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What is Doppler shift? Obtain an expression for the apparent frequency of sound heard when the observer is in motion with respect a source at rest?
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Doppler effect – observer is in motion with respect a source at rest ( For understanding purpose)
The Doppler shift, also known as the Doppler effect, is a change in the frequency or wavelength of a wave that is observed by an observer moving relative to the source of the wave. This effect is most commonly observed in the case of sound waves, where it results in a change in the perceived pitch of a sound. The Doppler shift can also occur with electromagnetic waves, such as light waves, and is used in a variety of scientific and practical applications.
When the observer is moving towards the source of a sound wave, the frequency of the wave will appear to be higher than its actual frequency. This is known as a blue shift. On the other hand, if the observer is moving away from the source, the frequency will appear to be lower, known as red shift.
An expression for the apparent frequency of sound heard when the observer is in motion with respect to a source at rest is given by:
f’ = (v – vo) / (v) * f
where:
f’ is the apparent frequency heard by the observer,
f is the actual frequency of the sound wave,
v is the speed of sound,
vo is the velocity of the observer.
It is important to note that the above formula holds true only for the non-relativistic case where the velocity of the observer is much smaller than the speed of sound. When the velocity of the observer is comparable to the speed of sound, the wave equation changes and is more complex.
The Doppler effect is used in a variety of fields, including meteorology, astronomy, and navigation. In meteorology, the Doppler effect is used to measure wind speeds by bouncing radar waves off of precipitation. In astronomy, the Doppler effect is used to determine the velocities of stars and galaxies. In navigation, the Doppler effect is used to determine the velocity of ships and airplanes.
In summary, the Doppler effect is the change in frequency or wavelength of a wave observed by an observer moving relative to the source of the wave. It is most commonly observed in the case of sound waves, where it results in a change in the perceived pitch of a sound. The expression for the apparent frequency of sound heard when the observer is in motion with respect to a source at rest is given by f’ = (v – vo) / (v) * f, where v is the speed of sound, vo is the velocity of the observer and f is the actual frequency of the sound wave.
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