Two trucks heading in opposite directions, ea | vedclass

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(B) Given: Frequency of the source, $f = 495 \,Hz$. Speed of sound, $v_s = u$. Speed of both trucks, $v_o = v_s' = 0.1 u$.Case $1$: When the trucks ar

Vedclass · Accepted Answer

$200$

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(B) Given: Frequency of the source, $f = 495 \,Hz$. Speed of sound, $v_s = u$. Speed of both trucks, $v_o = v_s' = 0.1 u$.Case $1$: When the trucks are approaching each other.Using the Doppler effect formula for a moving source and moving observer approaching each other:$v_1 = f \left( \frac{v_s + v_o}{v_s - v_s'} ight) = 495 \left( \frac{u + 0.1 u}{u - 0.1 u} ight) = 495 \left( \frac{1.1 u}{0.9 u} ight) = 495 	imes \frac{11}{9} = 55 	imes 11 = 605 \,Hz$.Case $2$: When the trucks have passed each other (receding).Using the Doppler effect formula for a moving source and moving observer receding from each other:$v_2 = f \left( \frac{v_s - v_o}{v_s + v_s'} ight) = 495 \left( \frac{u - 0.1 u}{u + 0.1 u} ight) = 495 \left( \frac{0.9 u}{1.1 u} ight) = 495 	imes \frac{9}{11} = 45 	imes 9 = 405 \,Hz$.The magnitude of the difference is:$|v_1 - v_2| = 605 \,Hz - 405 \,Hz = 200 \,Hz$.

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