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(B) The general formula for the Doppler effect with wind velocity $w$ is given by $f_2 = f_1 \left( \frac{V + w - v_o}{V + w - v_s} \right)$,where $v_

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$(A, B)$

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(B) The general formula for the Doppler effect with wind velocity $w$ is given by $f_2 = f_1 \left( \frac{V + w - v_o}{V + w - v_s} \right)$,where $v_o$ and $v_s$ are the velocities of the observer and source relative to the ground,respectively.Case $1$: Wind blows from source to observer.The effective speed of sound is $(V + w)$. The observer moves towards the source with speed $u$,and the source moves towards the observer with speed $u$. Using the sign convention (positive direction from source to observer): $v_o = -u$ and $v_s = u$.$f_2 = f_1 \left( \frac{(V + w) - (-u)}{(V + w) - u} \right) = f_1 \left( \frac{V + w + u}{V + w - u} \right)$.Since $(V + w + u) > (V + w - u)$,we have $f_2 > f_1$.Case $2$: Wind blows from observer to source.The effective speed of sound is $(V - w)$.Using the sign convention: $v_o = -u$ and $v_s = u$.$f_2 = f_1 \left( \frac{(V - w) - (-u)}{(V - w) - u} \right) = f_1 \left( \frac{V - w + u}{V - w - u} \right)$.Since $(V - w + u) > (V - w - u)$,we have $f_2 > f_1$.In both cases,the observed frequency $f_2$ is greater than the source frequency $f_1$. Thus,statements $(A)$ and $(B)$ are correct.

Similar Questions

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