Waves

JEE Main level, single correct, medium

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Question 83 of 142

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

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Answer: (D) 360 m/s360 \mathrm{~m} / \mathrm{s}

Fundamental frequency in close/organ pipe
(f)=v4ℓf1=v4ℓ1&f2=v4ℓ2\begin{aligned} & (\mathrm{f})=\frac{\mathrm{v}}{4 \ell} \\ & \mathrm{f}_1=\frac{\mathrm{v}}{4 \ell_1} \& \mathrm{f}_2=\frac{\mathrm{v}}{4 \ell_2}\end{aligned}
Beat =(f1−f2)=v4(1ℓ1−1ℓ2)=\left(\mathrm{f}_1-\mathrm{f}_2\right)=\frac{\mathrm{v}}{4}\left(\frac{1}{\ell_1}-\frac{1}{\ell_2}\right)
15=v4(11−11.2)v=(15×4×1.20.2)=60×6=360 m/s\begin{aligned} & 15=\frac{\mathrm{v}}{4}\left(\frac{1}{1}-\frac{1}{1.2}\right) \\ & \mathrm{v}=\left(\frac{15 \times 4 \times 1.2}{0.2}\right)=60 \times 6=360 \mathrm{~m} / \mathrm{s}\end{aligned}

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