Pressure on the eardrum If two tuning forks are struck

Chapter 6, Problem 6.5.40

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Pressure on the eardrum If two tuning forks are struck simultaneously with the same force and are then held at the same distance from the eardrum, the pressure on the outside of the eardrum at time t is given bywhere a, , and are constants. If and are almost equal, a tone is produced that alternates between loudness and virtual silence. This phenomenon is known as beats. (a) Use a sum-to-product formula to express as a product.(b) Show that may be considered as a cosine wave with approximate period and variable amplitude Find the maximum amplitude.(c) Shown in the figure is a graph of the equationNear-silence occurs at points A and B, where the variable amplitude in part (b) is zero. Find the coordinates of these points, and determine how frequently near-silence occurs.(d) Use the graph to show that the function p in part (c) has period . Conclude that the maximum amplitude of 2 occurs every units of time.