Lesson Notes By Weeks and Term v5 - Grade 12
Waves, Sound and Light: Doppler Effect – Week 10 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Waves, Sound and Light: Doppler Effect – Week 10 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Physical Sciences
Class: Grade 12
Term: 1st Term
Week: 10
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
The Doppler effect is a fundamental phenomenon in physics that describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It's not just an abstract scientific concept; it's all around us! For instance, consider an ambulance speeding past you with its siren blaring. The siren sounds higher-pitched as it approaches you and lower-pitched as it moves away. This is the Doppler effect in action.
2. 1. What is the Doppler Effect? The Doppler effect is the change in frequency (or wavelength) of a wave in relation to an observer who is moving relative to the wave source. It occurs because the motion of the source alters the way the waves are perceived by the observer.
Think of it like this: if a source of waves is moving toward you, each successive wave crest is emitted from a position closer to you than the previous one. This causes the waves to arrive closer together, increasing the frequency (and decreasing the wavelength). Conversely, if the source is moving away from you, the wave crests are emitted from positions further apart, decreasing the frequency (and increasing the wavelength). 2.
2. The Doppler Effect for Sound For sound waves, the Doppler effect is described by the following equation: f L = f S * (v ± v L ) / (v ± v S )
Where: f L = Observed frequency (frequency heard by the listener) f S = Emitted frequency (frequency produced by the source) v = Speed of sound in the medium (approximately 343 m/s in air at room temperature) v L = Speed of the listener (observer) relative to the medium v S = Speed of the source relative to the medium Sign Conventions are CRUCIAL: Use "+" in the numerator (v ± v L ) if the listener is moving towards the source. Use "-" if the listener is moving away from the source. Use "-" in the denominator (v ± v S ) if the source is moving towards the listener. Use "+" if the source is moving away from the listener. 2.
3. The Doppler Effect for Light For light waves, the Doppler effect is described by the following equation (for non-relativistic speeds): Δλ / λ ≈ v / c Where: Δλ = Change in wavelength (observed wavelength – emitted wavelength) λ = Emitted wavelength v = Relative velocity between the source and the observer c = Speed of light (approximately 3 x 10 8 m/s) A positive Δλ indicates a redshift (longer wavelength, moving away), and a negative Δλ indicates a blueshift (shorter wavelength, moving towards). For more accurate calculations, especially when velocities approach the speed of light, the relativistic Doppler effect equation should be used.
However, for Grade 12 purposes, the non-relativistic approximation is usually sufficient unless otherwise stated. 2.4 Worked
Examples: Example 1: Sound - Ambulance Siren An ambulance is traveling at 30 m/s with its siren emitting a sound at a frequency of 800 Hz. You are standing still on the side of the road. What frequency do you hear as the ambulance approaches and after it passes? (Assume the speed of sound is 343 m/s).
Approaching: f L = f S * (v + v L ) / (v - v S ) (Listener stationary, Source moving towards) f L = 800 Hz * (343 m/s + 0 m/s) / (343 m/s - 30 m/s) f L = 800 Hz * (343 m/s) / (313 m/s) f L ≈ 875.4 Hz Receding: f L = f S * (v + v L ) / (v + v S ) (Listener stationary, Source moving away) f L = 800 Hz * (343 m/s + 0 m/s) / (343 m/s + 30 m/s) f L = 800 Hz * (343 m/s) / (373 m/s) f L ≈ 734.6 Hz You hear a higher frequency (875.4 Hz) as the ambulance approaches and a lower frequency (734.6 Hz) as it moves away. This demonstrates the Doppler effect clearly.
Example 2: Sound - Moving Listener A train emits a whistle at a frequency of 500 Hz. You are standing on the platform and the train is approaching you at 20 m/s. You then start running towards the train at 5 m/s. What frequency do you hear? (Assume the speed of sound is 343 m/s). f L = f S * (v + v L ) / (v - v S ) (Listener moving towards, Source moving towards) f L = 500 Hz * (343 m/s + 5 m/s) / (343 m/s - 20 m/s) f L = 500 Hz * (348 m/s) / (323 m/s) f L ≈ 538.7 Hz Example 3: Light - Redshift A distant galaxy emits light with a wavelength of 650 nm. The observed wavelength on Earth is 680 nm. Calculate the galaxy's velocity relative to Earth. Δλ = 680 nm - 650 nm = 30 nm λ = 650 nm v / c ≈ Δλ / λ v ≈ c * (Δλ / λ) v ≈ (3 x 10 8 m/s) * (30 nm / 650 nm) v ≈ (3 x 10 8 m/s) * (30 / 650) v ≈ 1.38 x 10 7 m/s The positive value indicates a redshift, meaning the galaxy is moving away from Earth at approximately 1.38 x 10 7 m/s. Guided Practice (With Solutions)
Question 1: A car is traveling at 25 m/s towards a stationary observer. The car's horn emits a frequency of 440 Hz. What frequency does the observer hear? (Assume the speed of sound is 343 m/s).
Solution: f L = f S * (v + v L ) / (v - v S ) f L = 440 Hz * (343 m/s + 0 m/s) / (343 m/s - 25 m/s) f L = 440 Hz * (343 m/s) / (318 m/s) f L ≈ 474.8 Hz
Commentary: This is a straightforward application of the Doppler effect equation for sound. The observer is stationary (v L = 0), and the source is moving towards the observer, so we use a minus sign in the denominator.
Question 2: A train is moving away from a station at 35 m/s. A person standing on the train platform hears the train whistle at a frequency of 320 Hz. What is the actual frequency of the whistle? (Assume the speed of sound is 343 m/s).