Question

Find the fundamental, first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is 340$m{s}^{-1}$.

• A. 120, 240 360 Hz
• B. 850 Hz, 1750 Hz, 2550 Hz
• C. 150, 300 450 Hz
• D. None of these

Answer 1

The correct option is B

850 Hz, 1750 Hz, 2550 Hz

Fundamental frequency First overtone

$\frac{\lambda }{2}=L$ $2\left(\frac{\lambda }{2}\right)=L$

$\lambda =2L$ $f=\frac{v}{L}$

$\lambda f=v$ $\frac{v}{f}=2L$

$f=\frac{v}{2L}$

If $V=340\frac{m}{s},L=20cm=20\times {10}^{-2}m$

Fundamental frequency $=\frac{V}{2L}=\frac{340}{2\times 20\times {10}^{-2}}=850Hz$

we know first overstone $=\frac{2V}{2L}=\frac{2\times 340}{2\times 20\times {10}^{-2}}\left(foropenpipe\right)=1750Hz$

Second overtone $=3\left(\frac{V}{2L}\right)=3\times 850=2550$