The electric field in a plane electromagnetic wave is represented with the equation, E = 2.52 x 10^4 Cos [80πt – 35x] V/m, what is the period of the wave*1 point0.025s0.035s0.040s0.050s
Question
The electric field in a plane electromagnetic wave is represented with the equation, E = 2.52 x 10^4 Cos [80πt – 35x] V/m, what is the period of the wave*1 point0.025s0.035s0.040s0.050s
Solution
The period of a wave is the reciprocal of the frequency. The frequency in this case can be found from the coefficient of the time variable t in the cosine function.
The general form of the equation for a wave is E = E0 cos(wt - kx), where w is the angular frequency.
In the given equation, E = 2.52 x 10^4 Cos [80πt – 35x] V/m, the coefficient of t is 80π.
The angular frequency w is related to the frequency f by the equation w = 2πf.
So, we can set 80π equal to 2πf and solve for f:
80π = 2πf f = 80/2 = 40 Hz
The period T is the reciprocal of the frequency, so T = 1/f = 1/40 = 0.025 s.
So, the period of the wave is 0.025 s.
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