# Worksheet: Doppler Shift

In this worksheet, we will practice explaining the effect of the motions of the sources and observers of waves on the measured frequencies of the waves.

Q1:

The graphs show the change in frequency with time of the sound of the horn of a fast-moving car that is heard by a person walking slowly by the side of the road as the car approaches and passes them. Which of the graphs (A), (B), (C), and (D) most correctly shows the changes in frequency that the pedestrian hears? • A(D)
• B(C)
• C(B)
• D(A)

Q2:

A firework is set up to launch horizontally in a fireworks display. As the firework’s fuse burns, it emits sound waves that have a frequency of 100 Hz and a wavelength of 3 m. When the rocket launches, it accelerates in a negligible time to a constant speed of 225 m/s and continues to emit sound waves with the same frequency and wavelength as before the launch, as shown in the diagram. An unwary person accidentally enters the firework display area and the firework travels directly toward them. The person is not moving. According to the person, at what speed do wave fronts emitted from the rocket before it is launched travel?

According to the person, at what speed do wave fronts emitted from the flying rocket travel before the rocket reaches the point where the person stands?

The person manages to duck and avoid being hit by the firework, which then moves directly away from the person. According to the person, at what speed do wave fronts emitted from the rocket after it passes the person travel?

What is the frequency of the sound of the approaching firework as heard by the person?

What is the frequency of the sound of the receding firework as heard by the person?

Q3:

Which of the following combinations of motion of a sound wave source and a sound wave observer produces the largest Doppler shift of the frequency of the wave as measured by the observer?

• AA sound wave source moves at 30 m/s in the same direction as an observer moving at 20 m/s.
• BAn observer moves toward a stationary sound wave source at 30 m/s.
• CA sound wave source moves at 15 m/s toward an observer moving in the opposite direction to the sound wave source at 20 m/s.
• DA sound wave source moves toward a stationary observer at 25 m/s.
• EA sound wave source moves at 20 m/s away from an observer moving in the opposite direction to the sound wave source at 20 m/s.

Q4:

Which of the following combinations of motion of a sound wave source and a sound wave observer does not result in the observer measuring a different frequency of the sound wave to the frequency of the sound wave as measured at the source? Assume that all motion of sound wave sources and observers are at the same speed.

• AA sound wave source moves away from an observer moving in the opposite direction to the sound wave source.
• BA sound wave source moves toward an observer moving in the opposite direction to the sound wave source.
• CAn observer moves toward a stationary sound wave source.
• DA sound wave source moves toward a stationary observer.
• EA sound wave source moves in the same direction as a moving observer.

Q5:

Which of the following statements is a correct description of the Doppler shift?

• AThe Doppler shift is the apparent change in the direction of waves depending on how the source of the waves moves compared to an observer of the waves.
• BThe Doppler shift is the apparent change in the amplitude of waves depending on how the source of the waves moves compared to an observer of the waves.
• CThe Doppler shift is the motion of a source of sound waves due to the reaction force produced by the waves when they are emitted.
• DThe Doppler shift is the apparent change in the frequency of waves depending on how the source of the waves moves compared to an observer of the waves.

Q6:

Sound waves are produced by person A, who moves at a speed toward a second person, person B. Person B is moving toward person A at a speed , where is less than . Which person perceives the sound waves produced by person A as having higher frequency?

• APerson B
• BBoth people perceive the same frequency.
• CPerson A

Q7:

Sound waves are produced by a person who is moving in a straight line at a constant speed. How does the perceived frequency of the sound waves to a stationary observer that the person is moving away from compare to the perceived frequency of the sound waves to the moving person?

• A
• B
• C

Q8:

An observer listens to a motorcycle that moves at a uniform speed in a circle, starting from point , then moving to , then , then , and then back to , as shown in the diagram. Where on the circle is the average frequency of the sound heard by the observer the highest?

• AFrom to
• BFrom to
• CFrom to
• DFrom to

Where on the circle is the average frequency of the sound heard by the observer the lowest?

• AFrom to
• BFrom to
• CFrom to
• DFrom to

Between which two pairs of points are the average frequencies of the sound heard by the observer equal?

• A to and to
• B to and to
• C to and to
• D to and to
• E to and to

Q9:

Sound waves are produced by a person who is moving in a straight line at a constant speed. How does the perceived frequency of the sound waves to a stationary observer being approached by the person compare to the perceived frequency of the sound waves to the moving person?

• A
• B
• C

Q10:

A person moves toward a source of sound waves, as shown in the diagram. The sound source starts to emit sound at the same moment that the person starts to move. The sound from the source moves a distance equal to the wavelength of the sound wave in a time interval . How many wave fronts from the sound source will have reached or passed the person by the time that the person has moved from their initial position to the point P? 