The Doppler Effect is the apparent change in a wave's frequency resulting from the relative velocity between the source of the waves and the observer. Although the Doppler Effect is generally associated with sound waves, it is applicable to any type of wave. As a rule of thumb, if the distance between the source and the observer decreases, the apparent frequency (called "f prime" or f') is higher than the actual, real frequency of the source.
Case 1: Observer moving.
If the observer is moving but the source is stationary, the apparent frequency change is evidenced directly and can be calculated with the formula: Δf / f = v / v_{w} where
- Δf is the apparent change in frequency,
- f is the original frequency,
- v is the velocity of the observer with respect to the stationary source,
- v
_{w} is the speed of the wave.
To calculate the final frequency the observer records you would use the relationships:
- when the observer approaches a wave source: f ' = f + Δf --- a higher frequency
- when the observer recedes from a wave source: f ' = f - Δf --- a lower frequency
Remember that the actual frequency of the source remains unchanged and that this apparent change in frequency is due to the relative velocity between the source and the observer. Also remember that it is the frequency that is manipulated mathematically when the observer is moving either towards or away from the source.
An analogy. Suppose that you are a parent watching your child play at the beach. If the child stands still in the shallow water, you note that one wave reaches your child's position each second. However, suppose that the child decides to "rush out to meet" the waves. The child will encounter the waves more frequently as he rushes out towards the deeper water. Instead of one wave reaching him each second, he might meet two or three each second. Conversely, if the child "runs away from the waves" back into the shore, instead of one wave reaching him every second, a wave might only reach him once every 1.5 to 2 seconds. The child can change the "apparent frequency" of the oncoming waves through his motions. How much the frequency changes depends on the child's relative speed. |