An engine whistling at a constant frequency \( \mathrm{n}_{0} \) and moving with a constant velocity goes past a stationary observer. As the engine crosses him, the frequency of the sound heard by him changes by a factor \( f \)
\( \mathrm{P} \) \( \left(f_{\text {after }}=f \times f_{\text {before }}\right) \). The actual difference in the frequencies of the sound heard by him before and after the engine crosses him is
W
(A) \( \frac{1}{2} \mathrm{n}_{0}\left(1-\mathrm{f}^{2}\right) \)
(B) \( \frac{1}{2} n_{0}\left(\frac{1-f^{2}}{f}\right) \)
(C) \( n_{0}\left(\frac{1-f}{1+f}\right) \)
(D) \( \frac{1}{2} \mathrm{n}_{0}\left(\frac{1-\mathrm{f}}{1+\mathrm{f}}\right) \)
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