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Q.

When a train approaches a stationary observer, the apparent frequency of the whistle is n' and when the same train recedes away from the observer, the apparent frequency is n ". Then, the apparent frequency n when the observer moves with the train is-


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a

Question Image

b

Question Image

c

Question Image

d

Question Image 

answer is D.

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Detailed Solution

Concept- In this question, we will look at two separate scenarios and solve them with different figures. We will use the apparent frequency formula in both cases and then add them after simplifying as requested by the question.
The frequency given by the question is Question Image.
Case Question ImageAs we all know, the apparent frequency formula is Question Image. Where Question Image is the actual frequency, Question Image is the observed frequency, Question Image is speed, Question Image is velocity of the observer and Question Image is the velocity of the source.
Here, Question ImageQuestion ImageQuestion ImageQuestion ImageThus, the equation for n' will be_
Question ImageQuestion ImageQuestion ImageLet the above equation be equation 1 –
Question Image (Equation 1)
Case 2-
Here, Question ImageQuestion ImageQuestion ImageQuestion ImageThe indicators will be inverted since the source is moving away from the observer.Question ImageQuestion ImageQuestion ImageLet the above equation be equation 2Question Image (equation 2)
Now, in equation 1-
Question ImageQuestion ImageInverting the above equation, we get-
Question ImageNow, inequation-
Question ImageQuestion ImageInverting the above equation, we get-
Question ImageAdding both the inverted equations, we get
Question ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageHence, option 4 is the correct answer.
 
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