Waves are disturbances that transfer energy from one place to another without transferring matter.
They can be classified based on how the particles of the medium move relative to the direction of wave propagation.
Transverse Waves: Particle Motion Perpendicular to Wave Propagation
In transverse waves, the particles of the medium oscillate perpendicularly to the direction of wave propagation.
Example
Water Waves:
In water waves, the water molecules move up and down while the wave travels horizontally across the surface.
Electromagnetic Waves:
Light waves, radio waves, and X-rays are all transverse waves.
In these waves, oscillating electric and magnetic fields are perpendicular to the direction of wave travel.
Note
Mechanical transverse waves can travel through solids and along the surface of liquids, but they generally do not propagate through liquids or gases in bulk.
This is because gases and liquids do not have the structural rigidity needed to support perpendicular oscillations.
Longitudinal Waves: Particle Motion Parallel to Wave Propagation
In longitudinal waves, the particles of the medium oscillate parallel to the direction of wave propagation.
Example
Sound Waves:
In sound waves, air molecules compress and rarefy as the wave travels through the air.
Compression Waves in a Slinky:
When you push and pull a slinky, coils move back and forth in the same direction as the wave.
Note
Longitudinal waves can travel through solids, liquids, and gases because they rely on compressions and rarefactions, which all states of matter can support.
Definition
Compression
A compression is a region in a longitudinal wave where the particles of the medium are close together, resulting in a high-pressure area. In sound waves, compressions correspond to regions of increased air density and pressure.
Definition
Rarefaction
A rarefaction is a region in a longitudinal wave where the particles of the medium are spread apart, resulting in a low-pressure area. In sound waves, rarefactions correspond to regions of decreased air density and pressure.
Key Wave Parameters: Wavelength, Frequency, Time Period, and Wave Speed
To fully describe a wave, we need to understand several key parameters:
Wavelength ($\lambda$)
The wavelength ($\lambda$) is the distance between two consecutive points in phase on a wave, such as crest to crest or trough to trough.
It is measured in meters (m).
Example
If the distance between two crests of a water wave is 2 meters, the wavelength of the wave is 2 m.
Definition
Crest
A crest is the highest point of a wave, where the displacement of the medium is at its maximum positive value relative to the equilibrium position. In a transverse wave, crests correspond to peaks in the wave motion.
Definition
Trough
A trough is the lowest point of a wave, where the displacement of the medium is at its maximum negative value relative to the equilibrium position. In a transverse wave, troughs correspond to the lowest points in the wave motion.
Frequency ($f$)
The frequency($f$) is the number of complete cycles or oscillations that occur each second at a given point.
It is measured in hertz (Hz), where 1 Hz = 1 cycle per second.
Example
If 5 cycles or oscillations occur at a point in 1 second, the frequency of the wave is 5 Hz.
Time Period ($T$)
The time period($T$) is the time taken for one complete cycle or oscillation to occur at a given point.
It is measured in seconds (s).
Note
Frequency and time period are reciprocally related: $$T = \frac{1}{f}$$
Wave Speed ($v$)
The wave speed ($v$) is the speed at which the disturbance travels through the medium.
It is measured in meters per second ($\text{m s}^{-1}$).
Two Ways to Graph a Wave: Position and Time
A displacement against position graph is a snapshot of the whole wave at one instant, and the distance between two points in phase is the wavelength $\lambda$.
A displacement against time graph tracks a single particle as time passes, and the time for one full oscillation is the period $T$.
Both graphs look like a sine curve, so always check the horizontal axis before reading a value off it.
Common Mistake
A displacement against position graph gives you the wavelength, not the period.
A displacement against time graph gives you the period, not the wavelength.
Reading a wavelength off a time axis, or a period off a distance axis, is a common exam mistake.
Wave Speed Equations
The speed of a wave is determined by its wavelength and frequency.
The relationship between these parameters is given by the wave speed equation: $$v = f\lambda$$
This equation can also be expressed in terms of the time period: $$v = \frac{\lambda}{T}$$
Tip
The wave speed depends only on the properties of the medium, not on the frequency or wavelength of the wave.
For example, the speed of sound in air is approximately $340 \text{ m s}^{-1}$, regardless of the frequency of the sound wave.
Example question
A sound wave has a frequency of 440 Hz and a wavelength of 0.78 m. What is its speed?