While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance at a column length of 18 cm during - Physics MCQ AIEEE 2026 | ExamTest.live

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While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then:

Solution & Step-by-step Explanation

Speed of sound v = f λ . For a closed tube:First resonance: l_{1} = λ_{1} /4 ⟹ λ_{1} = 4 l_{1} = 4 \times 18 = 72 cm .Second resonance: l_{2} = 3 λ_{2} /4 .Speed of sound depends on temperature: v \propto T .In summer, T is higher, so v_{summer} > v_{winter} ⟹ λ_{summer} > λ_{winter} . λ_{summer} > 72 cm . x = \frac{3}{4} λ_{summer} > \frac{3}{4} \times 72 = 54 cm So x > 54 .

Try it yourself before checking the explanation above.

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then:

18 > x

x > 54

54 > x > 36

36 > x > 18

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