If the bug produces disturbances at a frequency of 2 per second, then each observer would observe them approaching at a frequency of 2 per second. In fact, the frequency at which disturbances reach the edge of the puddle would be the same as the frequency at which the bug produces the disturbances. An observer at point A (the left edge of the puddle) would observe the disturbances to strike the puddle's edge at the same frequency that would be observed by an observer at point B (at the right edge of the puddle). These circles would reach the edges of the water puddle at the same frequency. The pattern produced by the bug's shaking would be a series of concentric circles as shown in the diagram at the right. Since each disturbance is traveling in the same medium, they would all travel in every direction at the same speed. If these disturbances originate at a point, then they would travel outward from that point in all directions. The bug is periodically shaking its legs in order to produce disturbances that travel through the water. Suppose that there is a happy bug in the center of a circular water puddle.
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