Sine Wave measurements vs equations

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Discussion Overview

The discussion revolves around the discrepancies between measured and calculated values for a sine wave described by the equation E(t)=7*sin(11000t+∏/3). Participants explore the implications of measurement techniques, the nature of the sine wave, and the accuracy of the formulas used for calculations, including RMS and average values.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents measured values and calculated values, noting significant discrepancies, particularly in the average value.
  • Another participant suggests that the measurements may not represent a pure sine wave or that the true RMS measurement is not being utilized, indicating that the average value should be close to zero for a pure sine wave.
  • A participant points out that the formula Peak*0.637 is appropriate for a full wave rectified sine wave, not for a pure sine wave, and clarifies that 0.637 is an approximation of 2/π.
  • Concerns are raised about the accuracy and calibration of measurement equipment, as well as the potential influence of external factors such as noise and interference on the measurements.
  • Another participant emphasizes the importance of considering the phase angle in the sine wave equation, which could affect the differences between calculated and measured values.
  • It is noted that while the formula for RMS value is correct under ideal conditions, real-world measurements may deviate due to non-ideal waveforms.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the formulas used and the nature of the sine wave being measured. There is no consensus on the reasons for the discrepancies between calculated and measured values, indicating ongoing debate and exploration of the topic.

Contextual Notes

Limitations include potential inaccuracies in measurement equipment, the assumption of a pure sine wave, and the effects of external noise or interference on measurements. The discussion also highlights the dependence of average and RMS values on the specific characteristics of the waveform being analyzed.

Yarnzorrr
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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
frequency = 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.


I'm using the formula Peak*0.637. Is this wrong? I'm not really sure. please help!
 
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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.
 
Yarnzorrr said:
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
frequency = 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.


I'm using the formula Peak*0.637. Is this wrong? I'm not really sure. please help!

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.
 
As yungman said, the average should be zero (or close to it). The value of 0.637 times the peak is for the (ideal) full wave rectified sine wave.

BTW. 0.637 is a numerical approximation of [itex]2/\pi[/itex], the theoretically exact value.

[tex]\frac{1}{\pi} \int_0^\pi \sin(x) dx = \frac{2}{\pi}[/tex]
 


I would like to point out that there are a few factors that could contribute to the discrepancy between the calculated and measured values. First, it is important to ensure that the measurement equipment used is accurate and properly calibrated. Additionally, external factors such as noise or interference could affect the measurements.

Furthermore, when dealing with sine waves, it is important to consider the phase angle. The equation given only provides the amplitude and frequency of the wave, but not the phase angle. This could also contribute to the difference between the calculated and measured values.

In terms of the formula used to calculate the RMS value, it is correct to use Peak*0.637 for a sine wave. However, it is important to note that this formula assumes a perfect sine wave, which may not always be the case in real-world measurements.

In conclusion, when comparing calculated values to measured values, it is important to consider the accuracy and calibration of the measurement equipment, external factors that may affect the measurements, and the limitations of the equations used. It may also be helpful to take multiple measurements and average them to improve accuracy.
 

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