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A transverse periodic wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t − 10.0 m−1 x). Another transverse wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t + 10.0 m−1 x). What is the equation that represents the superposition of the two waves?

Question

A transverse periodic wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t − 10.0 m−1 x). Another transverse wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t + 10.0 m−1 x). What is the equation that represents the superposition of the two waves?

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Solution

The superposition of two waves is simply the sum of the two waves. Therefore, the equation that represents the superposition of the two waves is:

y(x, t) = 1.50 cm sin(1,500 rad/s t − 10.0 m−1 x) + 1.50 cm sin(1,500 rad/s t + 10.0 m−1 x)

This equation represents the superposition of the two waves.

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