Consider a traveling wave described by the formula(adsbygoogle = window.adsbygoogle || []).push({});

y_1(x,t) = Asin(kx - wt).

This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

The expression for a wave of the same amplitude that is traveling in the opposite direction is Asin(kx + wt).

The sum of these 2 waves can be written in the form y_s(x,t) = y_e(x)*y_t(t). Where y_e only depends on displacement and y_t depends on the time.

Find y_e(x) and y_t(t). Keep in mind that y_t(t) should be a trigonometric function of unit amplitude. Express your answers in terms of A, k, x, w, and t.

I know I'm meant to use the identity sin(A-B) = sinAcosB - cosAsinB, but I don't know how to apply it.

Any help would be great.

Thank you.

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# Homework Help: Wave equations

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