Read Moving Sirens: Separate Emission from Arrival Time
This short read prepares one exact NSEP pattern: arrival-time doppler shift from a rotating siren. Identify the physical condition before calculating.
Arrival-Time Doppler Shift from a Rotating Siren is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the physical model
Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.
Build the relation
The observed frequency is highest when the siren has maximum velocity component toward the observer. Initially the siren is at the nearest point and moving downward. With clockwise rotation and ω=π rad s⁻¹, it reaches the top after 1.5 s, where its tangential velocity is horizontally toward the observer and the Doppler shift is maximal. The sound then takes about 100/330≈0.30 s to reach the observer. First observation of maximum pitch occurs at about 1.5+0.30=1.8 s.
Check before selecting
Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.
OlympIQ exam lens
- ✓Name the governing law before using a formula.
- ✓Keep the stated geometry and direction information explicit.
- ✓Use one unit or limiting-case check.
The largest emitted frequency is observed only after the sound has travelled to the listener.
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