1. Wave Interference: Beats

2. Beats
Previously we considered two interfering waves with the same w. Now consider two different frequencies.
When waves of two slightly different frequencies arrive at a point, a detector (ear?) at that point is subjected to two different sinusoidal signals. The superposition of those two signals produces “beats”.

3. Beat frequency

4. What we perceive T
Tbeat

5. Doppler (frequency) shift
When the source and receiver are in relative motion, wave fronts get compressed or stretched in time.
Doppler link

6. Doppler shift for moving source
If the detector and medium are stationary,
What do the signs tell us?
v is the speed of wave (343 m/s for sound in air),
vs is the speed of the source,
f is the frequency of the wave as emitted and
f ’ is the detected (Doppler Shifted ) frequency.

7. Doppler shift for moving detector
If the source and medium are stationary,
v is the speed of wave (343 m/s for sound in air),
vD is the speed of the detector,
f is the frequency of the wave as emitted and
f’ is the detected (Doppler Shifted ) frequency.

8. Putting source and detector motion into one equation
We can combine these if we measure everything in a fixed medium.
D Toward
D Away
S Toward
S Away

9. Radar Guns: Detecting Doppler shift
Police radar uses electromagnetic waves (v=3x108 m/s), therefore the relative change in frequency due to reflection from an object travelling (100 m/s) is small.
The best way to detect the difference between the emitted and reflected waves is to add them together in your detector and observe the beats.