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What is Doppler Effect?
A police radar set emits a parallel beam of electromagnetic radiation at wavelength λo and velocity c, Which falls on a motor car moving directly towards the set with a velocity u.
(a.) Derive an expression for the time it takes for the wave front of the radiation initially a distance
λo from the car, to reach the car.
An observer travelling with a constant velocity of 20ms-1, passes close to a stationary source of sound and notices that there is a change of frequency of 50 Hz as he passes the source. What is the frequency of the source?
A car travelling at 10ms-1 sounds its horn, which has a frequency of 500 Hz, and this is heard in
another car which is travelling behind the first car, in the opposite direction, with a velocity of
20ms-1. The sound can also be heard in the second car by reflection from a bridge ahead, in the
direction of the first car. What frequencies will the driver in the second car hear?
Give an example of change in frequency due to motion of source or observer from some other
branch of physics, explaining either a use which is made of it, or a deduction from it.
Deduce expressions for the frequency heard by an observer
(a.) when he is stationary and a source of sound is moving towards him and
(b.) when he is moving towards a stationary source of sound.
Explain your reasoning carefully in each case.
A train, sounding its whistle, is travelling along a long section of track and passes under a low bridge.
Explain how the frequency of the note heard by an observer standing on the bridge differs from the
frequency emitted.
Compare the shift in frequency if a 2000Hz source is moving towards you at 15ms-1 versus if you are moving towards it at 15ms-1. Are the two frequencies exactly the same? Are they close? Repeat
the calculation for 150ms-1 and then again for 300ms-1. What can you conclude about the asymmetry of the Doppler formulas? Show that at low speeds (relative to the speed of sound), the two formulas-source approaching and detector approaching-yield the same result.
Two automobiles are equipped with the same single-frequency horn. When one is at rest and the
other is moving toward an observer at 15ms-1, a beat frequency of 5.5Hz is heard. What is the
frequency the horns emit? Assume T = 20°C.
In one of the original Doppler experiments, one tuba was played in a moving platform car at a
frequency of 75Hz, and a second identical one was played on the same tone while at rest in the railway station. What beat frequency was heard if the train approached the station at a speed of
10.0ms-1?
An ambulance travels down a highway at 120kmh-1, its siren emitting sound of frequency 400Hz. What is the frequency heard by a passenger in a car traveling at 90kmh-1 as the car approaches and
by-passes the ambulance?
