What is the amplitude of a function?
Amplitude, Period, Phase Shift and Frequency. Some functions (like Sine and Cosine) repeat forever. and are called Periodic Functions. The Period goes from one peak to the next (or from any point to the next matching point): The Amplitude is the height from the center line to the peak (or to the trough).
Amplitude. Amplitudes are always positive numbers (for example: 3.5, 1, 120) and are never negative (for example: -3.5, -1, -120). Amplitudes are positive because distance can only be greater than zero or equal to zero; negative distance does not exist.
- The amplitude, a, of a wave is the distance from the centre line (or the still position) to the top of a crest or to the bottom of a trough. Be careful with this quantity - the centre line is not always given in a diagram. Amplitude is measured in metres (m).
- (Mass does not affect the pendulum's swing. The longer the length of string, the farther the pendulum falls; and therefore, the longer the period, or back and forth swing of the pendulum. The greater the amplitude, or angle, the farther the pendulum falls; and therefore, the longer the period.)
- The energy transported by a wave is directly proportional to the square of the amplitude of the wave. This energy-amplitude relationship is sometimes expressed in the following manner.
This function has an amplitude of 1 because the graph goes one unit up and one unit down from the midline of the graph. This function has a period of 2π because the sine wave repeats every 2π units.
- An amplitude cannot be negative since it is defined as a half the distance, which cannot be negative, between the maximum value and the minimum value.
- The height from the center line to the peak (or trough) of a periodic function. Or we can measure the height from highest to lowest points and divide that by 2. Try adjusting the amplitude below: See: Periodic Function.
- Sine is an odd function, and cosine is an even function. You may not have come across these adjectives “odd” and “even” when applied to functions, but it's important to know them. A function f is said to be an odd function if for any number x, f(–x) = –f(x).
The amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest. Similarly, the amplitude can be measured from the rest position to the trough position.
- Amplitude is the size of the vibration, and this determines how loud the sound is. We have already seen that larger vibrations make a louder sound. Amplitude is important when balancing and controlling the loudness of sounds, such as with the volume control on your CD player.
- Frequency is how many waves pass by in a single second Wavelength is the distance between two crests or troughs. Frequency Frequency and Amplitude If you were at the beach, frequency is how often a wave hits you and amplitude is the height of the wave.
- Amplitude is an important parameter of waves and is the maximum displacement of points on a wave. Stated another way, amplitude is the vertical distance between a peak or a valley and the equilibrium point. Frequency is the number of wave cycles passing a point per unit time.
Updated: 2nd October 2019