Properties of Waves

Properties of Waves: Transverse, Longitudinal, Frequency, and Wavelength

Waves transfer energy and information from one place to another without transferring matter. Understanding the basic properties and types of waves is the foundation of the entire waves topic.

Transverse and Longitudinal Waves

All waves are either transverse or longitudinal.

Transverse waves — the oscillations (vibrations) are perpendicular (at right angles) to the direction of energy transfer.

Examples:

• Light and all electromagnetic waves
• Water waves (ripples on a pond)
• S-waves (seismic waves)
• Waves on a string or rope

Longitudinal waves — the oscillations are parallel to the direction of energy transfer. The particles vibrate back and forth along the same direction the wave travels, creating regions of compression (particles close together) and rarefaction (particles spread apart).

Examples:

• Sound waves
• P-waves (seismic waves)
• Ultrasound
• Waves in a slinky spring (pushed and pulled along its length)

Wave Properties

All waves can be described using four key properties:

Amplitude — the maximum displacement of a point on the wave from its rest position (equilibrium). Measured in metres (m). For a transverse wave, this is the height of a crest (or depth of a trough) from the middle. A larger amplitude means more energy is carried by the wave. For sound, a larger amplitude means a louder sound.

Wavelength (lambda) — the distance from one point on a wave to the same point on the next wave. This could be crest to crest, trough to trough, or any equivalent point. Measured in metres (m).

Frequency (f) — the number of complete waves passing a point per second. Measured in hertz (Hz), where 1 Hz = 1 wave per second. For sound, a higher frequency means a higher pitch.

Period (T) — the time taken for one complete wave to pass a point. Measured in seconds (s).

The relationship between frequency and period:

period = 1 / frequency

T = 1 / f

Example: A wave has a frequency of 50 Hz. Its period = 1/50 = 0.02 seconds.

The Wave Equation

The speed of a wave relates to its frequency and wavelength:

wave speed = frequency x wavelength

v = f x lambda

Where:

• v = wave speed (metres per second, m/s)
• f = frequency (hertz, Hz)
• lambda = wavelength (metres, m)

Example: A sound wave has a frequency of 256 Hz and a wavelength of 1.3 m.

v = f x lambda = 256 x 1.3 = 332.8 m/s

Reading Waves from Diagrams

On a displacement-distance graph (a snapshot of the wave):

• The wavelength is the horizontal distance between two identical points (e.g. crest to crest)
• The amplitude is the vertical distance from the rest position to a crest (or trough)

On a displacement-time graph (one point oscillating over time):

• The period is the horizontal distance for one complete oscillation
• The amplitude is the vertical distance from rest to peak
• Frequency = 1 / period

Measuring Wave Speed

Required Practical: Measuring the speed of waves on water (ripple tank):

1. Set up a ripple tank with a vibrating dipper to create waves

2. Use a stroboscope to "freeze" the wave pattern

3. Measure the distance covered by a set number of waves to find the wavelength

4. Count the number of waves passing a point in a measured time to find the frequency

5. Calculate speed using v = f x lambda

Alternatively, measure the distance a wave front travels in a known time and use speed = distance / time.

Measuring the speed of sound:

1. Two people stand a measured distance apart (e.g. 100 m)

2. One claps or makes a loud noise; the other starts a stopwatch when they SEE the clap and stops when they HEAR it

3. speed = distance / time

4. Repeat and take a mean (reaction time is a significant source of error at this scale)

A more accurate method uses two microphones connected to a computer — the computer measures the tiny time delay between the sound reaching each microphone.

Exam Tips

• Do not say waves transfer matter — they transfer energy (and information)
• Wavelength is measured from crest to crest, NOT from crest to trough (that would be half a wavelength)
• Be careful with units — convert kHz to Hz (x 1,000), nm to m (x 10^-9), etc. before calculating
• On graphs, always check whether it shows displacement-distance or displacement-time before reading values