Question

The fundamental frequency of an open organ pipe is $300\, Hz$. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $330\, m / \,s$, then the length of closed organ pipe is

• A. 41 cm
• B. 37 cm
• C. 31 cm
• D. 80 cm

Answer 1

Answer: (A)

For an open pipe, fundamental frequency $v=\frac{v}{2 L}$
$\therefore \,\,\,\,L=\frac{v}{2 v}=\frac{330}{2 \times 300}=\frac{11}{20}$
As frequency of $1^{\text {st }}$ overtone of open pipe
$=$ frequency of $1^{\text {st }}$ overtone of closed pipe
$\therefore \,\,\,\,\frac{2 v}{2 L}=\frac{3 v}{4 L'}$
or $\,\,\,L'=\frac{3 L}{4}=\frac{3}{4} \times \frac{11}{20}=0.4125\, m =41.25 \,cm \approx 41\, cm$