please answer throughly. 1 Bonus Problem Consider the following three functions:

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please answer throughly.

1 Bonus Problem Consider the following three functions: f(r, t) J sin Bt), (1) (2) h (z, t) f(z,t) g(z, t). (3) with A, B, C 0. Both f(r,t) and g(z, t) satisfy the wave equation. The sine one is one of the types we saw in class. As for g(z, t), plugging it into the wave equation, considering that (4) 2A (5) 2C. we find a value of v for which it is satisfied. In particular the speed of propagation for this wave to be v Va. Thus (2) satisfies the wave equation and it too must be a wave. Now, we know from the superposition principle (which is a theorem) that a linear combination of solutions to the wave equation is also a solution to the wave equation. Thus h ought also be a wave. Let's plug it into the wave equation to see what happens: 02h(a, t) 2A -sin (z Bt) (6) 20 B2 sin Bt), (7)

Explanation / Answer

here, f is a sin function and 'g' is a polynomial function;

Superposition principal applies to sign function,

A sin(theta 1) + B sin(theta 2) = C sin( phi);

every sin and cosine function can be written as above;

that is why superposition principal is application for sine waves but not for different waves;

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