The Doppler effect
All waves (electromagnetic, sound, even waves in water) are subject to the Doppler effect. The effect occurs when there is relative motion between the wave source and an observer.
The effect causes the observed frequency of waves to be different to the frequency of waves given out by the source.
The Doppler effect can be noticed when a vehicle with a siren approaches and moves away from a stationary observer.
If a fire engine passes us we notice the pitch of the siren to be higher coming towards us and lower going away from us.
The apparent shift in frequency is due to the relative motion of the fire engine to the observer:
- The firefighters are moving at the same velocity as the siren. There is no relative motion so they observe the sound at the same frequency as it is emitted by the siren.
- The observer the fire engine is moving towards hears the sound at a higher frequency than it is emitted at. As each complete sound wave is emitted, the distance has decreased between the source and observer. As a result the waves arrive at the observer more frequently.
- The observer the fire engine is moving away from hears the sound at a lower frequency than it is emitted at. As each complete sound wave is emitted, the distance has increased between the source and observer. As a result the waves arrive at the observer less frequently.
Observed frequency calculations
The observed frequency fo (o for observer) can be calculated if the frequency of the source fs (s for source), the speed of the source vs and the speed of sound v are known.
\(f_{o}=f_{s} \left(\frac{v}{v\pm v_{s}} \right )\)
The denominator is 'plus or minus' depending if the source is travelling towards or away from the observer:
- source travelling towards observer - subtract vs making the bottom of the fraction smaller to give an increased frequency
- travelling away from observer - add v and vs making the bottom of the fraction larger to give a decreased frequency
Example
If a fire engine is travelling away at 18 ms-1 (40 miles per hour) sounding a siren of frequency 512 Hz what is the frequency heard by a stationary observer?
The speed of sound, v, is given as 340 ms-1.
Put the known values into the Doppler equation. In this case add the speed of sound and the speed of the fire engine to make the denominator:
\(f_{o}=512 \left(\frac{340}{340+18} \right )\)
The terms in the brackets become a factor to multiply the source frequency.
\(f_{o}=512 \times 0.9497\)
\(f_{o}=486Hz\)
So there is a drop in pitch of 26 Hz as the fire engine passes and begins to move away.
Question
Do the occupants of a fire engine notice a doppler shift?
Not from their own siren as they are moving at the same speed.
If they were to hear a siren in a building as they passed, it would appear higher in pitch on approach and lower as they move away for similar reasons as above.