Lecture notes Unit 2 PHYA2 - Mechanics, Materials and Waves (7408)

A-Level Physics: Waves Revision Notes

1. What is a Wave?

A wave is a disturbance that transfers energy from one place to another without the
transfer of matter. Waves can be classified into two types: mechanical and
electromagnetic.

 Mechanical Waves: Require a medium (solid, liquid, or gas) to travel through.
Examples include sound waves, water waves, and seismic waves.
 Electromagnetic Waves: Do not require a medium and can travel through a
vacuum. Examples include light, radio waves, and X-rays.



2. Properties of Waves

The basic properties that describe a wave are:

 Wavelength (λ): The distance between two consecutive points in phase (e.g.,
crest to crest, trough to trough) in a wave. Measured in meters (m).
 Amplitude (A): The maximum displacement of a point on the wave from its
equilibrium position. It is related to the energy of the wave.
 Frequency (f): The number of complete oscillations or cycles per second.
Measured in Hertz (Hz).
 Period (T): The time taken for one complete cycle of the wave. Period is the
inverse of frequency: T=1fT = \frac{1}{f}T=f1
 Speed (v): The rate at which the wave propagates through the medium. It can
be calculated using: v=f×λv = f \times \lambdav=f×λ



3. Types of Waves

 Transverse Waves: In these waves, the oscillations are perpendicular to the
direction of energy transfer. Examples: Light waves, water waves, and
seismic S-waves.
o Characteristics: The oscillations move up and down while the wave
propagates horizontally.
o Equation: For a wave travelling along the x-axis:
y(x,t)=Asin⁡(kx−ωt)y(x,t) = A \sin(kx - \omega t)y(x,t)=Asin(kx−ωt)
where kkk is the wave number and ω\omegaω is the angular
frequency.

,  Longitudinal Waves: In these waves, the oscillations are parallel to the
direction of energy transfer. Examples: Sound waves, seismic P-waves.
o Characteristics: The wave involves compressions and rarefactions.
o Equation: For a wave travelling along the x-axis:
ΔP(x,t)=P0cos⁡(kx−ωt)\Delta P(x,t) = P_0 \cos(kx - \omega
t)ΔP(x,t)=P0 cos(kx−ωt) where P0P_0P0 is the maximum pressure
variation.



4. Wave Behavior

 Reflection: When a wave strikes a boundary and bounces back. If the wave
hits the boundary at an angle, the angle of incidence equals the angle of
reflection.
 Refraction: The bending of waves when they pass from one medium to
another. This is described by Snell's Law:
sin⁡(θ1)sin⁡(θ2)=v1v2=n2n1\frac{\sin(\theta_1)}{\sin(\theta_2)} =
\frac{v_1}{v_2} = \frac{n_2}{n_1}sin(θ2 )sin(θ1 ) =v2 v1 =n1 n2 where nnn is
the refractive index, and vvv is the wave speed in the respective medium.
 Diffraction: The spreading of waves as they pass through a gap or around an
obstacle. The extent of diffraction depends on the wavelength and the size of
the gap.
 Interference: When two waves meet and combine. The principle of
superposition states that the resulting displacement is the sum of the
displacements of the individual waves.
o Constructive Interference: When two waves are in phase and
combine to form a larger wave.
o Destructive Interference: When two waves are out of phase and
cancel each other out.



5. The Wave Equation

The general wave equation is given by:

y(x,t)=Asin⁡(kx−ωt)y(x,t) = A \sin(kx - \omega t)y(x,t)=Asin(kx−ωt)

Where:

 y(x,t)y(x,t)y(x,t) is the displacement of the wave at position xxx and time ttt.
 AAA is the amplitude of the wave.
 k=2πλk = \frac{2\pi}{\lambda}k=λ2π is the wave number.
 ω=2πf\omega = 2\pi fω=2πf is the angular frequency.