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(D) For a tube closed at one end, the fundamental frequency is given by $f_c = \frac{v}{4L}$.Given that the beat frequency is $f_{c1} - f_{c2} = 2$, w

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$4$

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(D) For a tube closed at one end, the fundamental frequency is given by $f_c = \frac{v}{4L}$.Given that the beat frequency is $f_{c1} - f_{c2} = 2$, where $f_{c1} = \frac{v}{4L_1}$ and $f_{c2} = \frac{v}{4L_2}$.Thus, $\frac{v}{4L_1} - \frac{v}{4L_2} = 2$.For a tube open at both ends, the fundamental frequency is given by $f_o = \frac{v}{2L}$.The new beat frequency is $f_{o1} - f_{o2} = \frac{v}{2L_1} - \frac{v}{2L_2}$.We can rewrite this as $2 	imes (\frac{v}{4L_1} - \frac{v}{4L_2})$.Substituting the known value, the new beat frequency is $2 	imes 2 = 4$ beats per second.

The air columns in two tubes closed at one end vibrating in their fundamental modes produce $2$ beats per second. The number of beats produced per second when the same tubes are vibrated in their fundamental mode with their both ends open are

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