Question

Sound Waves Sound is a result of waves applying pressure to a person's eardrum. For a particular sound wave radiating outward, the trigonometric function P = cos(TT-10001) can be used to express the pressure P at a radius of r feet from the source after 1 seconds. In this formula, a is the maximum sound pressure at the source, measured in pounds per square foot. (Source: L. Beranek, Noise and Vibration Control.) (a) Let a = 0.4,1 = 1, and graph the sound pressure for 0 < r = 20. What happens to the pressure P as the radius r increases?

Answer 1

The trigonometric function P = cos(πr-10001) can be used to express the pressure of a sound wave at a certain radius. As the radius increases, the pressure will vary and we will observe fluctuations in the sound pressure graph.

Step-by-step explanation:

The given trigonometric function P = cos(πr-10001) represents the pressure P at a radius of r feet from the source after 1 second, where a is the maximum sound pressure at the source. The value of a is given as 0.4 and we need to graph the sound pressure for 0 < r ≤ 20.

To create the graph, we can substitute different values of r into the equation P = cos(πr-10001) and calculate the corresponding values of P. Using these values, we can plot a graph with r on the x-axis and P on the y-axis.

As the radius r increases, the value of the trigonometric function P = cos(πr-10001) will vary. This means that the pressure P at a particular radius will change. Graphically, we will observe fluctuations in the sound pressure as the radius increases.