The amplitude of a sound wave produced by a speaker decreases over time due to air resistance. The amplitude y y (in decibels) of the sound wave at time t t (in seconds) is given by the equation: y = 5 e − t 3 cos ⁡ ( π t 6 ) y=5e^{-\frac{t}{3}}\cos\left(\frac{\pi t}{6}\right) Draw the graph of the amplitude function on [ 0 , 9 ] \left\lbrack0,9\right\rbrack .

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4. Applications of Derivatives

Motion Analysis

4. Applications of Derivatives

Motion Analysis: Study with Video Lessons, Practice Problems & Examples

2PRACTICE PROBLEM

ANSWERS OPTIONS

Graph of a decaying amplitude function, showing a red curve decreasing from 5 decibels to near zero over time.

Graph of a sound wave amplitude function, showing a decreasing trend over time from 0 to 9 seconds.

Graph of a sound wave amplitude function, showing a red curve fluctuating between -6 and 2 on a grid from 0 to 9 seconds.

Graph of a decaying amplitude function, showing a red curve on a grid from 0 to 9 on the x-axis and -2 to 6 on the y-axis.