Question 11

According to the Doppler effect formula for moving source and observer:

In Case 1 (moving towards each other):

$f' = f_s \left( \frac{c + v}{c - v} \right)$

Given $f_s = 240$ Hz and $f' = 288$ Hz:

$288 = 240 \left( \frac{c + v}{c - v} \right) \implies \frac{288}{240} = \frac{6}{5} = \frac{c + v}{c - v}$

$6c - 6v = 5c + 5v \implies c = 11v \implies \frac{v}{c} = \frac{1}{11}$

In Case 2 (moving away from each other):

$f'' = f_s \left( \frac{c - v}{c + v} \right)$

$n = 240 \left( \frac{1 - v/c}{1 + v/c} \right) = 240 \left( \frac{1 - 1/11}{1 + 1/11} \right)$

$n = 240 \left( \frac{10/11}{12/11} \right) = 240 \times \frac{10}{12} = 200$

Final answer is 200.