The speed of sound in air is $v$. Both the source and observer are moving towards each other with equal…

The speed of sound in air is $v$. Both the source and observer are moving towards each other with equal speed $u$. The speed of wind is $w$ from source to observer. Then, the ratio $\left(\frac{f}{f_0}\right)$ of the apparent frequency to the actual frequency is given by
  1. $\frac{v + u}{v - u}$
  2. $\frac{v + w + u}{v + w - u}$
  3. $\frac{v + w + u}{v - w - u}$
  4. $\frac{v - w + u}{v - w - u}$

Solution

When wind blows at a speed $v_w$ from the source to the observer, take $v \rightarrow v + v_w$ in equation $f' = \left( \frac{v + v_o}{v - v_s} \right) f_0$ $f' = \left( \frac{v + w + u}{v + w - u} \right) f_0$ $[\because v_o = v_s = u \text{ and } v_w = w]$ $\cdot\!\cdot\!\cdot \quad \frac{f'}{f_0} = \frac{v + w + u}{v + w - u}$

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