Properties of Waves: Phase Relationships

What is the phase of a wave? Phase is a difficult concept for new physics students to master.

The most basic wave shape is a harmonic wave, which is described using a sine or cosine function. The unit circle that is commonly used to introduce trigonometric functions is also helpful in understanding harmonic waves. The cosine and sine functions can be generated by looking at the projection of a point on the circle at an angle θ on the x and y axes, respectively. As the point moves around the circle in a counter-clockwise direction (positive rotation), these projections change and trace out cos(θ) and sin(θ) as functions of θ.

  Imagine that the angular position θ of the point on the unit circle (white dot) increases at a constant rate ω, so that θ=θ t. What if a constant offset (phase constant) φ were added so that the angular position is now given by: θ=θ t+φ? The simulation below illustrates how changing the phase constant shifts the wave in time. Change the phase constant φ by choosing ONE checkbox and then drag the white dot around the unit circle in the counter-clockwise direction. Notice how the phase constant φ shifts the starting point on th unit circle at time t=0, causing the sine function to shift.

Experiment with this simulation to develop a more thorough understanding shifting a wave with a phase constant. What value fo the phase constant will convert this sine function into: a cosine? a negative sine? a negative cosine?

Use the above simulation to answer the following questions?