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Use the definitions given in Equations 1 and 2 for the mean value \(\bar{y}\) and the effective value \(y_{RMS}\) to show that the values given in Table 1 are correct. Table 1. Average and RMS values of a sine wave. \begin{tabular}{|l|l|l|} \hline waveform & \(\bar{y}\) & \(y_{RMS}\) \\ \hline sinusoidal & 0 & A/\(\sqrt{2}\) \\ \hline \end{tabular} Definition equation 1: Mathematically, the average value of a wave of function \(y = y(t)\) is defined as the average of the scal values of the wave in a time interval T. The average value \(\bar{Y}\) is zero for the case of periodic waves. lla with identical semicycles on the positive and negative side of the Cartesian plane, otherwise it is necessary to apply Equation 1. \(\bar{Y} = \frac{1}{T} \int_{T} y(t)dt\) (1) Definition equation 2: Mathematically, the effective or mean square value \(Y_{RMS}\) (equation 2) of a wave function then cy = y(t) is defined as the square mean of the area obtained by the values that the wave has, considering all the certain values that it acquires in a gation time interval T. \(Y_{RMS} = \sqrt{\frac{1}{T} \int_{T} y(t)^{2}dt}\) (2)

          Use the definitions given in Equations 1 and 2 for the mean value \(\bar{y}\) and the effective value \(y_{RMS}\) to show that the values given in Table 1 are correct.
Table 1. Average and RMS values of a sine wave.
\begin{tabular}{|l|l|l|}
\hline
waveform & \(\bar{y}\) & \(y_{RMS}\) \\
\hline
sinusoidal & 0 & A/\(\sqrt{2}\) \\
\hline
\end{tabular}
Definition equation 1:
Mathematically, the average value of a wave of function \(y = y(t)\) is defined as the average of the scal values of the wave in a time interval T. The average value \(\bar{Y}\) is zero for the case of periodic waves. lla with identical semicycles on the positive and negative side of the Cartesian plane, otherwise it is necessary to apply Equation 1.
\(\bar{Y} = \frac{1}{T} \int_{T} y(t)dt\)
(1)
Definition equation 2:
Mathematically, the effective or mean square value \(Y_{RMS}\) (equation 2) of a wave function then cy = y(t) is defined as the square mean of the area obtained by the values that the wave has, considering all the certain values that it acquires in a gation time interval T.
\(Y_{RMS} = \sqrt{\frac{1}{T} \int_{T} y(t)^{2}dt}\)
(2)

Use the definitions given in Equations 1 and 2 for the mean value y̅ and the effective value yRMS to show that the values given in Table 1 are correct.
Table 1. Average and RMS values of a sine wave.

waveform y̅ yRMS

sinusoidal 0 A/√(2)

Definition equation 1:
Mathematically, the average value of a wave of function y = y(t) is defined as the average of the scal values of the wave in a time interval T. The average value Y̅ is zero for the case of periodic waves. lla with identical semicycles on the positive and negative side of the Cartesian plane, otherwise it is necessary to apply Equation 1.
Y̅ = (1)/(T)∫T y(t)dt
(1)
Definition equation 2:
Mathematically, the effective or mean square value YRMS (equation 2) of a wave function then cy = y(t) is defined as the square mean of the area obtained by the values that the wave has, considering all the certain values that it acquires in a gation time interval T.
YRMS = √((1)/(T)∫T y(t)^2dt)
(2)

Added by Gloria R.

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