4.6.1 Progressive Waves: Longitudinal & Transverse

• In mechanical waves, particles oscillate about fixed points
• A progressive wave is an oscillation that transfers energy and information
  • The substance in which the waves move through are disturbed (eg. water, air)
  • The particles of the substance oscillate about a fixed position
  • This is sometimes called a travelling wave

• There are two types of waves
  • Transverse
  • Longitudinal

• The type of wave can be determined by the direction of the oscillations in relation to the direction the wave is travelling

Transverse Waves

• A transverse wave is defined as:

A wave in which the particles oscillate perpendicular to the direction of the wave travel (and energy transfer)

• Examples of transverse waves are:
  • Electromagnetic waves e.g. radio, visible light, UV
  • Vibrations on a guitar string

• Transverse waves can be shown on a rope
• Transverse waves can be polarised

Longitudinal Waves

• A longitudinal wave is defined as:

A wave in which the particles oscillate parallel to the direction of the wave travel (and energy transfer)

• Examples of longitudinal waves are:
  • Sound waves
  • Ultrasound waves

• Longitudinal waves can be shown on a slinky spring
• Longitudinal waves cannot be polarised

Waves can be shown through vibrations in ropes or springs

• Displacement (x) of a wave is the distance of a point on the wave from its equilibrium position
• • It is a vector quantity; it can be positive or negative

• Amplitude (A) is the maximum displacement of a particle in the wave from its equilibrium position

Diagram showing the amplitude and wavelength of a wave

• Wavelength (λ) is the distance between points on successive oscillations of the wave that are in phase
• Displacement, amplitude and wavelength are all measured in metres (m)

A wavelength on a longitudinal wave is the distance between two compressions or two rarefactions

• Period (T) or time period, is the time taken for one complete oscillation or cycle of the wave
  • Measured in seconds (s)

Diagram showing the time period of a wave

• Frequency (f) is the number of complete oscillations or wavelengths passing a point per unit time
  • Measured in Hertz (Hz) or s^-1

• Speed (v) is the distance travelled by the wave per unit time, and defined by the wave equation
  • Measured in metres per second (m s^-1)

Phase

• The phase difference tells us how much a point or a wave is in front or behind another
• It is defined as:

How far the cycle of one point is compared to another point on the same wave

• This can be found from the relative positive of the crests or troughs of two different waves of the same frequency
  • When the crests or troughs are aligned, the waves are in phase
  • When the crest of one wave aligns with the trough of another, they are in antiphase

• The diagram below shows the green wave leads the purple wave by ¼ λ

Two waves ¼ λ out of phase

• In contrast, the purple wave is said to lag behind the green wave by ¼ λ
• Phase difference is measured in fractions of a wavelength, degrees or radians
• The phase difference can be calculated from two different points on the same wave or the same point on two different waves
• The phase difference between two points:
  • In phase is 360^o or 2π radians
  • In anti-phase is 180^o or π radians