A car is traveling north at 30m/s along a road at night. Thetemperature is 0C. A

Question

A car is traveling north at 30m/s along a road at night. Thetemperature is 0C. A truck is traveling south at 20m/s on the sameroad. The truck driver thinks the car is in the wrong lane andhonks his horn (f=200Hz). The driver of the car does the same(f=205Hz). The wind is blowing towards the south at 25m/s. aWhat is the beat frequency heard by the driver of thecar? b) Would the answer be different if the wind were blowingtowards the east? Explain. c) Would the answer be different if the truck were moving tothe east? Explain. A car is traveling north at 30m/s along a road at night. Thetemperature is 0C. A truck is traveling south at 20m/s on the sameroad. The truck driver thinks the car is in the wrong lane andhonks his horn (f=200Hz). The driver of the car does the same(f=205Hz). The wind is blowing towards the south at 25m/s. aWhat is the beat frequency heard by the driver of thecar? b) Would the answer be different if the wind were blowingtowards the east? Explain. c) Would the answer be different if the truck were moving tothe east? Explain.

Explanation / Answer

a)The apparent frequency heard by the driver of the caris:              n1 = [(V + W + Vo)/(V + W - Vs)] xn <=>       n1 =[(330 + 25 + 30)/(330 + 25 - 20)] x 200 <=>       n1 =229.85 Hz => the beat frequency heard by the driver of the caris:          (n1 - n) = (229.85 - 200) = 29.85 Hz. b) If the wind were blowing towards the east,then the apparentfrequency is:          n1= [(V - W + Vo)/(V - W - Vs)] x n <=>   n1 = [(330 - 25 + 30)/(330 +25 - 20)] x 200 <=> n1 = 200 Hz => the beat frequency heard by the driver of the caris:          (n1 - n) = (200 - 200) = 0 => no frequency is heard by the driver of the car. c) When the truck is moving to the east then:          n1= [(V + W - Vo)/(V + W + Vs)] x n <=> n1 = [(330 + 25 - 30)/(330 +25 + 20)] x 200 <=>   n1 = 173.33 Hz => the beat frequency heard by the driver of the caris 26.67 Hz.The beat frequency heard by the driver of the car isreduced as the truck is receeding from the car.

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