Chapter 6.2
Amplitude, Period and Phase Shift
by Cary
| Word Problem | Jenny was given a project in ICM class which required her to find some kind of wave in the world and find its amplitude, period and phase shift. Jenny, being real, real cool, decided she would measure her own hair, as it was extremely wavy and nasty. Cutting off a large chunk of her hair, Jenny examined it closely. Her father, who obviously was the only intelligent one in the family, told Jenny that her hair had the equation of y = 5 sin 4 x. How can Jenny find the amplitude, period and phase shift of her hair (assuming it has any of them). |
Lesson Plan
1. Amplitude, which is basically the height of the wave, is the most easiest found of all the requirements. In the equation y = 5 sin 4 x, as in all equations with sin/cos, the number before the trig. function is the amplitude. In this case, the amplitude is 5, meaning it probably goes up and down 5 cm below the x-axis. Only sin/cos functions have amplitudes, as tangents increase and decrease without bound for values that approach certain multiples of 90 degrees.
2. Period, which is how long it takes the graph to repeat itself, is usually expressed in degree measure or in pi. To find the period of an equation with sin/cos, follow this equation: y = (Amp) sin (K) (X). To find the period in this function, use the equation 360/K. This equation works because the normal period for a sin/cos equation is 360 degrees, or 2 pi. For a tangent equation, one must use the equation 180/K, since tangent equations have a shorter period.
3. The phase shift is basically if and/or how much the equation is moved from its normal starting position. This equation for Jenny's hair has no phase shift. However, finding the phase shift can be made easy using this equation: y = (Amp) (sin/cos/tan) (K*X + C). To find the phase shift, simply follow the equation -C/K. For example, if the equation was y = 3 sin (4X + 3), the phase shift would be -3/4. This means one would shift 3/4 units to the right.
Quote: "We cannot expect people to have respect for law and order until we teach respect to those we have entrusted to enforce those laws."
- Hunter S. Thompson
http://www.quoteproject.com/subject.asp?subject=60
Explanation: This quote relates to the character trait of responsibility. We all have the responsibility to follow the laws of our country, but on that same note, so do the police and the rest of law enforcement. As long as the police continue to abuse their power, it is increasingly difficult to treat the laws they uphold with any type of dignity. This also includes the legislators as well as our military. The less and less these people listen to their constituency, the less those very same people are likely to give them any consideration in the future.
| Mrs. Blackwell | Math Power | Related Site to Word Problem www.mpipks-dresden.mpg.de/mpi-doc/julichergruppe/julicher/auditory_sensitivity/node3.html |
Cary B. III