Two identical sinusoidal waves with wave lengths of 3.00 m travel in the same direction at a speed of 2.00 m/s. The second wave originates from the same point as the first, but at a later time. The amplitude of the resultant wave is the same as that of each of the two initial waves. Determine the minimum possible time interval (in sec) between the starting moments of the two waves.

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Detailed Solution

$\begin{array}{l} 2 A_{0} \cos (\frac{ϕ}{2}) = A_{0} \\ So, \frac{ϕ}{2} = \cos^{- 1} (\frac{1}{2}) = 60^{\circ} = \frac{π}{3} \end{array}$

Thus, the phase difference is $ϕ = 120^{\circ} = \frac{2 π}{3}$

This phase difference results if the time delay is , $\frac{T}{3} = \frac{1}{3 f} = \frac{λ}{3 v}$

Time delay $= \frac{3 m}{3 (2 m / s)} = 0 .500 s$

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