Question

Two closed pipes produce $10$ beats per second when emitting their fundamental notes. If their lengths are in ratio of $25:26$, then their fundamental frequency in Hz are _______.

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

Answer 1

The correct option is C $260,250$

We know that the fundamental frequency of a closed end pipe is given by

$f=\frac{v}{4L}$

$f_1=\frac{v}{4L_1}$ and $f_2=\frac{v}{4L_2}$

$\frac{f_1}{f_2}=\frac{L_2}{L_1}=\frac{26}{25}$

$⟹f_1=\frac{26}{25}{f}_2$

Now, $beat=f_1-f_2=10$

$⟹\frac{26}{25}{f}_2-f_2=10$

$⟹f_2=250Hz$

And, $f_1=\frac{26}{25}{f}_2=260Hz$

Answer-(C)