3.In a resonance air column experiment,first and second resonances are obtained at lengths of air columns L1 and L2, the third resonance will be obtained at a length of ---------

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Solution

$\frac{λ}{2} = L_{2} - L_{1} \Rightarrow λ = 2 (L_{2} - L_{1})$
The third resonance will be obtained at a length of
$L_{3} = \frac{5}{4} λ = \frac{5}{4} \times 2 \times (L_{2} - L_{1}) = \frac{5}{2} (L_{2} - L_{1})$

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3.In a resonance air column experiment,first and second resonances are obtained at lengths of air columns L1 and L2, the third resonance will be obtained at a length of ---------

λ2=L2-L1⇒λ=2L2-L1 The third resonance will be obtained at a length of L3=54λ=54×2×L2-L1=52L2-L1

$\frac{λ}{2} = L_{2} - L_{1} \Rightarrow λ = 2 (L_{2} - L_{1})$
The third resonance will be obtained at a length of
$L_{3} = \frac{5}{4} λ = \frac{5}{4} \times 2 \times (L_{2} - L_{1}) = \frac{5}{2} (L_{2} - L_{1})$