Progressive and stationary waves revision notes

Progressive Waves

Key Definitions

• Wavelength (λ): The distance between successive crests or troughs of a wave, measured in meters (m).
• Frequency (f): The number of complete waves passing a point per second, measured in hertz (Hz).
• Period (T): The time taken for one complete wave to pass a point, measured in seconds (s). It is the inverse of frequency: T = 1/f.
• Amplitude (A): The maximum displacement of points on a wave from their rest position, measured in meters (m).
• Phase: The position of a point in time on a waveform, often measured in degrees or radians.

Wave Speed Equation

The speed of a wave (v) can be calculated using the equation:

v = f × λ

Where:

• v = wave speed (m/s)
• f = frequency (Hz)
• λ = wavelength (m)

Displacement-Time and Displacement-Distance Graphs

• Displacement-Time Graphs: Show how the displacement of a wave varies with time at a fixed point. The slope of the graph indicates the wave's speed.
• Displacement-Distance Graphs: Illustrate how displacement varies along the length of the wave at a fixed time. The distance between successive crests represents the wavelength.

Energy Transfer by Progressive Waves

Progressive waves transfer energy from one point to another without the transfer of matter. The energy carried by a wave is proportional to the square of its amplitude. Higher amplitude waves carry more energy.

Longitudinal and Transverse Waves

Distinguishing Wave Types

• Longitudinal Waves: The oscillation of particles is parallel to the direction of wave travel. Examples include sound waves.
• Transverse Waves: The oscillation of particles is perpendicular to the direction of wave travel. Examples include light waves and waves on strings.

Compressions and Rarefactions in Longitudinal Waves

• Compressions: Regions where particles are close together, resulting in higher pressure.
• Rarefactions: Regions where particles are spread apart, resulting in lower pressure.

Polarisation Evidence for Transverse Waves

Polarisation is the phenomenon where waves oscillate in a particular direction. It is only possible with transverse waves, providing evidence that light is a transverse wave.

Superposition and Stationary Waves

Principle of Superposition

The principle of superposition states that when two or more waves overlap, the resultant displacement at any point is the sum of the displacements of the individual waves.

Formation of Stationary Waves

Stationary waves are formed when two progressive waves of the same frequency and amplitude travel in opposite directions. This results in a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement).

Identifying Nodes, Antinodes, and Harmonics

• Nodes: Points on a stationary wave where there is no movement.
• Antinodes: Points where the displacement is maximum.
• Harmonics: The frequencies at which standing waves can form, with the fundamental frequency being the lowest.

Required Practical: Investigating Stationary Waves

In this practical, students investigate how string length, tension, and mass per unit length affect the formation of stationary waves. Key observations include:

• Increasing tension increases the frequency of the stationary wave.
• Longer strings produce lower frequency stationary waves.
• Mass per unit length affects the wave speed and frequency.

Conclusion

Understanding progressive and stationary waves is crucial in various fields of physics, including optics, sound, and quantum physics. Mastery of these concepts allows for a deeper comprehension of wave behavior and applications in real-world scenarios.

Wave reasoning for AQA A-Level Physics

When revising waves, keep the physical quantities separate. Frequency counts oscillations per second, wavelength measures one complete spatial cycle, amplitude shows maximum displacement, and wave speed links frequency and wavelength. In exam answers, define the quantity first, then explain how it changes in the situation described.

For interference, diffraction and stationary-wave questions, focus on path difference, phase difference, nodes, antinodes and boundary conditions. Do not simply say that waves overlap; explain whether the superposition is constructive or destructive and connect that to the observable pattern. For optical questions, distinguish refraction, reflection, total internal reflection and diffraction because they depend on different physical conditions.

For practical or graph-based questions, identify what is measured directly and what is calculated. Quote units carefully, show substitutions when equations are used, and finish with a sentence linking the result back to the wave phenomenon in the question.