A juggler may not understand the mathematical representation of phase, but they are using the effect as they throw balls in the air at different times.
It is important to understand the concept of phase before starting the Waves section. In short: a full wave cycle consists of 2π radians.
Key Concepts
The oscillations of two pendula can be represented by two sine or cosine curves. If the pendulums don't swing at the same time, the curves will not be together and instead will be separated by an angle φ. This is called the phase difference or phase angle.
A phase angle of π means that the pendula are completely out of phase (antiphase), whereas phase angles of 0 or 2π make the pendula oscillate in phase.
Use quizzes to practise application of theory.
START QUIZ!
The two lines on the graph below represent two oscillating bodies.
The phase difference between the bodies is:
The oscillations are 1/4 of a cycle out of phase. 1 cycle is 2π
The two lines on the graph below represent two oscillating bodies.
The phase difference between the bodies is:
The oscillations are 1/2 of a cycle out of phase. 1 cycle is 2π
The two lines on the graph represent two oscillating bodies:
The ratio of frequency of red/frequency of blue is
Between the two points where the oscillations are in phase there are 2 red cycles and 3 blue cycles. So ratio of time periods is 3/2. Frequency = 1/T so ratio of frequencies =2/3
The animation is of 2 bodies executing SHM
1/4 cycle out of phase, when Ais in the middle B is at the top
The animation is of 2 bodies executing SHM
The phase difference is
half a cycle
The displacement of two bodies can be represented by the equations:
y1 = Asin(2πft + π)
y2 = A sin(2πft + π/4)
The phase difference is
The phase angle of 1 is π and 2 is π/4. The phase difference is the difference in phase angle
Tow bodies execute SHM with different frequency.
If they start in phase they will
The time between them being in phase depends on the difference in frequency
The anim,ation shows 2 points oscillating out of phase
Which phase diagram represent this situation?
Phase difference is less than π/2
The graphs y = sin θ (red) and y = cos θ (blue) are shown below
The equation relating the functions is
cos (0) is the same as sin (0 + π/2)
How much of Phase have you understood?
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