Three electromagnetic waves travel through a certain point p along an x axis. they are polarized parallel to a y axis, with the following variations in their amplitudes.

find their resultant at p. e1 = (4 × 10^-5 v/m) sin[(5 × 10^14 rad/s)t]e2 = (6 × 10^-6 v/m) sin[(5 × 10^14 rad/s)t + 45°]e3 = (6 × 10^-6 v/m) sin[(5 × 10^14 rad/s)t - 45°]

Explanation:

Frequency of each electromagnetic wave is same thus we can interfere them along X axis in Phase diagram.

In phase diagram indicate each wave as vector with amplitude as length and phase difference as angle. (shown in attachment)

Now take component of E2 and E3 amplitude along X direction.

Net amplitude of all E in X direction = + cos(45)[ +   ]

⇒  

Final resultant have no change in frequency

So , resultant is

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