A transverse wave is represented by y = 4 sin(5x+20t), where x is measured in metres and t in seconds. By examining the constant-phase condition, determine the direction of propagation of the wave.
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Question

A transverse wave is represented by y = 4 sin(5x+20t), where x is measured in metres and t in seconds. By examining the constant-phase condition, determine the direction of propagation of the wave.

G1 Physics · Accepted Answer

The phase is 5x+20t. For a fixed phase, 5x+20t = constant. Differentiating with respect to time, 5 dx/dt+20 = 0. Therefore, dx/dt = −4 m/s. The negative sign means the wave propagates towards decreasing x. Correct option: B.