Second overtons frequency of a pipe and fourth harmonic frequency of an pipe are same. Then, choose the correct options.

Options

A. Fundamental frequency of closed pipe is more than the fundamental frequency of open pipe
B. First overtone frequency of closed pipe is more than the first overtone frequency of open pipe
C. Fifteenth harmonic frequency of closed pipe is equal to twelfth harmonic frequency of open pipe
D. Tenth haromic frequency of closed pipe is equal to eigth harmonic fequency of open pipe

Answer

B, C, D

Explanation

Let `f_(1) =` fundamental frequency of closed pipe and
`f_(2) =` fundamental frequency of open pipe.
Given, `5 f_(1) = 4 f_(2)`
or `f_(2) = (5)/(4) f_(1)`
`:. f_(2) gt f_(1)` (b) First overtone frequency of closed pipe `= 3 f_(1)`
and first overtone frequency of open pipe
`= 2 f_(2) = 2((5)/(4) f_(1)) = 2.5 f_(1)` (c ) Fifteenth harmonic of closed pipe = `15 f_(1)`
Twelfth harmonic of open pipe
`= 12 f_(2) = 12 ((5)/(4) f_(1)) = 15 f_(1)` (d) Tenth haromic of closed pipe `= 10 f_(1)`
Eighth haromic of open pipe
`= 8 f_(2) = 8 2((5)/(4) f_(1)) = 10 f_(1)`