What is Doppler Effect? Obtain an expression for the apparent frequency of sound heard when the source is in motion with respect to an observer at rest?

The Doppler Effect is a phenomenon that occurs when there is relative motion between a sound source and an observer. It describes the change in frequency or wavelength of a wave (such as sound or light) as perceived by an observer moving relative to the wave source. The effect is named after the Austrian physicist Christian Doppler, who first described it in 1842.

When the source of sound is moving towards the observer, the apparent frequency of the sound heard by the observer will be higher than the actual frequency of the sound emitted by the source. On the other hand, if the source of sound is moving away from the observer, the apparent frequency will be lower than the actual frequency of the sound emitted.

The formula to calculate the apparent frequency (f') of sound heard by an observer when the source is in motion with respect to the observer at rest is given by:

f' = (v + vₒ) / (v + vₛ) * f

where:
f' = Apparent frequency of sound heard by the observer (in Hz)
f = Actual frequency of the sound emitted by the source (in Hz)
v = Speed of sound in the medium (in m/s)
vₒ = Speed of the observer (in m/s) (positive if moving towards the source, negative if moving away)
vₛ = Speed of the source (in m/s) (positive if moving away from the observer, negative if moving towards)

Note: The above formula assumes that both the source and the observer are moving in the same direction (towards or away from each other). If they are moving in opposite directions, the formula slightly changes and becomes:

f' = (v + vₒ) / (v - vₛ) * f

Remember that the Doppler Effect is only noticeable when there is a relative motion between the source and the observer along the line of sight. If they are moving perpendicular to the line of sight, there will be no apparent frequency shift.