Wave Motion 5 Question 2

2. In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is $0.1 m$. When this length is changed to $0.35 m$, the same tuning fork resonates with the first overtone. Calculate the end correction.

$(2003,2 M)$

(a) $0.012 m$

(b) $0.025 m$

(c) $0.05 m$

(d) $0.024 m$

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Answer:

Correct Answer: 2. (b)

Solution:

  1. Let $\Delta l$ be the end correction.

Given that, fundamental tone for a length $0.1 m$ $=$ first overtone for the length $0.35 m$.

$$ \frac{v}{4(0.1+\Delta l)}=\frac{3 v}{4(0.35+\Delta l)} $$

Solving this equation, we get $\Delta l=0.025 m=2.5 cm$



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