Resonance in a closed-end air column

Steps:

• Resonance occurs in a tube closed at the water end and open at the loudspeaker end, with lengths satisfying L = (2n-1)λ/4.
• First resonance (n=1) at x = λ/4.
• Second resonance (n=2) at y = 3λ/4.
• Subtract: y - x = 3λ/4 - λ/4 = λ/2, so λ = 2(y - x).

Why C is correct:

• Matches the formula for successive resonances in a closed tube, where the difference between first and second positions is λ/2.

Why the others are wrong:

• A: x = λ/4, not the full wavelength.
• B: 4y = 4*(3λ/4) = 3λ, exceeds the wavelength.
• D: 4(y-x) = 4*(λ/2) = 2λ, twice the wavelength.

Final answer: C