Question

Two similar open organ pipes of length $50\text{cm}$ and $50.5\text{cm}$ produce $3\text{beats per second}$ when sounded together in fundamental nodes. The velocity of sound in air is

• A. $303\text{m/s}$
• B. $330\text{m/s}$
• C. $151.5\text{m/s}$
• D. $603\text{m/s}$

Answer 1

The correct option is A $303\text{m/s}$

Given that, $L_1=50\text{cm},L_2=50.5\text{cm}$

$n_1-n_2=3\text{beats/s}$

As$L_2>L_1$ so $n_2<n_1$

For open pipe, in case of fundamental node

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

$\therefore \frac{v}{2}(\frac{1}{L_1}-\frac{1}{L_2})=3$

$\therefore \frac{v}{{10}^{-2}}(\frac{1}{50}-\frac{1}{50.5})=6$

$\therefore v=\frac{6\times 50\times 50.5\times {10}^{-2}}{0.5}=303\text{m/s}$

Why this question? In open organ pipe resonance occurs when length of the pipe $L=n\frac{\lambda }{2}$ where n=1,2,..etc