OCR · A-Level · Physics

    Course version: H556 · Version from Sept 2015

    (f) Doppler equation f f c v T T . . m m for a source of electromagnetic…

    Full specification wording

    Cosmology: (f) Doppler equation f f c v T T . . m m for a source of electromagnetic radiation moving relative to an observer

    The Doppler equation for electromagnetic radiation relates the fractional change in wavelength or frequency to the relative speed of the source and observer.

    Checked against the OCR H556 specification (opens in a new tab) on .

    • Point 8 of 17
    • 2 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    The Doppler equation for electromagnetic radiation relates the fractional change in wavelength or frequency to the relative speed of the source and observer. It is expressed as \(\frac{\Delta \lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}\), where \(\Delta \lambda\) is the change in wavelength, \(\lambda\) is the emitted wavelength, \(\Delta f\) is the change in frequency, \(f\) is the emitted frequency, \(v\) is the relative speed along the line of sight, and \(c\) is the speed of light. This approximation is valid for speeds much less than \(c\) (\(v \ll c\)). For a receding source, the observed wavelength increases (red-shift) and frequency decreases. For an approaching source, wavelength decreases (blue-shift) and frequency increases. You must be able to calculate \(v\), \(\Delta \lambda\), or \(\Delta f\) using this relationship.

    What earns the marks

    • State and apply the Doppler equation \(\frac{\Delta \lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}\) for electromagnetic radiation.
    • Identify \(\Delta \lambda\) and \(\Delta f\) as the shift in wavelength and frequency, respectively, relative to the emitted values \(\lambda\) and \(f\).
    • Recognise that this equation is an approximation valid only when the relative speed \(v\) is much less than the speed of light \(c\).
    • Determine whether a shift corresponds to approach (blue-shift, frequency increases) or recession (red-shift, wavelength increases).

    Common mistakes and how to put them right

    • Using the observed wavelength or frequency in the denominator instead of the emitted (laboratory) values.

      Put it right: Divide the shift by the original emitted value.

    • Forgetting to calculate the shift (\(\Delta \lambda\) or \(\Delta f\)) and substituting the absolute observed value into the numerator.

      Put it right: Subtract the emitted value from the observed value to find the shift first.

    • Applying the equation to objects moving at relativistic speeds (close to \(c\)).

      Put it right: This form is an approximation for \(v \ll c\).

    Exam tips

    • When given observed and laboratory wavelengths, calculate \(\Delta \lambda\) before substituting into the equation.
    • Ensure units for \(v\) and \(c\) are consistent, typically both in \(\text{m s}^{-1}\).
    • Remember that a positive \(\Delta \lambda\) (red-shift) indicates the source is moving away from the observer.

    Try the lesson

    The start of the Cosmology: (f) Doppler equation f f c v T T . . m m for a source of electromagnetic radiation moving relative to an observer lesson, made from checked teaching notes for this specification point.

    Listen

    The Doppler equation for electromagnetic radiation relates the fractional change in wavelength or frequency to the relative speed of the source and observer. It is expressed as \(\frac{\Delta \lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}\), where \(\Delta \lambda\) is the change in wavelength, \(\lambda\) is the emitted wavelength, \(\Delta f\) is the change in frequency, \(f\) is the emitted frequency, \(v\) is the relative speed along the line of sight, and \(c\) is the speed of light. This approximation is valid for speeds much less than \(c\) (\(v \ll c\)). For a receding source, the observed wavelength increases (red-shift) and frequency decreases. For an approaching source, wavelength decreases (blue-shift) and frequency increases. You must be able to calculate \(v\), \(\Delta \lambda\), or \(\Delta f\) using this relationship. A strong answer earns marks for these points. State and apply the Doppler equation \(\frac{\Delta \lambda}{\lambda} \approx \frac{\Delta f}{f} \approx \frac{v}{c}\) for electromagnetic radiation. Identify \(\Delta \lambda\) and \(\Delta f\) as the shift in wavelength and frequency, respectively, relative to the emitted values \(\lambda\) and \(f\). Recognise that this equation is an approximation valid only when the relative speed \(v\) is much less than the speed of light \(c\). Determine whether a shift corresponds to approach (blue-shift, frequency increases) or recession (red-shift, wavelength increases). A common slip: Using the observed wavelength or frequency in the denominator instead of the emitted (laboratory) values. Instead, divide the shift by the original emitted value. Exam tip: When given observed and laboratory wavelengths, calculate \(\Delta \lambda\) before substituting into the equation.

    See it

    A flowchart starting from a node labelled with the Doppler equation Δλ/λ ≈ Δf/f ≈ v/c. One branch leads to a node stating it is valid only when v ≪ c. Another branch leads to a node for a source moving relative to an observer, which splits into two: a receding source, which leads to wavelength increases (red-shift) and frequency decreases; and an approaching source, which leads to wavelength decreases (blue-shift) and frequency increases.
    It shows the Doppler equation for electromagnetic radiation, its validity condition, and how recession and approach affect wavelength and frequency.

    Key words

    Say what each word means before you turn the card.

    Red-shift and blue-shift

    Try answering aloud or in your head before turning the card.

    Relative motion

    Try answering aloud or in your head before turning the card.

    See every definition
    Red-shift and blue-shift
    For a receding source the observed wavelength increases and frequency decreases, while for an approaching source the wavelength decreases and frequency increases.
    Relative motion
    Movement of a source of electromagnetic radiation relative to an observer, with the relative speed taken along the line of sight.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A flowchart starting from a node labelled with the Doppler equation Δλ/λ ≈ Δf/f ≈ v/c. One branch leads to a node stating it is valid only when v ≪ c. Another branch leads to a node for a source moving relative to an observer, which splits into two: a receding source, which leads to wavelength increases (red-shift) and frequency decreases; and an approaching source, which leads to wavelength decreases (blue-shift) and frequency increases.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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