Doppler Effect (DP IB Physics: HL)

A train is moving away from an observer on a platform with a constant speed  where v is the speed of sound. The train emits sound of frequency f.

What is the observed speed of sound and the observed frequency as the train recedes?

In the laboratory on Earth, hydrogen emits a spectral line that is measured by an observer to have a wavelength of 400 nm. The same spectral line is emitted by a galactic source that is moving away from Earth at speed of 0.2c, where c is the speed of light.

What is the wavelength of the same spectral line from the galaxy as measured by the observer on Earth?

A car travels in a straight line towards a stationary observer at a speed of 0.2v, where v is the speed of sound. The car's horn emits a pure sound of frequency ƒ.

What is the frequency of the sound of the horn as heard by the observer?

An observer approaches a stationary source of sound. The speed of the emitted sound and its wavelength, measured at the source, are  and λ respectively.

Which of the following is the observed wave speed and the observed wavelength, as measured by the moving observer?

A spectral line is observed at 530 nm in the laboratory. The same spectral line is observed in a galaxy which is receding from Earth at a velocity of 3.00 × 10⁶ m s⁻¹. 

What is the wavelength of the spectral line from the galaxy?

A star emits light of frequency . This light is observed on Earth to have a frequency  which is of a lower frequency than .

Which of the following correctly describes the speed and direction of motion of the star?

A siren on a fire engine emits sound of wavelength λ. The speed of sound in still air is v.

What would be the wavelength of the sound recorded by a stationary observer when the ambulance travels towards them at speed of 0.15 v?

Two lines P and Q in the emission spectrum of a gas are measured on the Earth by a stationary observer.

The observer then moves towards the gas sample, and the emission spectrum is recorded as they are moving.

What is the correct pattern for the shifted spectral lines, P' and Q'?

Which of the following statements is true about redshift?

A car of terrified observers drive away from a stationary, but hungry T. rex, at a speed of 10 m s⁻¹. They hear the roar of the T. rex at a frequency of 170 Hz. The speed of sound in air is 340 m s⁻¹.

What is the frequency of the sound as emitted by the T. rex?

A stationary source emits sound wave with frequency . An observer moving towards the source measures the sound as having frequency . The speed of the observer is 20% of the speed of sound.

What is the the value of when the emitted frequency is 10 Hz?

The flow of blood can be monitored using a machine which emits ultrasound of 10 MHz and is then able to measure the change in frequency when the pulse returns having reflected off a red blood cell.

When a wave is reflected from a moving object, the change in frequency is doubled compared to a situation where a sound is detected by a moving observer. Assume that the speed of sound in the body is the same as that of water, 1500 m s^–1.

What is the frequency detected if blood is flowing away at 0.15 m s⁻¹?

A boat sits on a lake, and is hit by 4 waves every 10 s. As the boat starts to move in the same direction as the waves, exactly 2 waves from behind hit the boat every 10 s. The speed of the boat is 1.5 m s⁻¹.

What is the speed of the waves?

In a binary star system, two stars orbiting each other can be observed using a spectrometer. The star system as a whole is moving away from the Earth at a constant velocity. The spectral lines appear to fluctuate. A graph can be plotted of relative velocity of each star compared to the observer.

At which point on the graph will the stars be in the following position?

Photographs of lines in the spectrum of the Sun show changes in wavelength. The atmosphere of the sun rotates at a speed , anti-clockwise as observed from its north pole.

What is an expression for the observed change in wavelength of a spectral line from light emitted from the right hand edge of the Sun as viewed from the northern hemisphere on the Earth?

Assume the Earth's orbit is circular.

An asteroid which entered the Earth's atmosphere 64 million years ago emitted a sound of frequency 100 Hz due to the interaction with the atmosphere on its entry.

A T. rex directly under the asteroid hears the noise, but hears it at a frequency of 200Hz. The distance from the top of the atmosphere to the ground is 102 km. 

How long does the T. rex have before the asteroid hits?

The graph shows the dominant wavelength of light emitted by 4 different stars, and the same light observed from the Earth.

Which pair of stars are moving away from Earth at the same speed?

A bat is flying towards a tree using echolocation to navigate. The bat emits an ultrasound pulse of 45 kHz. On reflection from the tree, the bat detects a frequency of 50 kHz. The bat is 170 m away from the tree. Due to reflection, the speed of the bat is halved because the Doppler effect is doubled.

How long does the bat have to change course before hitting the tree?