)=2n1
is the first overtone or second harmonic.
n3 =v/ λ3=3v/2l=3n1
is the second overtone or third
the frequency of Pth overtone is (P + 1) n1 where n1 is
the fundamental frequency.
frequencies of harmonics are in the ratio of 1 : 2 : 3 ....