I need help with part B and E only! Thanks- I will rate and give you points if a

Question

I need help with part B and E only! Thanks- I will rate and give you points if answer if correct!

Frequency can create beats and to interpret the superposition as a "walking" wave. Consider two similar traveling transverse waves, which might be traveling along a string for example: They are similar because we assume that k1 and k2 are nearly equal and also that omega 1and omega 2 are k_1 equal. The principle of superposition states that if two waves each separately satisfy the wave equation then the sum (or difference) also satisfies the wave equation. This follows from the fact that every term in the wave equation is linear in the amplitude of the wave. Consider the sum of the two waves given in the introduction, that is, These waves have been chosen so that their sum can be written as follows: where C is a constant, and the functions yenvelope and ycarrier are trigonometric functions of x and t. (Figure 1.) This form is especially significant because the first function, called the envelope, is a slowly varying function of both position (x) and time (t), whereas the second varies rapidly with both position (x) and time (t). Traditionally, the overall amplitude is represented by the constant C, while the functions yenvelope and ycarrier are trigonometric functions with unit amplitude.

Explanation / Answer

Part B)
C = 2A
y envelope = cos ( (((k1-k2)/2)*x) + (((w2-w1)/2)* t))
y carrier = sin ( (((k1+k2)/2)*x) - (((w2+w1)/2)* t))
Part E)
velocity of propogation of envelope = deltaw/deltak

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