JEE Mains · Physics · STD 11 - Waves and sound
- JEE Mains 2020
- Hard
- Numerical
A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at \(STP\). Assuming the speed of sound in air at \(STP\) is \(300\; \mathrm{m} / \mathrm{s}\), the frequency difference between the fundamental and second harmonic of this pipe is ___ \(\mathrm{Hz}\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(106\)
Step-by-step Solution
Detailed explanation
\(v_{s}=\sqrt{\frac{\gamma P}{\rho}}\)
\(\frac{\mathrm{v}_{\mathrm{gas}}}{\mathrm{v}_{\mathrm{air}}}=\sqrt{\frac{\rho_{\mathrm{air}}}{\rho_{\mathrm{gas}}}}\)
\(\Rightarrow \frac{\mathrm{v}_{\mathrm{gas}}}{300}=\frac{1}{\sqrt{2}}\)
\(\Rightarrow \mathrm{v}_{\mathrm{gas}}=\frac{300}{\sqrt{2}}\)
\(\therefore \mathrm{v}_{\mathrm{grs}}=150 \sqrt{2}\)
Now \(\mathrm{n}_{2}-\mathrm{n}_{1}=\frac{\mathrm{v}_{\mathrm{gss}}}{2 \ell}=\frac{150 \sqrt{2}}{2(1)}=75 \sqrt{2}\)
\(\Rightarrow \Delta \mathrm{n}=106.06 \mathrm{Hz}\)
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