Sine waves quantities
Properties of a Sine Wave
Key Properties
Peak Value: The maximum amplitude of the wave.
Peak to Peak Value: The difference between the maximum positive and maximum negative values; for a peak amplitude of 10V, peak to peak is 20V.
Periodic Time: The time required to complete one cycle of the wave.
Frequency: The number of cycles completed per second; measured in Hertz (Hz).
RMS (Root Mean Square): A measure which gives the effective value of the waveform.
Average Value: Represents the average level over one cycle.
Definition
A sine wave is a sinusoidal waveshape that represents one cycle of alternating voltage or current.
Horizontal Axis: Time
Vertical Axis: Voltage
Amplitude
Represents alternating voltage signal.
For example, peak amplitude = 10V, peak to peak amplitude = 20V.
Can also represent a current waveshape.
Mean Value
The mean value is the average of the wave's values over a half cycle.
Calculated as:
Mean Value = (Area above the line) = (Area below the line)
Quick method:
Mean value = Peak value x 0.636 (64% of peak value).
RMS Value
RMS: Defined as the square root of the mean of the squared values.
RMS Value of a pure sine wave = 70.7% (0.707) of peak value.
Example: For a sine wave with a peak value of 10V, RMS = 0.707 × 10 = 7.07V.
Significance: This RMS value produces the same heating effect as an equivalent DC voltage.
Periodic Time
Example: One complete cycle takes 8ms; therefore, periodic time = 8ms.
Frequency
Defined as the number of cycles per second.
Example: A wave completing 1000 cycles per second has a frequency of 1000 Hz (1kHz).
Relationship: Frequency = 1 / t (where t = periodic time).
For a periodic time of 8ms = 0.008s, Frequency = 1 / 0.008 = 125Hz.
Summary
A sine wave represents one cycle of alternating voltage or current with key properties such as peak value, peak to peak value, periodic time, frequency, RMS, and average.
Key formulas:
Peak Value = Half of Peak to Peak Value
Periodic Time = t = 1 / f
RMS = Peak x 0.707
Average = Peak x 0.636