Waves, Light & Sound
Wave Properties
1st Year · 2nd Year · 3rd Year (Junior Cert)
- ✓By the end of this lesson students will be able to distinguish between transverse and longitudinal waves.
- ✓By the end of this lesson students will be able to define and identify wavelength, frequency, and amplitude of a wave.
- ✓By the end of this lesson students will be able to state the relationship between wave speed, frequency, and wavelength.
- ✓By the end of this lesson students will be able to solve problems involving wave speed, frequency, and wavelength.
- ✓By the end of this lesson students will be able to give examples of transverse and longitudinal waves.
Key concepts
In a transverse wave, the particles of the medium oscillate (vibrate) perpendicular (at right angles) to the direction in which the wave is travelling. Examples include light waves, water waves, and waves on a string.
In a longitudinal wave, the particles of the medium oscillate (vibrate) parallel to the direction in which the wave is travelling. These waves consist of compressions (regions where particles are close together) and rarefactions (regions where particles are spread apart). An example is a sound wave.
The wavelength is the distance between two consecutive corresponding points on a wave. For a transverse wave, this could be from one crest to the next crest, or one trough to the next trough. For a longitudinal wave, it's the distance between two consecutive compressions or rarefactions. It is represented by the Greek letter lambda (λ).
The frequency of a wave is the number of complete waves (or oscillations) that pass a given point per second. The higher the frequency, the more waves pass by each second. It is measured in Hertz (Hz).
The amplitude of a wave is the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium (rest) position. For a transverse wave, it is the height of a crest or the depth of a trough from the undisturbed level. For a longitudinal wave, it relates to the degree of compression or rarefaction.
The speed of a wave is the distance the wave travels per unit time. It depends on the medium through which the wave is travelling. It is related to frequency and wavelength by the wave equation.
Key facts to remember
- 1Waves transfer energy without transferring matter.
- 2Transverse waves have oscillations perpendicular to the direction of wave travel.
- 3Longitudinal waves have oscillations parallel to the direction of wave travel.
- 4Wavelength (λ) is the distance between two identical points on consecutive waves, measured in metres (m).
- 5Frequency (f) is the number of waves passing a point per second, measured in Hertz (Hz).
- 6Amplitude (A) is the maximum displacement from the equilibrium (rest) position.
- 7Wave speed (v) is calculated using the formula: speed = frequency × wavelength (v = fλ).
- 8Light waves are transverse waves; sound waves are longitudinal waves.
Worked examples
Example 1
A sound wave has a frequency of 250 Hz and a wavelength of 1.36 m. Calculate the speed of the sound wave.
Answer
340 m/s
Example 2
Light travels at a speed of 3.0 × 10^8 m/s in a vacuum. If a particular colour of light has a frequency of 5.0 × 10^14 Hz, what is its wavelength?
Answer
6.0 × 10^-7 m
Remember to use standard form (scientific notation) for very large or small numbers, and ensure your calculator is set up correctly for this.
Example 3
Describe the key difference between a transverse wave and a longitudinal wave. Give one example of each type of wave.
Answer
A transverse wave is a wave in which the particles of the medium vibrate perpendicular to the direction of wave propagation. An example of a transverse wave is a light wave or a wave on the surface of water. A longitudinal wave is a wave in which the particles of the medium vibrate parallel to the direction of wave propagation. An example of a longitudinal wave is a sound wave.
Common mistakes
- ✗Confusing the definitions of transverse and longitudinal waves, especially the direction of particle vibration.
- ✗Mixing up the units for frequency (Hz) and wavelength (m) or forgetting to include units in the final answer.
- ✗Incorrectly rearranging the wave equation (v = fλ) when trying to solve for frequency or wavelength.
- ✗Measuring amplitude from the trough to the crest instead of from the equilibrium position to the crest (or trough).
- ✗Assuming all waves require a medium to travel (e.g., light waves can travel through a vacuum, but sound waves cannot).
Exam tips
- ★Always draw a diagram of a wave and label its properties (wavelength, amplitude) to help visualise the concepts.
- ★When solving problems, always write down the formula first, then substitute the values, and finally calculate the answer. This helps in getting marks even if there's a calculation error.
- ★Pay close attention to the units given in the question and ensure your final answer has the correct SI unit.
- ★Practise rearranging the wave equation (v = fλ) to solve for any of the three variables (v, f, or λ).
- ★Learn the precise definitions of all key terms (wavelength, frequency, amplitude, transverse, longitudinal) as they are often asked in short-answer questions.
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