Mode of
Vibration in closed organ pipe :-
CLASS XII - PHYSICS
A hollow
wooden or metallic tube used to produce is called an organ pipe. It is a wind
instrument. If one end of the pipe is closed is known as closed organ pipe.
First mode of vibration or fundamental mode
of vibration :-
In a closed
organ pipe an antinode is formed at the open end and node is formed at closed
end because the movement of air is greater in antinode and less in node.
The mode of vibration in which one antinode & one node are formed on
the open and closed end of the pipe respectively , which is known as first mode
of vibration. Let 'l' be the length of pipe and V be the velocity of sound.
Then, frequency of first mode of vibration is given by,
If V is the
velocity of sound and f1 is it's frequency of vibration, then we
have,
2nd mode of vibration or 1st Overtone
:-
Overtone
refers to the phenomena in which the notes of higher frequency are obtained
when a blast of air is blown into the pipe.
The mode of
vibration in which two antinode & node are formed with an antinode and node on
the open and closed end of the pipe respectively , which is known as second
mode of vibration or 1st Overtone.
Let 'l' be
the length of pipe and V be the velocity of sound. Then, frequency of first
mode of vibration is given by,
If V be the
velocity then,
3rd mode of vibration :-
The mode of
vibration in which three antinode & node are formed with an antinode and node on
the open and closed end of the pipe respectively , which is known as third mode
of vibration or 2nd Overtone.
Let 'l' be
the length of pipe and V be the velocity of sound. Then, frequency of first
mode of vibration is given by,
f1:f2:f3
= 1:3:5
Conclusions:-
a.
The frequencies of various harmonics are odd
integral multiples of fundamental frequency.
b.
The frequency of nth overtone is (2n+1)f1
c.
The even harmonics are missing.
d.
Since only odd harmonics are present, so that
the sound is poorer in quality.
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