While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition 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 (a) 18 > x (b) x > 54 (c) 54 > x > 36 (d) 36 > x > 18

Answer: (b). Winter: 18 + e = (λ)/(4), so the second resonance would be at (3λ)/(4) - e = 54 + 2e > 54 cm. In summer the temperature is higher, so v and λ = v/n increase. So the second resonance length is even larger: x > 54 cm. So the answer is (b) x > 54.

While measuring the speed of sound by performing a resonance column… | JEE Main 2008 (AIEEE)

Q118JEE Main 2008 · AIEEEMedium

Organ Pipes & Resonance Tube

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

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Answer: (b)

Winter: $18 + e = \frac{\lambda}{4}$ , so the second resonance would be at $\frac{3\lambda}{4} - e = 54 + 2e > 54$ cm.
In summer the temperature is higher, so $v$ and $\lambda = \frac{v}{n}$ increase.
So the second resonance length is even larger: $x > 54$ cm.
So the answer is (b) $x > 54$ .

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