Question

The lengths of two open organ pipes are $l$ and $l+\Delta l,(\Delta l<<l)$. If $u$ is the speed of sound, then the frequency of beats between them will be approximately (neglect end correction)

• A. $\frac{u}{2l}$
• B. $\frac{u}{4l}$
• C. $\frac{u\Delta l}{l^2}$
• D. $\frac{u\Delta l}{2l^2}$

Answer 1

The correct option is D $\frac{u\Delta l}{2l^2}$

$\delta =\frac{u}{2l}$

${\delta }_1=\frac{u}{2l}{\delta }_2=\frac{u}{2(l+\Delta l)}$

Beat $={\delta }_1-{\delta }_2$

$=\frac{u}{2l}-\frac{u}{2(l+\Delta l)}$

$=\frac{u}{2}(\frac{1}{l}-\frac{1}{l\Delta l})$

$=\frac{u}{2}\left(\frac{\Delta l}{l^2}\right)(\therefore \Delta l<<l)$

$=\frac{u\left(\Delta l\right)}{2l^2}$