For destructive interference to occur, the phase difference between the two interfering waves must be an odd multiple of \(pi\) (i.e., \(180^0\), \(540^0 \), etc.). From the options, \(180^0 \) is correct.

The ratio of maximum to minimum intensity is given by \(frac{I_{\text{max}}}{I_{\text{min}}} = \left(\frac{\sqrt{I_1/I_2} + 1}{\sqrt{I_1/I_2} - 1}\right)^2\). Substituting \(\frac{I_1}{I_2} = 9\) yields \(\left(\frac{3 + 1}{3 - 1}\right\)^2 = 4\), which is \(4:1\).

For two waves of amplitude \(A\) and phase difference \(phi\), the resultant amplitude is \(A_r = 2A \cos(\frac{\phi}{2})\). Given \(A_r = A\), so \(A = 2A \cos(\frac{\phi}{2})\), which means \(cos(\frac{\phi}{2}) = \frac{1}{2}\). Thus \(\frac{\phi}{2} = 60^\circ\), so \(\phi = 120^\circ\). Hence (A) is true. The resultant amplitude is the sum only if \(\phi = 0\). So (R) is false.

Interference describes the variation of intensity with position due to superposition of waves, so (A) is true. Beats describe the periodic variation in intensity with time at a point due to superposition of two waves with slightly different frequencies, so (R) is true. (R) does not explain (A).

Sound waves, being waves, exhibit interference. Thus, Assertion (A) is true. In Quincke's tube, interference is primarily due to path difference. An initial phase difference is not typically considered in a standard setup. Therefore, Reason (R) is false.

Assertion (A) is true. For sustained interference, sources must be coherent, meaning same frequency and constant phase difference. Two violins produce incoherent waves. Reason (R) is true and correctly states the condition for interference.

Energy is always conserved in interference phenomena; it is merely redistributed, not created or destroyed. Thus, both Assertion (A) and Reason (R) are false.