Glossary
Amplitude (A)
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. It represents the wave's intensity or energy.
Example:
When you turn up the volume on your stereo, you are increasing the amplitude of the sound waves, making them louder.
Angular Frequency (ω)
A measure of the rate of rotation or oscillation, expressed in radians per second. For waves, it is related to frequency by the equation ω = 2πf.
Example:
In a circuit, an AC voltage oscillating at 60 Hz has an angular frequency of 120π radians per second.
Frequency (f)
The number of complete wave cycles that occur in one second. It is measured in hertz (Hz), which is equivalent to cycles per second (s⁻¹).
Example:
A radio station broadcasting at 98.7 MHz means the electromagnetic waves oscillate with a frequency of 98.7 million cycles per second.
Period (T)
The time required for one complete cycle of a wave to pass a given point. It is measured in seconds (s).
Example:
If a buoy bobs up and down every 4 seconds as ocean waves pass, its period is 4 seconds.
Periodic Wave
A wave that exhibits a repeating pattern over time and space, characterized by consistent properties like period, frequency, and wavelength.
Example:
The consistent ripples spreading outwards after a raindrop hits a puddle are an example of a periodic wave.
Pitch
The perceptual quality of sounds that allows their ordering on a frequency-related scale, primarily determined by the frequency of the sound wave. Higher frequency corresponds to higher pitch.
Example:
A piccolo produces a very high pitch because it generates sound waves with a high frequency.
Position-Dependent Wave Equation
A mathematical expression, typically $y(x) = A \cos(2 \pi \frac{x}{\lambda})$, that describes the displacement of a wave at a specific time as a function of its position along the wave's path.
Example:
The Position-Dependent Wave Equation allows you to map out the shape of a frozen ocean wave at a particular instant, showing its peaks and troughs across space.
Time-Dependent Wave Equation
A mathematical expression, typically $x(t) = A \cos(\omega t)$, that describes the displacement of a wave at a specific location as a function of time.
Example:
Using the Time-Dependent Wave Equation, you can predict the exact vertical position of a point on a vibrating guitar string at any given moment after it's plucked.
Wave Equation (λ = v/f)
A fundamental relationship stating that the wavelength of a wave is equal to its speed divided by its frequency. This equation applies to all types of periodic waves.
Example:
If you know the speed of light and the frequency of a specific color of light, you can use the Wave Equation to calculate its wavelength.
Wave Speed (v)
The rate at which a wave propagates through a medium. It depends on the properties of the medium itself.
Example:
Sound travels much faster in water than in air, meaning its wave speed is greater in water.
Wavelength (λ)
The spatial period of a periodic wave, which is the distance over which the wave's shape repeats. It is typically measured from one peak to the next or trough to the next.
Example:
In a slinky stretched across a room, the distance from one compressed coil to the next identical compressed coil represents the wavelength of the pulse.