Rankers Physics

Principle of Superposition, Interference and Beats: Practice Problem & Solution

A cylindrical tube ($L = 125 \text{ cm}$) is resonant with a tuning fork of frequency $330 \text{ Hz}$. If it is filling by water then to get resonance again, minimum length of water column is ($v = 330 \text{ m/s}$): (1999)
$50 \text{ cm}$
$60 \text{ cm}$
$25 \text{ cm}$
$20 \text{ cm}$

Solution Explained:

To solve this problem, we apply the core principles of Principle of Superposition, Interference and Beats. Understanding the underlying formula is key to arriving at the correct answer below:

Wavelength $\lambda = \frac{v}{f} = \frac{330}{330} = 1 \text{ m} = 100 \text{ cm}$. Resonance occurs at air column lengths $L_{air} = \lambda/4, 3\lambda/4, 5\lambda/4... = 25 \text{ cm}, 75 \text{ cm}, 125 \text{ cm}$. With water filling, to find minimum water length, we need the maximum resonant air length less than the tube length, which is $75 \text{ cm}$. Minimum water length = $125 - 75 = 50 \text{ cm}$.

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