Two closed pipe produce 10 beats `s^(-1)` when emitting their fundamental nodes. If their lengths are in ratio of 25 : 26 their fundamental frequency (in Hz), are

Options

A. 270, 280
B. 260, 270
C. 260, 250
D. 250, 260

Answer

D

Explanation

Using the relationg `f_(1)=v/(4 l_(1))` and `f_(2)=v/(4 l_(2))`
`implies f_(1)-f_(2)=10` ...(1)
`f_(1)/f_(2)=l_(2)/l_(1)=26/25`
`implies f_(1) =26/25 f_(2)` ...(ii)
On solving from Eqs. (i) and (ii) , we get
`26/25 f_(2)-f_(2)=10`
So, `f_(2)=250 Hz`
and `f_(1)=260 Hz`