First slide

Superposition of waves

Question

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.

Moderate

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App