Question

A biker rides down the street at a constant velocity hears a frequency of 875 Hz as they approach to a parked car with the alarm system going off. After the biker passes the car, they hear the car horn at a frequency of 861 Hz. If the temperature outside is 5.00°C, what is the speed of the biker in m/s?

Answer 1

velocity of sound = 331 + (0.61)T

put T = 5 degree

V_sound = 334.05 m/s

using doppler's formula

f_observed = f_emitted (V_sound + V_observer)/(V_sound - V_source)

substituting the given values

875 = f_emitted(334.05 + V)/(334.05-0)

292293.75 = f_emitted(334.05 + V) ....(1)

case 2:

861 = f_emitted (334.05 - V)/(334.05-0)

287617.05 = f_emitted (334.05 -V) ...(2)

dividing equation (2) by (1)

0.984 = (334.05 - V)/(334.05+V)

328.7052 + 0.984V = 334.05 - V

-5.3448 = -1.984 V

V = 2.7

Speed of biker = 2.7 m/s

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