Waves & The Electromagnetic Spectrum

The basic equation

v = f × λ

• where:
  • v = wave speed (m/s)
  • f = frequency (Hz)
  • λ = wavelength (m)
• The equation applies to every kind of wave, including sound, water ripples, and every band of the electromagnetic spectrum
• Rearrangements:
  • λ = v / f (a higher-frequency wave has a shorter wavelength at fixed speed)
  • f = v / λ

Linking frequency to period

f = 1 / T

• When a question gives you the period rather than the frequency, find f first, then use the wave equation

Examples

Example A — a sound wave in air travels at 340 m/s. A concert orchestra plays an A note at a frequency of 440 Hz. Find the wavelength of the sound.

• Use λ = v / f
• λ = 340 / 440 = 0.77 m (to 2 s.f.)

Example B — a local radio station transmits at 1.5 MHz. Radio waves travel through the air at 3.0 × 10⁸ m/s. Find the wavelength of the broadcast.

• Convert the frequency: 1.5 MHz = 1.5 × 10⁶ Hz
• λ = v / f = (3.0 × 10⁸) / (1.5 × 10⁶) = 200 m

Example C — a violet light wave has a frequency of 7.5 × 10¹⁴ Hz. Find the period of one complete oscillation.

• T = 1 / f = 1 / (7.5 × 10¹⁴) = 1.33 × 10⁻¹⁵ s