Question

Derive an expression for the apparent frequency received by observer when alone observer is in motion. (Assume media to be at rest).

Solution

Let a source at rest be emitting the waves of frequency f and wavelength X.

When the observer is also at rest, he is receiving f waves in one second.
Now let the observer start moving with velocity u towards a stationary source.
When the observer starts moving with velocity u, he will receive waves

space straight u over straight lambda

more than f.
Total number of waves received by observer in 1 second is,

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Frequency is the number of waves received by the observer in 1 second.
Therefore, apparent frequency of wave received by observer,

straight f apostrophe equals fraction numerator straight V plus straight u over denominator straight V end fraction straight f

If the observer moves away from the source, the observer will receive waves

straight u over straight lambda equals straight u over straight V straight f

less than f.
Therefore apparent frequency, when observer moves away is,

straight f apostrophe equals fraction numerator straight V minus straight u over denominator straight V end fraction straight f

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Mechanical Properties Of Fluids

Derive an expression for the apparent frequency received by observer when alone observer is in motion. (Assume media to be at rest).

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