A point source of sound moves at constant speed through still air. The diagram shows some wavefronts at one instant. Observer P is in front of the source and observer Q is behind the source.

A hydrogen spectral line has a laboratory wavelength of $486.1\ \text{nm}$. The same line is observed from a star at a wavelength of $486.7\ \text{nm}$. Use $c=3.00\times10^8\ \text{m s}^{-1}$.

The spectra from a laboratory sample and from a galaxy are compared.

An ambulance siren emits sound of frequency $700\ \text{Hz}$. The ambulance moves directly away from a stationary observer at $25\ \text{m s}^{-1}$. The speed of sound in air is $340\ \text{m s}^{-1}$.

A stationary loudspeaker emits sound of frequency $512\ \text{Hz}$ in still air. An observer moving directly towards the loudspeaker detects a frequency of $548\ \text{Hz}$. The speed of sound in air is $340\ \text{m s}^{-1}$.

A small loudspeaker emits pulses of sound at a constant frequency while moving at constant speed through still air. The diagram shows wavefronts at one instant. Observers A and B are stationary relative to the air.

A stationary sound source emits regular pulses. Two sensors record the arrival time of successive wavefronts. Sensor X is stationary relative to the air. Sensor Y moves directly towards the source at constant speed. The graph shows arrival time against pulse number for both sensors.

A spectral line with laboratory wavelength $121.6\ \text{nm}$ is observed from a distant object at $158.1\ \text{nm}$. A student suggests using $\Delta\lambda/\lambda\approx v/c$ to find the speed.

Light from a rotating star is observed from Earth. The equator of the star is viewed edge-on.

A sound source emits frequency $400\ \text{Hz}$ in still air. The speed of sound is $340\ \text{m s}^{-1}$. Two separate situations are considered: in situation 1 the source moves towards a stationary observer at $20\ \text{m s}^{-1}$; in situation 2 the observer moves towards a stationary source at $20\ \text{m s}^{-1}$.

A medical Doppler ultrasound probe emits ultrasound of frequency $5.0\ \text{MHz}$ into tissue. The speed of ultrasound in the tissue is $1540\ \text{m s}^{-1}$. Echoes from blood cells give a frequency shift of $4.0\ \text{kHz}$. The ultrasound beam makes an angle of $60^\circ$ with the direction of blood flow.

A stationary police radar emits microwaves of frequency $24.0\ \text{GHz}$ towards a car moving directly towards the radar. The frequency of the reflected wave differs from the emitted frequency by $2.40\ \text{kHz}$. Use $c=3.00\times10^8\ \text{m s}^{-1}$.

The hydrogen line with laboratory wavelength $656.3\ \text{nm}$ is observed in the spectrum of a star. The spectrum is compared with a laboratory spectrum.

The same absorption line, with laboratory wavelength $486.1\ \text{nm}$, is observed in four galaxies. The graph shows observed wavelength against independently estimated distance from Earth.

Three stars are observed using the same spectral line of laboratory wavelength $589.0\ \text{nm}$. The table gives the measured wavelength and the direction of the star's motion in the plane of the sky as inferred from images taken several years apart.

A siren emits sound at frequency $500\ \text{Hz}$ while moving in a straight line past a stationary microphone. The speed of sound in air is $340\ \text{m s}^{-1}$. The graph shows the frequency recorded by the microphone.

A stationary dipper produces water waves of frequency $8.0\ \text{Hz}$ in a ripple tank. The wave speed is $0.40\ \text{m s}^{-1}$. A small detector moves directly towards or away from the dipper. The graph shows the detected frequency for different detector velocities, where positive velocity is towards the dipper.

A speed camera emits microwaves of frequency $24.0\ \text{GHz}$ along a straight road. The reflected signal from a car has a Doppler frequency shift. The table shows the shift for several cars; a positive shift indicates that the reflected frequency is greater than the transmitted frequency.

A siren emitting sound of frequency $800\ \text{Hz}$ moves at constant speed along a straight line through still air. A stationary microphone detects a constant frequency of $850\ \text{Hz}$ during one interval of the motion. The speed of sound is $340\ \text{m s}^{-1}$.

