The length of the other pipe is 2.7 m.
Two open organ pipes, sounding together, produce a beat frequency of 8.0 Hz . The shorter one is 2.40 m long.
The formula for the frequency of open ended pipes can be expressed as:
f= n×v÷2L
f= 1×343÷2×2.4
f=71.45
the beat frequency was given as 8.0 Hz
Then,
The lower frequency of the longer pipe = ( 71.45 - 8.0 )Hz
The lower frequency of the longer pipe = 63.45 Hz
From the above equation;
let L be the length of longer pipe
therefore,
The length of the longer pipe is L = n×v÷2f
The length of the longer pipe is L = 2.7m
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