Waves and Wave Properties - Quick Reference

Basic Wave Concepts

• Waves transfer energy from one place to another; most require a medium, except electromagnetic (EM) waves which can travel in a vacuum.
• A pulse is a short section of a wave.

Wave Types

• Longitudinal: particles move parallel to the direction of wave travel (e.g. sound).
• Transverse: particles move perpendicular to the direction of wave travel (e.g. water waves).

Wave Parameters

• Wavelength, $\lambda$: distance from crest to crest (one complete wave).
• Frequency, $f$: waves per second (Hz).
• Time period, $T$: time for one complete wave to pass.
• Amplitude, $A$: maximum displacement (height).
• Speed, $v$: how fast the wave travels.
• Core relation: $v = f\lambda$
• Inverse relations: $\lambda = \dfrac{v}{f}, \quad T = \dfrac{1}{f}$

Electromagnetic Waves

• EM waves travel at the speed of light in vacuum: $c = 3.0 \times 10^{8}\ \text{m s}^{-1}$.
• All EM waves are transverse and can travel through vacuum.
• Visible light: red has longer wavelength and lower frequency; blue has shorter wavelength and higher frequency.
• Light is shown to be transverse using polarising lenses.

Wavelengths of Radio and Light

• For FM radio, $f = 91.3\ \text{MHz}$; wavelength $\lambda = \dfrac{c}{f} \approx \dfrac{3.0\times10^{8}}{91.3\times10^{6}} \approx 3.29\ \text{m}$.
• Similar calculation for other stations (e.g. 93.4 MHz) yields around $3.21\ \text{m}$.
• AM wavelengths are much longer (e.g. hundreds of metres) than FM wavelengths.

Sound and Hearing

• Audible range: approximately $40\ \text{Hz}$ to $20\ \text{kHz}$.
• Speed of sound in air: about $v \approx 330\ \text{m s}^{-1}$.
• Corresponding wavelengths:
  • $\lambda<em>{\text{min}} = \dfrac{v}{f</em>{\text{max}}} = \dfrac{330}{20000} = 0.0165\ \text{m}$
  • $\lambda<em>{\text{max}} = \dfrac{v}{f</em>{\text{min}}} = \dfrac{330}{40} = 8.25\ \text{m}$

Reflection

• Law: angle of incidence equals angle of reflection with respect to the normal.

Diffraction

• Diffraction explains how waves bend around obstacles and through gaps; signals can be detected despite obstacles.
• Longer wavelengths diffract more than shorter wavelengths.
• Maximum diffraction occurs when the gap size is comparable to the wavelength; little diffraction when the gap is much larger; almost all waves are reflected when the gap is smaller than the wavelength.
• AM (longer wavelength) diffracts more around hills/obstacles than FM (shorter wavelength).

Electromagnetic Spectrum (Key Points)

• All EM waves share: speed ~$c = 3.0\times10^{8}\ \text{m s}^{-1}$, travel in vacuum, and are transverse.
• Our eyes see only a small portion of the spectrum; red light has longer wavelength than blue light; blue light has higher frequency.
• Diffraction can be demonstrated with polarisation and diffraction experiments (e.g., around obstacles, through gaps).

Quick Reference Equations

• $v = f\lambda$
• $\lambda = \dfrac{v}{f}$
• $T = \dfrac{1}{f}$
• $c = 3.0\times10^{8}\ \text{m s}^{-1}$
• For EM waves: $v = c$; for radio/light waves, use $\lambda = \dfrac{c}{f}$

Review Tips

• If given frequency, find wavelength using $\lambda = \dfrac{c}{f}$; if given wavelength, find frequency with $f = \dfrac{c}{\lambda}$.
• To assess diffraction potential, compare gap size to wavelength: similar sizes yield maximum diffraction; much larger gap yields little diffraction.
• Remember the audible range and corresponding wavelengths to intuit which sounds diffract more around barriers.