The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave. It occurs with all types of waves, including sound and electromagnetic waves (like light).
When the source and observer are moving closer together, the observed frequency increases (higher pitch). When they are moving apart, the observed frequency decreases (lower pitch).
The general Doppler Effect formula (for sound in air) is:
\[ f' = f \cdot \frac{v \pm v_o}{v \mp v_s} \]
Important: Use the upper sign when the object is moving toward and the lower sign when moving away. Be consistent with signs!
In the case of light, a similar effect occurs, but the formulas differ due to the constancy of the speed of light and relativistic effects.
The Doppler Effect is a powerful tool in both classical physics and modern astrophysics, providing insight into the motion of distant objects and systems.
A person is running toward a stationary sound source emitting a frequency of \( 500 \ \text{Hz} \). The speed of sound in air is \( 340 \ \text{m/s} \), and the observer runs at \( 10 \ \text{m/s} \). What is the frequency heard by the observer?
\[ f' = f \cdot \frac{v + v_o}{v} = 500 \cdot \frac{340 + 10}{340} = 500 \cdot \frac{350}{340} \approx 514.7 \ \text{Hz} \]
Answer: The observer hears a frequency of approximately \( 514.7 \ \text{Hz} \).
An ambulance moves toward a stationary listener at \( 20 \ \text{m/s} \), emitting a siren sound of frequency \( 600 \ \text{Hz} \). Find the frequency heard by the listener. Use the speed of sound as \( 340 \ \text{m/s} \).
\[ f' = f \cdot \frac{v}{v - v_s} = 600 \cdot \frac{340}{340 - 20} = 600 \cdot \frac{340}{320} = 600 \cdot 1.0625 = 637.5 \ \text{Hz} \]
Answer: The listener hears a frequency of \( 637.5 \ \text{Hz} \).
Written by Thenura Dilruk