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Q.
A closed pipe has certain frequency. Now its length is halved. Considering the end correction, its frequency will now become
Oscillations
Solution:
For a closed pipe,
$f _{ n }=\frac{(2 n -1) v }{4( L + D )},$
where, $f _{ n }$ is the frequency,
$n =$ integer,
$v =$ velocity;
$L =$ length of the pipe and
$D =$ diameter of the pipe.
When length is halved, the frequency becomes, $f _{ n }'=\frac{(2 n -1) v }{4[( L / 2)+ D )]}$
Comparing these two equations, we can say frequency will become little less than double.