[Q. Nos. 3-4] Difference in frequencies between 3rd overtone of closed pipe and 5th haronic of the same pipe is 400 Hz. Futher 3rd hormonic of this closed pipe os equal to 6th hormonic of another open pipe.
Fundamental frequencies of closed pipe and open pipe are

Options

A. 200Hz,400Hz
B. Hz,75Hz
C. 200Hz,100Hz
D. 400Hz,300Hz

Answer

C

Explanation

For closed pipe,
`3^(rd)` overtone = `7^(th)` harmonic = `n_(7) = (7v)/(4l_(c))`
`5^(th)` harmonic `n_(5) = (5v)/(4l_(c))`
`n_(7) - n_(5) = (2v)/(4l_(c))` = 400 Hz implies `n_(0) = (v)/(4l_(c)) = 200 Hz` (fundametal frequency of closed pipe) Now `3^(rd)` harmonic of closed pipe is equal to `6^(th)` harmonic of open pipe
`(v)/(4l_(c)) = (6v)/(2l_(0))`
implies`(v)/(l_(0)) = (v)/(4l_(c))` = 200 Hz
Fundamental frequency of open pipe = `(v)/(2l_(0))` = 100 Hz
Further `l_(0) = (330)/(4 xx 200)` = 0.4125 m
`l_(0) = (330)/(2 xx 100)` = 1.65 m