How do you calculate the observed frequency using the Doppler formula?

The observed frequency using the Doppler formula is calculated by multiplying the source frequency by the ratio of the speed of sound to the sum or difference of the speed of sound and the speed of the observer or source.

The Doppler effect is a phenomenon in physics that describes how the frequency of a wave changes for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.

The Doppler formula is used to calculate the observed frequency. The formula is:

f' = f (v + vo) / (v + vs)

where:
- f' is the observed frequency,
- f is the source frequency,
- v is the speed of sound in the medium,
- vo is the speed of the observer relative to the medium (positive if the observer is moving towards the source),
- vs is the speed of the source relative to the medium (positive if the source is moving away from the observer).

If the observer is moving towards the source, the observed frequency increases and if the observer is moving away from the source, the observed frequency decreases. Similarly, if the source is moving towards the observer, the observed frequency increases and if the source is moving away from the observer, the observed frequency decreases.

The Doppler formula allows us to calculate the observed frequency based on the speed of the observer and the source. It's important to note that the speeds of the observer and the source are relative to the medium in which the wave is travelling, not to each other. This formula is a key tool in understanding wave phenomena and has applications in many areas of physics, including acoustics, optics, and astrophysics.