In the resonance experiment, two air columns (closed at one end) of...

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 :

Options

A $335 \mathrm{~m} / \mathrm{s}$
B $370 \mathrm{~m} / \mathrm{s}$
C $340 \mathrm{~m} / \mathrm{s}$
D $360 \mathrm{~m} / \mathrm{s}$

Correct answer

D. $360 \mathrm{~m} / \mathrm{s}$

Step-by-step solution

Fundamental frequency in close/organ pipe

\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

=\left(\mathrm{f}_1-\mathrm{f}_2\right)=\frac{\mathrm{v}}{4}\left(\frac{1}{\ell_1}-\frac{1}{\ell_2}\right)

\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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