MCQ
In the resonance tube experiment, first resonant length is $l_1$ and second  resonant length is $l_2$ then the third resonant length will be
  • A
    $5l_2$
  • B
    $2(l_2-l_1)$
  • $2l_2-l_1$
  • D
    $3l_2-2l_1$

Answer

Correct option: C.
$2l_2-l_1$
c
for first resonance

$\ell_{1}+\varepsilon=\frac{v}{4 \mathrm{f}_{0}}$

for second resonance

$\ell_{2}+\varepsilon=\frac{3 \mathrm{v}}{4 \mathrm{f}_{0}}$

$\ell_{3}+\varepsilon=\frac{5 \mathrm{v}}{4 \mathrm{f}_{0}}$

Solving get $\ell_{3}=2 \ell_{2}-\ell_{1}$

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