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An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer?
(Speed of light = 3 × 108 ms–1)
- a)17.3 GHz
- b)15.3 GHz
- c)10.1 GHz
- d)12.1 GHz
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
An observer is moving with half the speed of light towards a stationar...
Explanation:
- When an observer is moving towards a stationary source of waves, the frequency of the waves observed by the moving observer is increased. This effect is known as the Doppler effect.
- The formula to calculate the apparent frequency observed by the moving observer is given by:
\[f' = f \left( \frac{c + v}{c} \right)\]
where:
- \(f'\) is the apparent frequency observed by the moving observer
- \(f\) is the frequency of the source
- \(c\) is the speed of light
- \(v\) is the speed of the observer
- In this case, the observer is moving with half the speed of light towards the microwave source emitting waves at a frequency of 10 GHz.
- Plugging in the values, we get:
\[f' = 10 \times \left( \frac{3 \times 10^8 + 1.5 \times 10^8}{3 \times 10^8} \right) = 17.3 \text{ GHz}\]
Therefore, the frequency of the microwave measured by the observer is 17.3 GHz. So, the correct answer is option 'A'.
- When an observer is moving towards a stationary source of waves, the frequency of the waves observed by the moving observer is increased. This effect is known as the Doppler effect.
- The formula to calculate the apparent frequency observed by the moving observer is given by:
\[f' = f \left( \frac{c + v}{c} \right)\]
where:
- \(f'\) is the apparent frequency observed by the moving observer
- \(f\) is the frequency of the source
- \(c\) is the speed of light
- \(v\) is the speed of the observer
- In this case, the observer is moving with half the speed of light towards the microwave source emitting waves at a frequency of 10 GHz.
- Plugging in the values, we get:
\[f' = 10 \times \left( \frac{3 \times 10^8 + 1.5 \times 10^8}{3 \times 10^8} \right) = 17.3 \text{ GHz}\]
Therefore, the frequency of the microwave measured by the observer is 17.3 GHz. So, the correct answer is option 'A'.
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Community Answer
An observer is moving with half the speed of light towards a stationar...
Doppler effect in light (speed of observer is not very small compared to the speed of light)
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An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer?(Speed of light = 3 × 108ms–1)a)17.3 GHzb)15.3 GHzc)10.1 GHzd)12.1 GHzCorrect answer is option 'A'. Can you explain this answer?
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