# Sine Wave measurements vs equations

## Main Question or Discussion Point

I have the equation E(t)=7*sin(11000t+∏/3) and I measured the following:

E(.22ms) = .422V
Frequency = 1.751kHz
Period = 572.0 μs
Peak = 7V
Peak-Peak = 14V
E(rms) = 4.8V
E(average) = 105mV

I've calculated the following to compare
E(.22ms) = .422V
Frequecy = 1.75 kHz
Period = 571.4μs
Peak = 7v
Peak - Peak = 14v
E(rms) = 4.95v
E(average)=4.459V--------------------This value is no where near the measured value.

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Looks like you do not have a pure sine or not measuring TRUE RMS - and the measured "Average" includes the + and - side of the wave form ...~ 0v. Also "measured" RMS and Average totally depend on the instrument being used to measure with.

I have the equation E(t)=7*sin(11000t+∏/3) and I measured the following:

E(.22ms) = .422V
Frequency = 1.751kHz
Period = 572.0 μs
Peak = 7V
Peak-Peak = 14V
E(rms) = 4.8V
E(average) = 105mV

I've calculated the following to compare
E(.22ms) = .422V
Frequecy = 1.75 kHz
Period = 571.4μs
Peak = 7v
Peak - Peak = 14v
E(rms) = 4.95v
E(average)=4.459V--------------------This value is no where near the measured value.

Average is average value over time. For a sine wave with no offset, the top half is equal and opposite to the bottom half. So if you average out over time, it should be zero. Your assumption is not correct of Peak*0.637.

Then fact you measure 105mV average might due to the sine wave is not pure, containing even harmonic that create DC offset when averaging out.

uart
BTW. 0.637 is a numerical approximation of $2/\pi$, the theoretically exact value.
$$\frac{1}{\pi} \int_0^\pi \sin(x) dx = \frac{2}{\pi}$$