Progressive Waves (CIE AS Physics)

• Energy is transferred through moving oscillations or vibrations. These can be seen in vibrations of ropes or springs

Waves can be shown through vibrations in ropes or springs

• The oscillations/vibrations can be perpendicular or parallel to the direction of wave travel:
  • When they are perpendicular, they are transverse waves
  • When they are parallel, they are longitudinal waves

Ripple tanks

• Waves can also be demonstrated by ripple tanks. These produce a combination of transverse and longitudinal waves

Wave effects can be demonstrated using a ripple tank

• Ripple tanks may be used to demonstrate the wave properties of reflection, refraction and diffraction

• Displacement (x) of a wave is the distance 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
• Wavelength (λ) is the distance between points on successive oscillations of the wave that are in phase
  • These are all measured in metres (m)

Diagrams showing the amplitude and wavelength of a wave

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

Diagrams showing the time period of a wave

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

Frequency equation

• Speed (v) is the distance travelled by the wave per unit time. 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
• This can be found from the relative positions 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

• Waves transfer energy between points, without transferring matter
• When a wave travels between two points, no matter actually travels with it:
  • The points on the wave simply vibrate back and forth about fixed positions

• Waves that transfer energy are known as progressive waves
• Waves that do not transfer energy are known as stationary waves