Waves:

A wave is a disturbance that transfers energy and information without transferring matter. In some waves, the energy and information is transferred by oscillations (repeated vibrations) of the particles in solids, liquids and gases. Waves like this are called mechanical waves and include sound waves and water waves. In other waves the energy and information is transferred by oscillating magnetic and electric fields. These are known as electromagnetic waves; light, radio waves and infrared radiation are all electromagnetic waves.

Transverse waves:

A transverse wave is a wave in which the oscillations are at right angles or perpendicular to the direction the wave is travelling.

Note: It is important to describe the oscillations as perpendicular rather than up-and-down because they are only up-and-down if the wave is travelling horizontally, but are always perpendicular regardless of direction.

Important examples of transverse waves include:

• Water waves
  • We can see this experimentally by placing a floating object like a rubber duck on some wavy water. As the waves pass, the duck just bobs up and down rather than travelling along with the wave.
  • Note: strictly speaking, the movement of particles in water waves is a bit more complex than this, but at GCSE level, it is fine to call them transverse.
• Seismic s-waves – waves produced in the ground by earthquakes (put the s in s-waves with the s in transverse).
• Light and other electromagnetic waves

Longitudinal waves:

A longitudinal wave is a wave in which the particles oscillate parallel to the direction the wave is moving.

Note: It is important to describe the oscillations as parallel rather than left-and-right because they are only left-and-right if the wave is travelling horizontally, but are always parallel regardless of the direction.

Important examples of longitudinal waves include:

• Sound waves
  • We can see this experimentally by holding a floating helium balloon in front of a loudspeaker. As the sound waves pass through it, the balloon vibrates back and forth parallel to the line between you and the speaker, but does not get pushed along by the sound waves; you can feel these vibrations if you touch the balloon.
• Seismic p-waves – waves produced in the ground by earthquakes.

Anatomy of a wave:

• Equilibrium (resting) point: this is the position that the wave’s particles would have if the oscillations stopped. In the example of water, if there were no waves at all, the equilibrium position of the surface particles would be the flat surface of the water.
• Transverse waves:
  • Crest: this is the maximum displacement of oscillations in one direction.
    • For a horizontal transverse wave, this is the top of the wave.
  • Trough: this is the maximum displacement of oscillations in the other direction.
    • For a horizontal transverse wave, this is the bottom of the wave.
• Longitudinal waves:
  • Compression: this is the part of the wave where the particles are grouped closer together.
  • Rarefaction: this is the part of the wave where the particles are spread further apart.

Describing waves:

We can describe the differences between waves using a number of important quantities:

• Wave speed: This is the speed of a wave in metres per second. The speed of a particular type of wave is mainly determined by the material and the conditions, so for example sound travels through air at about 343 m/s (at 20 °C with dry air), whilst light travels through a vacuum at 300,000,000 m/s.
• Frequency: This is the number of complete waves that pass a point in a single second (this is equivalent to the number of complete oscillations each particle does in one second). Frequency is measured in units called hertz, Hz (1 Hz = 1 wave per second) or kilohertz, kHz (1 kHz = 1000 waves per second).
  • Note: The frequency of a wave is related to the amount of energy it transfers each second: if the amplitude (maximum displacement, see below) is kept the same, then a higher frequency wave will transfer more energy than a lower frequency one. This makes sense if you imagine making waves on a long rope by shaking it up and down; to increase the frequency of the waves you would have to shake it faster which requires more energy.
• Wavelength: This is the distance, in metres, between the same point on two neighbouring waves, i.e. the distance from crest to crest (transverse) or compression to compression (longitudinal).
  • Note: Because the speed of a given wave is fixed in a given medium, as you increase the frequency you decrease the wavelength and if you decrease the frequency you increase the wavelength.
• Period: This is the time it takes for a single wave to pass a point (this is also the time taken for a particle to complete one full cycle of its oscillation). The period can be found by dividing 1 second by the frequency of the wave.
  Period (s) = 1 frequency (Hz)
• Amplitude: This is the maximum displacement, in metres, of a particle from its equilibrium point with each oscillation (i.e. the furthest the particle moves).
  • Note: For waves of a given frequency, the amplitude is related to the amount of energy the wave transfers each second; greater amplitude transfers more energy.

Measuring wave speed:

The speed of a wave can be measured in two ways:

• Distance and time
  • The speed of anything can be found by using the equation speed (m/s) = distance travelled (m) ÷ time taken (s) and waves are no different.
    • E.g. If a wave travelled 300 m in 4 s, its speed would be speed = 300 ÷ 4 = 75 m/s.
  • We can measure this experimentally as follows:
    1. Measure a distance for the wave to travel with a ruler or measuring tape.
    2. Time how long the wave takes to travel that distance with a stopwatch.
    3. Divide the distance travelled by the time taken to get the speed.
• Wavelength and frequency
  • If the wavelength of a wave is how long each of its waves is, and the frequency of a wave is the number of waves each second, the speed can be calculated by speed (m/s) = frequency (Hz) × wavelength (m).
    • If a wave has a frequency of 10 Hz and wavelength of 2 m, its speed is given by speed = 10 × 2 = 20 m/s. This works because we are saying that in one second, there are 10 waves (frequency = 10 Hz) that are each 2 m long (wavelength = 2 m), so the total distance they must travel is 20 m.
  • We can measure this experimentally as follows:
    1. Count the number of waves that pass a point in 10 s.
    2. Divide the number of waves counted by 10 to get the frequency in Hz.
    3. Measure the distance between two neighbouring waves in metres with a ruler or tape measure (crest to crest or compression to compression is easiest); this gives the wavelength.
    4. Calculate the speed by multiplying the frequency by the wavelength.

Try this in the simulation:

• Click the Transverse and Longitudinal titles at the top of the screen to see the difference in oscillations between the two types of wave. Under Graph and demonstrations toggle Rotatable mode on and drag on the ring to change the orientation of the wave. Notice how whilst the direction of the oscillations changes (for example up-down oscillations can become left-right oscillations), whether they are oscillating parallel or perpendicular to the wave direction does not change.
• Adjust the sliders for Frequency, Wavelength, Wave speed and Amplitude and see their effect on the wave. Notice how as you increase the frequency, the wavelength decreases and vice versa.
• Switch the Mode toggle to Pulse; click the Emit button once to move the turquoise paddle and observe how a single wave propagates through the particles. Notice also how when there is no source of vibrations, the wave stops.
• Under Graph and demonstrations toggle Play tone on, then explore how adjusting the Wave settings sliders affects the pitch of the tone you can hear: increasing the amplitude should make it louder, increasing the frequency / decreasing the wavelength should increase the pitch.