A resonance occurs with a tuning fork and an air column of size $$12$$ cm. The next higher resonance occurs with an air column of $$38$$ cm. What is the frequency of the tuning fork? Assume that the speed of sound is $$312$$ $$m/s$$.

Question

Infinity Learn · Accepted Answer

Since the standing wave mode has a displacement antinode at the opening, there is a displacement node at the $$water-air$$ interface. By increasing the height of the air column, to go from one harmonic to the next, an additional length equal ½ of wavelength is required. Henceλ$$2=(0.38$$−$$0.12)m$$⇒λ$$=0.52mFinally$$. from $$v=f$$λ, we find that $$f=v/$$λ$$=312/0.52=600Hz$$

A resonance occurs with a tuning fork and an air column of size 12 cm. The next higher resonance occurs with an air column of 38 cm. What is the frequency of the tuning fork? Assume that the speed of sound is 312 m/s.

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