A spectral line from a rotating star is observed to be broadened. The same line has a laboratory wavelength of $656.30\ \text{nm}$. The radius of the star is $7.0\times 10^8\ \text{m}$. Assume that the broadening is caused only by rotation and that the equator is viewed edge-on.

A Doppler ultrasound probe emits ultrasound of frequency $5.0\ \text{MHz}$ into tissue. The speed of ultrasound in the tissue is $1540\ \text{m s}^{-1}$. The frequency shift of the reflected signal is measured for different angles $\theta$ between the beam and the direction of blood flow.

A loudspeaker on a trolley emits sound of frequency $480\ \text{Hz}$ while moving directly away from a stationary sensor. The speed of sound in air is $336\ \text{m s}^{-1}$. The sensor records the pressure variation with time after the trolley has reached constant speed.

Light from a distant galaxy contains a hydrogen spectral line that has a laboratory wavelength of $656.28\ \text{nm}$. The same line is observed from the galaxy at $657.90\ \text{nm}$.

Two situations are shown for sound waves in still air. In situation A, a source moves towards a stationary observer. In situation B, an observer moves towards a stationary source. The emitted frequency is the same in both situations.

A student compares the Doppler effect for sound from a siren and for light from a star.

A stationary detector beside a straight road detects sound from a car horn. The horn emits sound of frequency $900\ \text{Hz}$. The speed of sound in air is $340\ \text{m s}^{-1}$. As the car approaches the detector, the detected frequency is $960\ \text{Hz}$.

A stationary loudspeaker emits sound of frequency $2.50\ \text{kHz}$ in still air. A detector moves directly away from the loudspeaker and records a frequency of $2.42\ \text{kHz}$. The speed of sound in air is $340\ \text{m s}^{-1}$.

A mechanical wave of speed $330\ \text{m s}^{-1}$ in a medium is emitted at frequency $600\ \text{Hz}$. In two separate trials, the same detected frequency $660\ \text{Hz}$ is produced. In trial 1 the source moves towards a stationary detector. In trial 2 the detector moves towards a stationary source.

A rotating star has radius $6.0\times10^8\ \text{m}$. A spectral line from the star has a laboratory wavelength of $486.10\ \text{nm}$. Light from one edge of the star is observed at $486.06\ \text{nm}$ and from the opposite edge at $486.14\ \text{nm}$. The rotation axis is perpendicular to the line of sight.

The observed wavelength of a sodium absorption line from a nearby star varies periodically about its laboratory value of $589.0\ \text{nm}$. The maximum displacement from the laboratory value is $0.012\ \text{nm}$.

An absorption line from a galaxy has a laboratory wavelength of $517.0\ \text{nm}$ and is observed at $526.3\ \text{nm}$. For this galaxy, use $c=3.00\times10^8\ \text{m s}^{-1}$. A speed-distance relation for distant galaxies is given by $v=H_0d$, where $H_0=70\ \text{km s}^{-1}\ \text{Mpc}^{-1}$.

A Doppler ultrasound probe emits ultrasound of frequency $5.00\ \text{MHz}$ into tissue. The speed of ultrasound in the tissue is $1540\ \text{m s}^{-1}$. Echoes from blood cells give a frequency shift of $3.20\ \text{kHz}$. The ultrasound beam makes an angle of $60^\circ$ with the direction of blood flow.

A police radar emits microwaves of frequency $24.125\ \text{GHz}$ towards a car moving directly towards the radar. The reflected signal is $3.20\ \text{kHz}$ higher than the transmitted signal. Use $c=3.00\times10^8\ \text{m s}^{-1}$.

A small motor boat on still water produces waves of frequency $2.00\ \text{Hz}$. The wave speed relative to the water is $1.20\ \text{m s}^{-1}$. A stationary sensor directly ahead of the boat records a frequency of $2.40\ \text{Hz}$.

A laboratory tests two speed-measuring systems. System A uses sound from a stationary source of frequency $1800\ \text{Hz}$ and a detector moving directly towards the source. The detector records $1875\ \text{Hz}$ when the speed of sound is $330\ \text{m s}^{-1}$. System B uses reflected microwaves of frequency $10.0\ \text{GHz}$ and measures a returned frequency shift of $900\ \text{Hz}$ from a moving target.