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COMEDK · Physics · 16. Waves and Sound

Resonance is produced between a turning fork and a resonance column tube with upper end open and lower end closed by water surface. If the frequency of the tuning fork is 800Hz, and first two resonances are observed at lengths 9.75 cm, 31.25 cm, Find the length at which the third resonance occurs? Also find the speed of sound.

  1. A \(52.75\) cm and \(344\ ms^{-1}\)
  2. B \(43.10\) cm and \(340\ ms^{-1}\)
  3. C \(62.60\) cm and \(335\ ms^{-1}\)
  4. D \(31.25\) cm and \(330\ ms^{-1}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(52.75\) cm and \(344\ ms^{-1}\)

Step-by-step Solution

Detailed explanation

Let \(L_1\), \(L_2\), and \(L_3\) be the lengths of the first, second, and third resonances respectively, and \(e\) be the end correction. The resonance lengths for a tube closed at one end are given by: \(L_1 + e = \dfrac{\lambda}{4}\) \(L_2 + e = \dfrac{3\lambda}{4}\)…
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