Waves And Sound Question 2
Question 2 - 2024 (27 Jan Shift 2)
A closed organ pipe $150 \mathrm{~cm}$ long gives 7 beats per second with an open organ pipe of length $350 \mathrm{~cm}$, both vibrating in fundamental mode. The velocity of sound is $\mathrm{m} / \mathrm{s}$.
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Answer: (294)
Solution:
$\mathrm{f}{\mathrm{c}}=\frac{\mathrm{v}}{4 \ell{1}} \quad \mathrm{f}{\mathrm{o}}=\frac{\mathrm{v}}{2 \ell{2}}$
$\left|\mathrm{f}{\mathrm{c}}-\mathrm{f}{0}\right|=7$
$\frac{\mathrm{v}}{4 \times 150}-\frac{\mathrm{v}}{2 \times 350}=7$
$\frac{\mathrm{v}}{600 \mathrm{~cm}}-\frac{\mathrm{v}}{700 \mathrm{~cm}}=7$
$\frac{\mathrm{v}}{6 \mathrm{~m}}-\frac{\mathrm{v}}{7 \mathrm{~m}}=7$
$\mathrm{v}\left(\frac{1}{42}\right)=7$
$\mathrm{v}=42 \times 7$
$=294 \mathrm{~m} / \mathrm{s}$
