Wave Function

What do you use the wave function for?

To combine different waves

When do we use the wave function to solve equations?

When the sinx and cosx functions have the same coefficient of x. If you are solving an equation in the form sin2x + cosx = 1 then you must use the double angle formula expansion for 2x to solve since the coefficients are different and can’t be solved using wave function.

How would you find the maximum value of a combined wave?

Find the value of K (amplitude) then ensure the graph has not been transformed from +a or –a.You must write the maximum in relation to the wave function equation found.

What are the 4 expansions used in the wave function?

Sin(x + a)Sin (x – a)

Cos(x + a) Cos(x – a) easiest to use if not directed to a specific expansion in question.

How do you find the value of k?

k=√(a^2+b^2 ) when a and b are the matching coefficients a=kcosa, b = ksina

K should always be positive as you won’t have a negative square root.

How do you find the value of the phase angle?

Tanα = b/a

How do you express acosx + bsinx in another form using the wave function method?

1. Expand brackets in given form

2.Equate coefficients You must write a=kcosα and b = ksinα

3. Find k

4. Find a by tan^-1 and CAST diagram

5. Write down final combined equation.

How do we sketch the graph of the wave function?

You must check amplitude, number of cycles, of trig graph and phase shift angle and draw changes in relation to the original trig graph. All critical points must be shown for amplitude and where curve crosses x axis or is at max and min points.