While working on a sound lab assignment in your science class, your instructor assigns you an interesting problem. Your lab partner is assigned to speak into a microphone, and you are to record how "loud" the sound is using a device that plots the sound wave on a graph. Unfortunately, you don't know what part of the graph to read to understand "loudness". Your instructor tells you that "loudness" in a sound wave corresponds to "amplitude" on the graph, and that you should plot the values of the amplitude of the graph that is being produced.
Here is a picture of the graph:
Can you accomplish this task? By the end of this Concept, you'll understand what part of a graph the amplitude is, as well as how to find it.
In the first part of this video you'll learn about the amplitude of trigonometric functions.
James Sousa: Amplitude and Period of Sine and Cosine
No matter the basic function; linear, parabolic, or trigonometric, the same principle holds. To dilate (flatten or steepen, wide or narrow) the function, multiply the function by a constant. Constants greater than 1 will stretch the graph vertically and those less than 1 will shrink it vertically.
Solution: The 10 indicates that the amplitude, or height, is 10. Therefore, the function rises and falls between 10 and -10.
Amplitude: The amplitude of a wave is a measure of the wave's height.
1. The cosine function ranges from -1 to 1, therefore the minimum is -1 and the maximum is 1.
2. The sine function ranges from -1 to 1, and since there is a two multiplied by the function, the minimum is -2 and the maximum is 2.
3. The sine function ranges between -1 and 1, so the minimum is -1 and the maximum is 1.
Concept Problem Solution
Since you now know what the amplitude of a graph is and how to read it, it is straightforward to see from this graph of the sound wave the distance that the wave rises or falls at different times. For this graph, the amplitude is 7.
Determine the amplitude of each function.
Graph each function.
Identify the minimum and maximum values of each function.
- How does changing the constant k change the graph of y=ktan(x)?
- How does changing the constant k change the graph of y=ksec(x)?