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Waves and the Doppler Effect: Understanding Frequency Shifts in A-Level Science
What Is the Doppler Effect?
The Doppler Effect describes the perceived change in frequency when there is relative motion between a wave source and observer.
Key Equations
Sound Waves (Classical Doppler Effect)
![\[ f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right) \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-216a8132ab2a39391cdf12b0cac4181e_l3.png "Rendered by QuickLaTeX.com")
Where:
: Observed frequency (Hz)
: Source frequency (Hz)
: Wave speed (340 m/s for sound in air)
: Observer’s velocity (+ if moving toward source)
: Source’s velocity (+ if moving toward observer)
: Observed frequency (Hz)
: Source frequency (Hz)
: Wave speed (340 m/s for sound in air)
: Observer’s velocity (+ if moving toward source)
: Source’s velocity (+ if moving toward observer)Light Waves (Relativistic Doppler Effect)
![\[ \frac{\Delta \lambda}{\lambda} = \frac{v}{c} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-4d6360493308eb90adb8b2e2be27387b_l3.png "Rendered by QuickLaTeX.com")
Where:
: Original wavelength
: Observed wavelength shift
: Speed of light
: Original wavelength
: Observed wavelength shift
: Speed of lightApplications
Everyday Phenomena
- Emergency vehicle sirens: Pitch drops as vehicle passes
- Weather radar: Measures precipitation velocity
Astronomy
- Redshift (
): Indicates cosmic expansion - Blueshift: Reveals approaching celestial objects
): Indicates cosmic expansionMedical Technology
- Doppler echocardiography: Measures blood flow up to 5 m/s
- Fetal heart rate monitoring
Example Problem
Scenario: Train (30 m/s) approaches observer, emitting 500 Hz sound (v = 340 m/s).
- Identify formula: Source moving toward observer
- Calculate:
![\[ f' = f \left( \frac{v}{v - v_s} \right) \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-ee0d61e0e5edb3299ecad451991c3911_l3.png "Rendered by QuickLaTeX.com")
![\[ f' = 500 \left( \frac{340}{340 - 30} \right) \approx 548.4 \, \text{Hz} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-21b090afa95373538e455f41e41ef05b_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes
- Sign errors in velocity terms
- Using sound speed for light waves
- Neglecting relativistic effects when
Practice Problems
- Calculate the observed frequency when a car (20 m/s) emitting 400 Hz approaches a stationary observer.
- Derive the redshift formula
for 
. - Explain how Doppler ultrasound measures valve stenosis.
for 
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