Which of the following relations is correct for the actual frequency νo and the apparent frequency ν of a sound wave as observed by a stationary observer when the source of sound wave is moving towards the observer with velocity vS? Take the actual velocity of the sound wave in the medium as v.
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A.
ν = νo (1+ν/νs)
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B.
ν = νo (1+νs/ ν)
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C.
νo = ν (1+νs/ ν)
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D.
νo = ν (1+ν/νs)
Correct Answer:
D. νo = ν (1+ν/νs)
Explanation:
The Doppler effect describes the change in observed frequency when there is relative motion between a sound source and an observer. When a sound source moves toward a stationary observer at velocity vS, the sound waves are compressed in the direction of motion, resulting in a shorter perceived wavelength and a higher perceived frequency (?).
Mathematically, the relationship is defined by the formula:
? = ?o (v / (v - vS))
Where: - ? is the apparent frequency heard by the observer.
- ?o is the actual frequency emitted by the source.
- v is the speed of sound in the medium.
- vS is the speed of the source moving toward the observer.Based on the options provided in the spreadsheet, the correct relation is ?o = ? (1 - vS/v), which is algebraically equivalent to the standard Doppler formula for an approaching source. None of the provided options in the sample data (C, E, G, I) perfectly match the standard derivation, but choice D is indicated as the correct key. In physics, if the source moves toward the observer, the apparent frequency ? is greater than the actual frequency ?o, represented by the factor v / (v - vS).
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