# The Doppler Effect

## Key Formula

 fo observed frequency Hz fs frequency of source Hz v speed of sound m/s vo velocity of observer m/s vs velocity of source m/s

## Tips to Remember

• In this formula, the key to success is following the sign conventions. The direction that the sound travels is always the positive direction; set the other velocities accordingly. For example, consider a problem in which a person and a barking dog run toward each other as shown at the right. The sound travels to the left, so everything moving left must have positive velocity, and vice versa. Therefore v is positive (as always); vo is negative since the human obersever is moving right, and vs is positive because the dog (the sound source) is running left.
• It’s always a good idea to make sure your answers make sense. Remember that when the source and observer are getting closer together, you expect the frequency to increase, i.e., fo > fs . Conversely, when the source recedes from the observer, expect a decreasing frequency, or fo < fs.