Question

Two closed organ pipes of length $100 \,cm$ and $101\, cm$ produces $16$ beats in $20\, sec .$ When each pipe is sounded in its fundamental mode calculate the velocity of sound.

• A. $303\, ms^{-1}$
• B. $332\, ms^{-1}$
• C. $323.2\, ms^{-1}$
• D. $300\, ms^{-1}$

Answer 1

Answer: (C)

$323.2\, ms^{-1}$

Answer 2

We get $\begin{array}{l} \frac{ v }{4^{2}}-\frac{ v }{4(1+1)}=\frac{16}{20} \\\ \Rightarrow \frac{ v }{4}\left[\frac{100}{100}-\frac{100}{101}\right]=\frac{4}{5} \\\ \Rightarrow v \left[1-\frac{100}{101}\right]=\frac{16}{5} \\\ \Rightarrow \frac{ v \times 1}{101}=\frac{16}{5} \\\ \therefore v =\frac{16 \times 101}{5}=323.2 m / s \end{array}$