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  4. While determining the speed of sound in air using the resonance column, the air column resonates in the fundamental mode, with a tuning fork when its length is 0.1m . When this length is changed to 0.35m , the same tuning fork resonates with the first overtone. Find the end correction.

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Q. While determining the speed of sound in air using the resonance column, the air column resonates in the fundamental mode, with a tuning fork when its length is $0.1m$ . When this length is changed to $0.35m$ , the same tuning fork resonates with the first overtone. Find the end correction.

NTA AbhyasNTA Abhyas 2020

Solution:

Let $\Delta l$ be the end correction. Given that:
The fundamental tone for a length $0.1m=$ first overtone for the length $0.35m$ .
$\therefore \frac{v}{4 \left(0.1 + \Delta l\right)}=\frac{3 v}{4 \left(0.35 + \Delta l\right)}$ .
Solving this equation we get, $Δl=0.025m=2.5cm$ .