Assertion and Reason – Rankers Physics
Topic: Waves
Subtopic: Waves and its Characteristics

Assertion and Reason

In situation A, an observer moves with a certain velocity towards a stationary source of sound. In situation B, the source moves towards the stationary observer with the same velocity,
Assertion (A): The frequency heard would be the same in both the situations.
Reason (R): The velocity of the source as observed by the observer in both the situations is the same.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

For situation A (observer moving towards stationary source), the observed frequency is \(f_A' = f \frac{v + v_o}{v}\). For situation B (source moving towards stationary observer), the observed frequency is \(f_B' = f \frac{v}{v - v_s}\). If \(v_o = v_s\), then \(f_A' \neq f_B'\). Hence, (A) is false. Classical Doppler effect depends on motion relative to the medium. Although the magnitude of relative velocity between source and observer might be the same, the observed frequencies differ. Thus, (R) is also false as the 'velocity of source as observed by observer' is ambiguous and does not lead to the same frequency due to medium effects. Therefore, both (A) and (R) are false.

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