Waves

7.1 Progressive waves:

7.1.1 Wave motion:

• Wave motion is the transfer of energy through a medium without the physical transfer of matter. Examples include vibrations in ropes, springs, and ripple tanks.

7.1.2 Terms related to waves:

• Displacement: The distance and direction of a point on a wave from its equilibrium position.
• Amplitude: The maximum displacement of a wave from its equilibrium position.
• Phase difference: The difference in phase between two points on a wave.
• Period: The time taken for one complete oscillation or cycle of a wave.
• Frequency: The number of complete oscillations or cycles of a wave per unit time.
• Wavelength: The distance between two consecutive points in phase on a wave.
• Speed: The rate at which a wave propagates through a medium.
• The wave equation: v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.

7.1.3 Energy and intensity of progressive waves:

• Energy is transferred by a progressive wave as it propagates through a medium.
• Intensity is the power per unit area carried by a wave and is given by intensity = power/area.
• Intensity is proportional to the square of the amplitude of the wave (intensity ∝ amplitude²).

7.2 Transverse and longitudinal waves:

• Transverse waves: The displacement of the medium is perpendicular to the direction of wave propagation.
• Longitudinal waves: The displacement of the medium is parallel to the direction of wave propagation.

7.3 Doppler effect for sound waves:

• The Doppler effect describes the change in frequency observed when a source of sound waves moves relative to a stationary observer.
• The observed frequency (f_o) is given by f_o = f_s(v / (v ± v_s)), where fs is the source frequency, v is the speed of sound, and vs is the speed of the source relative to the observer.

7.4 Electromagnetic spectrum:

• The electromagnetic spectrum includes all electromagnetic waves, which are transverse waves that travel at the speed of light "c" in free space.
• The spectrum ranges from radio waves (long wavelength, low frequency) to gamma rays (short wavelength, high frequency).
• Visible light falls within the wavelength range of approximately 400-700nm.

7.5 Polarisation:

• Polarisation is a phenomenon associated with transverse waves.
• Malus's law (I = I₀ cos² θ) describes the intensity of a plane-polarised electromagnetic wave after transmission through one or more polarising filters, where I₀ is the initial intensity and θ is the angle between the transmission axis of the filter(s) and the direction of polarisation.