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(A) After $t = 1\, s$ of free fall,the velocity of the source is $v_s = g 	imes t = 10 	imes 1 = 10\, m/s$ (downward).The observer in the balloon is

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$12$

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(A) After $t = 1\, s$ of free fall,the velocity of the source is $v_s = g 	imes t = 10 	imes 1 = 10\, m/s$ (downward).The observer in the balloon is moving upward with $v_o = 2\, m/s$.Let $v = 300\, m/s$ be the speed of sound.Before crossing,the source is moving towards the observer and the observer is moving towards the source. The observed frequency $n_1$ is:$n_1 = f_0 \left( \frac{v + v_o}{v - v_s} ight) = 150 \left( \frac{300 + 2}{300 - 10} ight) = 150 \left( \frac{302}{290} ight) \approx 156.21\, Hz$.After crossing,the source is moving away from the observer and the observer is moving away from the source. The observed frequency $n_2$ is:$n_2 = f_0 \left( \frac{v - v_o}{v + v_s} ight) = 150 \left( \frac{300 - 2}{300 + 10} ight) = 150 \left( \frac{298}{310} ight) \approx 144.19\, Hz$.The difference in frequency is $\Delta n = n_1 - n_2 = 156.21 - 144.19 = 12.02\, Hz \approx 12\, Hz$.

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