Question

The third overtone of a closed organ pipe is equal to the second harmonic of an open organ pipe. Then the ratio of their lengths is equal to

• A. $\frac{7}{4}$
• B. $\frac{3}{5}$
• C. $\frac{3}{2}$
• D. none of these

Answer 1

The correct option is A $\frac{7}{4}$

Let the length of closed pipe be $L^{\prime }$ and that of open pipe be $L$.

Third overtone of closed pipe ${\nu }_7^{\prime }=\frac{7v}{4L^{\prime }}$

Second harmonic of open pipe ${\nu }_2=\frac{2v}{2L}$

But ${\nu }_7^{\prime }={\nu }_2$

$\therefore$ $\frac{7v}{4L^{\prime }}$ $=\frac{2v}{2L}$

$⟹$ $\frac{L^{\prime }}{L}=\frac{7}{4}$