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Waves

The wave equation

  • 3 things to know
  • Unit AS 2

Overview

Wave equation and define each symbol, why the wave speed equals frequency multiplied by wavelength and speed of every electromagnetic wave in a vacuum.

What you need to know

Answer each one before you reveal it.

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Key term

State the wave equation and define each symbol.

Numbers

A note of frequency 256 Hz travels through air at 340 m s⁻¹. Calculate its wavelength.

Numbers

A radio station broadcasts at 100 MHz. Calculate the wavelength of the transmission.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the wave equation and define each symbol.

    Model answer

    v = fλ, where v is the wave speed in m s⁻¹, f is the frequency in Hz and λ is the wavelength in metres.

  2. 2

    Explain why the wave speed equals frequency multiplied by wavelength.

    Model answer

    In one period the wave advances exactly one wavelength, so v = λ/T, and since f = 1/T this becomes v = fλ.

  3. 3

    A note of frequency 256 Hz travels through air at 340 m s⁻¹. Calculate its wavelength.

    Model answer

    λ = v/f = 340/256 = 1.33 m, and 256 Hz × 1.33 m returns 340 m s⁻¹ as given.

  4. 4

    A radio station broadcasts at 100 MHz. Calculate the wavelength of the transmission.

    Model answer

    λ = c/f = 3.00 × 10⁸ / 1.00 × 10⁸ = 3.00 m, and 1.00 × 10⁸ Hz × 3.00 m returns 3.00 × 10⁸ m s⁻¹ as required.

  5. 5

    Calculate the frequency of light of wavelength 600 nm in a vacuum.

    Model answer

    f = c/λ = 3.00 × 10⁸ / 6.00 × 10⁻⁷ = 5.00 × 10¹⁴ Hz, and 5.00 × 10¹⁴ Hz × 6.00 × 10⁻⁷ m returns 3.00 × 10⁸ m s⁻¹.

  6. 6

    Water waves of frequency 2.0 Hz have a wavelength of 0.75 m. Calculate their speed.

    Model answer

    v = fλ = 2.0 × 0.75 = 1.5 m s⁻¹, and 1.5 m s⁻¹ ÷ 2.0 Hz returns the 0.75 m wavelength given.

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