9.5 Doppler Effect

A racing car is travelling at 300 km h⁻¹ on a race track.

The stationary observer hears a frequency of sound of 1550 Hz from the exhaust as the car approaches them (position 1). You can assume the speed of sound to be 340 m s⁻¹.

Determine the frequency of sound heard by: 

The car from part (a) opens its Drag Reduction System (DRS) increasing its top speed by 10 km h⁻¹. It then overtakes another car which is travelling at 300 km h⁻¹.

The equation which can be used when both source and observer are moving is:

The frequency of the sound emitted by the car exhaust is directly proportional to the speed.

Calculate the maximum and minimum frequency of sound heard from the faster car, as heard by the driver of the car being overtaken during this manoeuvre.

A scientist is doing some experiments on sound from the safety of the stands. An air horn emits a sound of frequency 450 Hz. The sound of the horn reflects off the car, which is moving away from the scientist, who measures the frequency as being 420 Hz.

Calculate the speed of the car.

A train is travelling at 45 m s⁻¹ and blows a whistle at a frequency of 750 Hz. A person is waiting at a level crossing for the train to pass. Take the speed of sound in air as 340 m s⁻¹.

Calculate the frequency observed by the person: 

After the train passes the level crossing, it slows down as it approaches a tunnel. Wind is funnelled down the tunnel towards the train reaching a velocity of 27 m s⁻¹. The observer at the level crossing hears the whistle at a frequency of 729 Hz. 

Calculate the new speed of the train.

After exiting the tunnel, the train stops at a station. The observer from part (a) is now walking to the platform to catch the train at a speed of 1.5 m s⁻¹. The human ear can distinguish between frequency differences of around 3.6 Hz.

Show that the change in frequency of the train's whistle, as heard by the running observer, can be considered negligible.

Once the train has left the station, it travels down a line with two tracks. Another train is approaching on the opposite track with a speed of 7.6 m s⁻¹. The speed of the departing train is 83% of the speed of the second train.

When both observer and source are moving, the following equation can be used to determine the new frequency:

Calculate the frequency of the whistle as observed by a passenger on the approaching train as a percentage of .

A ship is using low frequency sonar to map the sea bed. It sends out a pulse of sound which startles a nearby school of fish. The fish start to swim away at a speed of 20 km h⁻¹. The ship then sends out a second pulse with a wavelength that is 15 cm less than that of the original pulse. The fish perceive the two pulses to have the same frequency.

Determine the wavelength of the initial pulse.

The school of fish approach a second ship which is emitting the same frequency of pulse as the first ship. They approach this boat at an angle of 38 °.

Calculate the frequency of sound as observed by the fish, .

The boat uses the stars to navigate. The captain uses a diffraction grating on her telescope to observe the light from a nearby asteroid she has spotted. She observes a spectral absorption line with a frequency of 673.7 nm. 

The absorption line for that element is given as 673.8 nm from tests in the laboratory. 

Through use of a calculation, explain why the captain might be concerned.

Two stars, A and B, in a binary system move in an anti-clockwise direction. Both stars emit light with wavelength, λ = 5.89 × 10⁻⁷ m, which reaches an observer on Earth. In the laboratory, the light is shown to fluctuate between wavelengths of 5.86 × 10⁻⁷ m and 6.02 × 10⁻⁷ m.

Assume they orbit in a circle around their common centre of mass.

Draw a diagram which indicates the position of the stars relative to the Earth when:

The radius of orbit of star B is 4.98 × 10¹¹ m. 

Calculate the time taken for one orbit of star A about the common centre of mass.

An ambulance siren emits two pure sounds. The lower of the two sounds has a frequency of 650 Hz. It is travelling towards a stationary observer at 13.4 m/s. The speed of sound in air is 340 m s⁻¹.

Calculate the change in frequency, Δf, between the source frequency and that heard by the observer.

The ratio between the two frequencies emitted by the ambulance is 0.722. 

As the ambulance approaches a red light at which a number of cars are stopped, it changes its siren to a single monotone sound which the car drivers observe as 700 Hz. The ambulance slows further to 5.3 m s⁻¹.

Calculate the wavelength of sound emitted by the ambulance.

The ambulance pulls to a stop but continues to emit the 700 Hz tone. A car passes the ambulance. As it moves away the sound heard by the car driver has a frequency of 682 Hz.

Determine the speed of the car as it drives away from the ambulance

The diagram shows a stationary wave source, R, in water. The source produces waves with a constant frequency. The distance between each successive wavefront is equal to the wavelength of the waves produced by R.

The speed of the waves in water is v.

Sketch three successive wavefronts produced when the source is moving to the right at a speed of 0.75v. 

A scientist sits on a boat to the right of the source and measures the frequency of the waves as they approach.

Explain the observations the scientist will make.

The speed of the waves is 2.5 m s⁻¹. The wavelength of the waves as emitted by the source is 3.45 m. 

Calculate the frequency of the waves as observed by the stationary boat.

The boat starts to move. Source R is still moving at 0.75v to the right.

Discuss the effect the motion of the boat will have on the observed frequency of the water waves. Assume there is no acceleration.

Every year, an alien species holds a race between two teams. One of the teams has green lights on its spaceships and the other has purple light. During the race the two ships approach a space station.

From the point of view of the space station commander, on the space station, the two colours appear to be identical. as the ships approach the station.

Explain how the commander knows which spaceship is travelling faster.

The wavelength of light from the purple ship is 420 nm and from the green ship is 550 nm. The observed frequency of both ships from the space station is 405 nm.

The green space ship enters the atmosphere of a planet near the spaceship for the victory ceremony, which has amassed a large crowd. It slows down to 0.005% of its speed during the race. As it nears the surface it emits a continuous tone of frequency 2320 Hz. The speed of sound in the atmosphere of this planet is 5690 m s⁻¹.

Calculate the frequency of sound observed by the crowd.

The space station also has the capacity to detect light from other galaxies. In a laboratory, the frequency of electromagnetic radiation from a distant galaxy has been redshifted by 4.2 × 10⁹ Hz. In the laboratory, the same light has a frequency of 1.9 × 10¹² Hz.