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(C) Given: Velocity of source $v_s = 50 \ m/s$,Speed of sound $v = 350 \ m/s$,Frequency measured when moving towards observer $f' = 500 \ Hz$.Using th

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$375$

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(C) Given: Velocity of source $v_s = 50 \ m/s$,Speed of sound $v = 350 \ m/s$,Frequency measured when moving towards observer $f' = 500 \ Hz$.Using the Doppler effect formula for a source moving towards a stationary observer:$f' = f \left( \frac{v}{v - v_s} ight) ightarrow (1)$When the source moves away from the stationary observer,the apparent frequency $f''$ is given by:$f'' = f \left( \frac{v}{v + v_s} ight) ightarrow (2)$Dividing equation $(1)$ by equation $(2)$:$\frac{f'}{f''} = \frac{v + v_s}{v - v_s}$Substituting the values:$\frac{500}{f''} = \frac{350 + 50}{350 - 50} = \frac{400}{300} = \frac{4}{3}$$f'' = 500 	imes \frac{3}{4} = 375 \ Hz$.Thus,the apparent frequency is $375 \ Hz$.

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