Question

Two closed organ pipes $100\, cm$ and $101 \,cm$ long gives $16$ beats in $20 \,s$, 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

Number of beats per second $=$ difference of the frequencies of sound sources. Let $l$ be the length of pipe and $v$ is the velocity of sound, then the frequency of note emitted from the pipe is $n=\frac{v}{4 l}$ Number of beats in $1 s$ $=\frac{16}{20}=\frac{4}{5}$ For a closed organ pipe $x=n_{1}-n_{2}=\frac{v}{4}\left(\frac{1}{l_{1}}-\frac{1}{l_{2}}\right)$ $\frac{4}{5}=\frac{v}{4}\left(\frac{1}{1}-\frac{1}{1.01}\right)=\frac{0.01 v}{4 \times 1 \times 1.01}$ $\Rightarrow 0.01 \times 5 v=16 \times 1.01$ $\therefore v=\frac{16 \times 1.01}{0.05}=323.2\, m / s$