Topic 3.5: Doppler Effect Questions

State what is meant by the Doppler effect for sound.

A spectral line that has a laboratory wavelength of 587.6 nm is observed at 587.5 nm in the light from a star.

Identify whether the star is approaching or receding, and explain how you decided.

A bird call of constant frequency is emitted by a bird flying directly towards a stationary microphone.

Identify whether the frequency recorded by the microphone is higher than, lower than, or equal to the emitted frequency, and identify what happens to the wavelength of the sound reaching the microphone.

State what is meant by a redshift, and state what it tells you about the motion of the light source.

As a racing car drives past a spectator standing beside a straight track, the spectator records the frequency of the engine note against time.

Sketch and describe the shape of the frequency-against-time graph the spectator obtains, and explain why it has that shape in terms of the car's motion relative to the spectator.

A train sounds its horn at a constant frequency of 480 Hz as it travels along a straight track directly towards a stationary observer standing beside the track. The train is initially moving at 30 m s⁻¹ and brakes uniformly, coming to rest a short distance before it reaches the observer. The observer measures the relative frequency shift, defined as (f′ − f) / f, where f′ is the frequency heard and f = 480 Hz is the emitted frequency.

Which graph best shows how the relative frequency shift varies with time t from when braking begins until the train comes to rest?

[Diagram: x-axis from 0 to 10 label t, y-axis from -1 to 1 label s, polyline: (0,0.6)-(2,0.42)-(4,0.28)-(6,0.16)-(8,0.07)-(10,0) "A"]

A motorbike sounds a 520 Hz horn and rides directly towards a stationary observer at 24 m s⁻¹.

The speed of sound in the air is 340 m s⁻¹.

Calculate the frequency heard by the observer, and explain whether it is higher or lower than 520 Hz.

A car sounding a steady 256 Hz horn drives directly towards a stationary pedestrian at 30 m s⁻¹.

The speed of sound in the air is 343 m s⁻¹.

Calculate the frequency heard by the pedestrian.

A loudspeaker mounted on a drone emits a steady 480 Hz tone while the drone flies directly away from a stationary listener at 18 m s⁻¹.

The speed of sound in the air is 340 m s⁻¹.

Calculate the frequency heard by the listener and state whether it is higher or lower than 480 Hz.

Starting from the data-booklet relation Δλ/λ ≈ v/c, show that a source whose light is redshifted by a fractional amount of 2.0 × 10⁻³ is receding at a speed of about 6 × 10⁵ m s⁻¹.

Outline why the Doppler shift of light from nearby everyday sources (for example a car moving at 30 m s⁻¹) is far too small to see, whereas the shift from distant galaxies is easily measured.

A hydrogen spectral line has a laboratory wavelength of 656.3 nm.

In light from a distant galaxy the same line is measured at 666.3 nm.

Calculate the speed of the galaxy relative to Earth, state whether it is approaching or receding, and explain what the result suggests about the Universe.

A driver travelling along a straight road passes exactly midway between two identical roadside speakers, each emitting the same constant frequency.

At the instant the driver is level with both speakers, the driver hears both speakers at the same pitch.

The driver continues at constant speed.

Outline how the pitch of the speaker behind the car compares with the pitch of the speaker ahead of the car a moment later, and explain why.

Light from one point on the Sun's equator, where the surface is rotating directly toward Earth, is examined.

Explain why a known spectral line from that point is observed at a shorter wavelength than its laboratory value.

Two galaxies, X and Y, are observed.

The light from galaxy X shows a redshift of Δλ/λ = 0.010, and the light from galaxy Y shows a redshift of Δλ/λ = 0.030.

Deduce which galaxy is moving away from Earth faster, and state how many times faster it is moving.

A spectral line has a laboratory wavelength of 410.0 nm.

In the spectrum of a distant galaxy the same line is observed at 420.0 nm.

Determine the speed of the galaxy relative to Earth.

A point on the equator of the Sun is rotating directly toward Earth at a surface speed of 2.0 × 10³ m s⁻¹.

The Sun's radius is 7.0 × 10⁸ m.

Calculate the Sun's rotation period, giving your answer in days.

On a graph axis of relative frequency shift (heard frequency minus true frequency) against time, a sound source approaches a stationary observer and decelerates smoothly to rest just as it reaches the observer.

Sketch the shape of the relative-frequency-shift graph against time, and explain its shape.

A train sounds a steady whistle of frequency 1.20 kHz as it travels directly towards a stationary observer at the end of the platform.

The observer measures the frequency of the whistle as 1.32 kHz.

The speed of sound in the air is 340 m s⁻¹.

Deduce the speed of the train.

An iron spectral line with a laboratory wavelength of 525.000 nm is observed at 525.105 nm from the receding (left) edge of a rotating star and at 524.895 nm from the approaching (right) edge.

Calculate the rotation speed of the star's surface at its equator, and explain why the two edges give shifts in opposite directions.