3. The technical description and properties of a TRANSVERSE WAVE and equation

The above diagram gives an idea of a transverse wave where the oscillations/vibrations (disturbance) are at 90^o to the direction the wave moves.

• Expressing this another way - the disturbance of the medium is at 90^o to the direction the wave is travelling.

  •  Examples of transverse waves:

• electromagnetic radiation waves, ripples-waves on water, shaking a slinky spring or rope from side to side, earthquake waves of the S-waves type.

• You should know, understand and be able to use the terms frequency, wavelength and amplitude of a wave in terms of this diagram of a transverse wave.

  • The top of the wave form is called a crest and the bottom of the wave is called the trough see wave diagram above.

  • The wave amplitude = distance from the baseline of zero displacement (rest position) to the point of maximum displacement (to top of crest or to bottom of trough) - see wave diagram above.

    • The greater the amplitude, the greater the amount of energy the wave transfers.

  • One wavelength (m) = distance of one complete cycle or oscillation/vibration = horizontal distance from any point on the wave until where it begins to repeat = distance between two crests = distance between two troughs etc. - see wave diagram above.

    • The wavelength is sometimes defined as the distance between the same points on two adjacent/neighbouring disturbances. Both these definitions equate to one complete cycle of the wave oscillation-vibration.

    • Wavelength units are usually metres (m) but other units are commonly used e.g. nanometres (nm, 10^-9 m).

  • The frequency of a wave (Hz) = number of complete cycles/oscillations per second = number of complete cycles/waves passing a given point per second.

    • Frequency is measured in Hertz. 1 Hertz = 1 oscillation or vibration/s (1 Hz, 1 per sec or 1 s^-1).

  • The period of a wave is the time in seconds for one complete cycle to pass a certain point.

    • wave period (s) = 1 ÷ frequency (Hz, s^-1)

  • Symbols used: v = velocity, f = frequency, λ wavelength

    • More on calculations based on the equation v = f x λ in Part 10 wave calculations

  • Examples of transverse waves

    • Electromagnetic radiation

    • Water waves - here you can observe floating objects bobbing up and down at 90o to the wave direction.

    • Slinky spring - shaken from side to side to send a transverse wave along it.

      • You could shake the slinky spring over a metre ruler (at 90^o) and estimate the (i) amplitude and (ii) with another metre ruler alongside the spring, measure the wavelength.

      • You could also measure (iii) the frequency of shaking and from (ii) and (iii) estimate the speed of the slinky spring wave.

      • You could check your estimated speed by observing, with a stopwatch, how long it takes for a wave to travel several metres.

      • They are not very accurate experiments, but a bit of fun!