Observed Frequency Calculator

Formula

The formula to calculate the observed frequency (f') is:

\[ f' = f \left(\frac{v + vo}{v - vs}\right) \]

Where:

\( f' \) is the observed frequency (Hz)
\( f \) is the source frequency (Hz)
\( v \) is the speed of sound in the medium (m/s)
\( vo \) is the observer speed (m/s)
\( vs \) is the actual speed of the source (m/s)

Definitions

Observed Frequency: The frequency of a wave, such as sound or light, as detected by an observer. It is affected by the relative motion between the source of the wave and the observer, a phenomenon known as the Doppler effect.

Example

Let's say the source frequency (f) is 500 Hz, the speed of sound (v) is 343 m/s, the observer speed (vo) is 10 m/s, and the source speed (vs) is 20 m/s. Using the formula:

\[ f' = 500 \left(\frac{343 + 10}{343 - 20}\right) \]

We get:

\[ f' \approx 546.44 \, \text{Hz} \]

So, the observed frequency is approximately 546.44 Hz.