Wave Motion: Energy Transfer and Characteristics

• Wave motion is illustrated by vibrations in ropes and springs and by waves in a ripple tank, including the term wavefront.
• Waves transfer energy without transferring matter.
• Key terms include speed, frequency, wavelength, period, and amplitude, with graphical representation.
• The relationship: speed of wave = frequency × wavelength needs to be understood and recalled.
• Transverse and longitudinal waves should be comprehended with suitable examples.

What is a Wave?

• Wave examples include water wave, rope wave and a wave on a slinky.
• Wave propagation involves particles in a medium vibrating periodically around their equilibrium or rest position.
• Waves transfer energy in direction of motion but do not transfer matter.
• Wave motion involves a disturbance or periodic vibration propagating through space, transferring energy but not matter

Amplitude and Wavelength

• Displacement is the distance of a point on a wave from its equilibrium position.
• Amplitude refers to the maximum displacement from the equilibrium position.
• Wavelength is the shortest distance between two points in phase, vibrating in the same direction.

Quantities, Units and Symbols

• Amplitude is represented by the symbol "a" or "A" and measured in meters (m).
• Wavelength is represented by the symbol "λ" and measured in meters (m).
• Negative displacement means the particle is vibrating below the rest or equilibrium position.
• Two particles with the same displacement are not necessarily at the same stage of vibration; they could be moving in opposite directions.

Period and Frequency

• Period is the time taken for a particle to complete one full oscillation or for a wave to travel one wavelength.
• Frequency refers to number of oscillations each point on the wave completes in one second, or the number of complete oscillations per unit time.
• Important formulas for frequency are:
  • f = 1/T (where T is the period)
  • f = number of oscillations / time taken

Wave Speed

• Wave speed refers to the distance travelled by the wave per unit time.
• Wave speed is represented by the symbol "v" and has SI units of meters per second (m/s).
• Wave speed is calculated as distance travelled/time taken and is shortened to v = fλ
• Wave speed depends on the medium, and as the speed changes, so does the wavelength, frequency remains constant.

Wavefront

• Wavefront is an imaginary line joining adjacent points in phase on a wave.
• Wavefronts can be drawn by connecting the crests of a wave.
• The lines PQ, RS, TU, and VW are all wavefronts, in the diagram.
• Distance between two successive wavefronts equals one wavelength.
• Time taken for a wavefront to advance one wavelength is the period.
• Direction of wave travel is always perpendicular to the wavefront.
• Deeper water increases wave speed, shallower water decreases wave speed.
• Frequency remains constant, but wavelength decreases if speed decreases.

Transverse and Longitudinal Waves

• A transverse wave's direction of vibration is perpendicular to the direction of wave travel.
• Transverse wave examples: rope waves, water waves, slinky coil (vibrated side to side), all electromagnetic waves, and earthquakes.
• A longitudinal wave's direction of vibration is parallel to the direction of wave travel.
• Longitudinal Wave examples: slinky coil (pushed and pulled), sound waves, and earthquakes.
• Wavelength is the distance between two consecutive compressions or rarefactions.