High School

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If \( L_1 \) and \( L_2 \) are the lengths of the first and second resonating air columns in a resonance tube, then:

a) \( L_1 = L_2 \)
b) \( L_1 > L_2 \)
c) \( L_1 < L_2 \)
d) Relationship cannot be determined

Answer :

Final answer:

The length of the first resonating air column (L1) is greater than the length of the second resonating air column (L2). Therefore, the answer is b) L1 > L2.

Explanation:

In a resonance tube, the length of the air column affects the resonant frequencies. The resonant frequencies of a tube open at both ends are given by the formula fn = n, where n represents the number of the harmonic. This means that the frequency of the nth harmonic is n times the frequency of the fundamental frequency. If L1 and L2 are the lengths of the first and second resonating air columns, it can be concluded that L1 > L2. Therefore, the answer is b) L1 > L2.

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