The Doppler Effect

Introduction

• The Doppler effect is a phenomenon that affects all types of waves, including electromagnetic waves (light), sound waves, and even waves in water.
• It occurs when there is relative motion between a wave source and an observer.

The Doppler Effect Explained

• The Doppler effect leads to a change in the observed frequency of waves compared to the frequency of waves emitted by the source.
• This effect can be easily noticed when a vehicle equipped with a siren approaches and moves away from a stationary observer.

Sound of Approaching Vehicle

• When a vehicle, like a fire engine, approaches a stationary observer, the pitch of the siren is perceived as higher.

Sound of Receding Vehicle

• Conversely, when the vehicle moves away from the observer, the pitch of the siren is perceived as lower.

Explanation of Frequency Shift

• The apparent shift in frequency is a result of the relative motion between the vehicle and the observer.
• Imagine the firefighters inside the fire engine; they move at the same velocity as the siren, so there is no relative motion between them. Therefore, they hear the sound at the same frequency at which it is emitted by the siren.
• However, the observer towards whom the fire engine is approaching hears the sound at a higher frequency. This is because as each complete sound wave is emitted, the distance between the source (siren) and the observer decreases. Consequently, the waves arrive at the observer more frequently.
• On the other hand, the observer from whom the fire engine is receding hears the sound at a lower frequency.

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The Doppler Effect

Formula for Doppler Effect

• The Doppler effect can be mathematically described using the following formula:
• f' = f (v + vo) / (v - vs)
• Where:
  • f' is the observed frequency.
  • f is the frequency of the source.
  • v is the velocity of waves in the medium (e.g., speed of sound).
  • vo is the velocity of the observer relative to the medium.
  • vs is the velocity of the source relative to the medium.

Summary

• The Doppler effect is a phenomenon that occurs when there is relative motion between a wave source and an observer, resulting in a shift in the observed frequency of waves.
• It is commonly experienced with sirens from approaching and receding vehicles, where the pitch of the sound appears to change.
• The effect can be mathematically described using the Doppler effect formula, which considers the velocities of the wave source, observer, and the medium through which the waves travel.