Optional Unit V: Sound
C. Characteristics of Sound

3. The Doppler Effect

Key Concepts

When a source generating waves moves relative to an observer, or when an observer moves relative to a source, there is an apparent shift in frequency.

If the distance between the observer and the source is increasing the frequency apparently decreases, whereas the frequency apparently increases if the distance between the observer and the source is decreasing.

The relationship describing the Doppler Shift for a moving source is given by:

where f₂ is the apparent frequency, f₁ is the actual frequency emitted by the source, v is the speed of sound in the medium, v_s is the speed of the source through the medium (the negative sign is used if the source is moving towards the observer).

The relationship describing the Doppler Shift for a moving observer is given by:

where f_o is the observed frequency, f_s is the source frequency, v is the speed of sound, v_o is the speed of the observer (it is taken to be negative if the observer is receding from the source).

The above stated relationships describing the Doppler Shift can be combined as:

where the variables are as defined previously. The upper set of signs apply if the source/observer are approaching, and the lower set of signs are used if they are receding.

The Doppler Effect explains the apparent change in pitch of a passing automobile.

A similar effect (Doppler Shift for light) can also be used to determine the speed of a star relative to the earth. The red shift of the star's spectrum indicates that the distance between an observed star and the earth may be increasing.

The Doppler Shift for light describes a change in wavelength, not a change in frequency as with sound.

Short range radar devices use the Doppler Shift principle. A change in frequency between emitted and returning pulses can be used to find the relative speed.

Learning Outcomes

Students will increase their abilities to:

1. Explain that when a sound source generating waves moves relative to an observer, or when an observer moves relative to a source, there is an apparent shift in frequency.

2. Explain that the frequency apparently decreases when the distance separating the source and the observer increases.

3. Explain that the frequency apparently increases when the distance separating the source and the observer decreases.

4. Apply mathematical relationships describing the Doppler Shift to problem solving.

5. Describe a situation or an application which involves the Doppler Effect.

6. Transfer an understanding of the Doppler Effect to practical examples and common experiences.

Teaching Suggestions, Activities and Demonstrations

1. Inquire to see if a local police officer could bring some radar equipment to school to show students how it works.

2. Students might be interested in researching stealth technology, radar detection, and radar jamming methods .

3. Use a video camera to record the sound and motion of a vehicle with its horn sounding while it is stationary and as it passes by the camera on the highway. This provides an excellent illustration of the Doppler Effect.

4. Further research could be done to investigate the importance of the Doppler Effect to astronomers.

5. Ideas in this unit can be used for enrichment when teaching about light. Note, however, that the Doppler shift for light describes a change in wavelength, not a change in frequency as with sound.

6. The Doppler shift for lightwaves is:

   

   where c is the speed of light, v is the velocity of the light source, (e.g. star) and is considered positive if the source is receding, is the wavelength if v were 0 (emitted wavelength), and is the change in wavelength due to v.

   + is the observed wavelength.

   If v<<c,

   , from which the speed of the star can be found.

   If the object is receding, the wavelength shifts to a higher value (red shift). If the object is approaching, the wavelength shifts to a lower value (blue shift).

   Since most stellar objects are red shifted, it implies that the universe is expanding. This supports the "Big Bang" hypothesis.

   Note that, unlike the Doppler shift for sound, it does not matter whether the source or the observer is the one in motion. Only their relative velocity is needed.