JEE Main · 2008 · 27 Apr 2008 · Offline · Waves & Sound

The speed of sound in air grows with temperature as $v\propto \sqrt{T}$, and the resonating column lengths are proportional to the wavelength and hence to $v$. In winter the first resonance occurs at a quarter wavelength, $\frac{\lambda }{4}=18\mathrm{cm}$. In the warmer summer the sound speed, and so the wavelength, are larger, and the second resonance occurs at $\frac{3\lambda }{4}$. Even at unchanged temperature the second resonance would already be $3\times 18=54\mathrm{cm}$; the summer warming lengthens it further, so the measured column length must exceed $54\mathrm{cm}$.