Question

a stationary speed gun emits a microwave beam at 2.10 x 10^10 Hz. It reflects off a car and returns 1030 Hz higher. What is the speed of the car? (unit = m/s)

Answer 1

let the velocity of car be 'v_c' and approaching the source, and v is the speed of sound in air

frequency as heard by the car, f' = f*((v+v_c)/ v) = 2.1*10¹⁰*(1+(v_c/343))

frequency as heard back by the source,(now we'll consider the car to be the source with frequency f')

f'' = f'*(v/(v-v_c))

putting the respective values, and given that f'' = f+1030

f+ 1030 = f*((v+v_c)/ v)*(v/(v-v_c))

2.1*10¹⁰ + 1030 = 2.1*10¹⁰*(1+(v_c/343))*(343/(343-v_c))

1 + (1030/(2.1*10¹⁰)) = ((343 + v_c)/(343-v_c))

solving for v_c we get

v_c = 8.411*10^-6