ENVS 1200 Chapter Notes - Chapter 3: Phi, Radian, Electric Generator
13 May 2018
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ENVS 1200 Chapter 3 Notes – Summary
Introduction
• The size of an antenna is based on the wavelength of the signal that one is trying to
receive.
• Why a sine wave?
• Sine waves occur naturally throughout nature.
• Sound, radio waves, and light are all composed of sine waves.
• Even ripples on a pond are sinusoidal.
• Although the sine wave may seem an odd waveform to occur so commonly, the sine
wave is related in a simple way to a circle.
• Picture a marble rolling around a circle at constant speed.
• If you view the circle edgewise, the marble will trace out a sine wave in time.
• For this reason, points on the sine wave are often designated in degrees.
• The sie ae egis at 0 ◦ ad ages to 0 ◦ ad the epeats fo 0 ◦ agai.
• At any given instant in time, the amplitude of the wave is given by the position of the
marble for the specified angle.
• Matheatiall, that alue is epeseted the euatio [t] = A si [π ft. + ϕ] where
A is the maximum amplitude, corresponding to the radius of the circle.
• f is the number of times that the marble rolls around the circle per second.
• For mathematical reasons unimportant to us here, the angle is usually given in radians,
rather than degrees.
• When t=T, the marble has rolled aoud the ile oe, theefoe π adias is eual to
0 ◦.
• A adia is theefoe appoiatel . ◦.
• ϕ (the Greek letter phi), represents the angle of the marble when we begin our viewing,
i.e., when t=0.
• For the view shown in the figure, ϕ=0.
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