Question

The air column in a closed end organ pipe is vibrating in second overtone. The frequency of vibration is 440Hz. If the speed of sound in air is 330ms${}^{-1}$, the length of the air column is

• A. $\frac{15}{16}m$
• B. $\frac{16}{15}m$
• C. $\frac{3}{4}m$
• D. $\frac{4}{3}m$

Answer 1

The correct option is A $\frac{15}{16}m$

Second overtone in closed pipe $5{\nu }_c=\frac{5v}{4L}=440Hz$

$\Rightarrow \frac{5\times 330}{4L}=440$

$\Rightarrow L=\frac{5\times 330}{4\times 440}$$=\frac{15}{16}m$