An open organ pipe has a fundamental frequency of 300 Hz. The first overtone of a closed organ pipe has the…
An open organ pipe has a fundamental frequency of 300 Hz. The first overtone of a closed organ pipe has the same frequency as the first overtone of the open pipe. How long is each pipe? (Take, speed of sound in air = 330 ms -1)
Solution
Sol. Fundamental frequency of an open pipe,
$f_1=\frac{v}{2l_o}$.
\(\therefore\) $l_o=\frac{v}{2f_1}=\frac{330}{2\times 300}=0.55\ \text{m}=55\ \text{cm}$.
Given, first overtone of closed pipe = first overtone of open pipe.
\(\therefore\) $3\left(\frac{v}{4l_c}\right)=2\left(\frac{v}{2l_o}\right)$.
\(\therefore\) $l_c=\frac{3}{4}l_o=\left(\frac{3}{4}\right)(0.55)=0.4125\ \text{m}=41.25\ \text{cm}$
Answer: $l_c=0.4125\ \text{m}=41.25\ \text{cm}$