Question

In a closed organ pipe of length 105 centimetres standing waves are setup corresponding to 3rd overtone. What distance from the closed end a pressure node is formed? ANS:15 cm

Answer 1

Explanation:

Organ pipes are two types (a) closed organ pipes, closed at one end (b) open organ pipe, open at both ends.

A closed organ pipe is shown in the figure below.

Fundamental, first and second overtones are shown. The next :
third overtone

If `L` is length of the pipe we have

`lambda_7=(4L)/7`

For the given length

`lambda_7=(4xx105)/7=60cm`

It is seen that first pressure node is formed at a distance of `lambda_n/4` from the closed end.
`:.` in the given case first pressure node is formed at a distance of from the closed end`=lambda_7/4=60/4=15\ cm`

.-.-.-.-.-.-.-.-.-.-.-.

Figure above depicts location of amplitude of standing waves. For pressure waves location of nodes and anti-nodes is swapped.

See Figure below