Question

A police officer with an exceptionally good ear hears an approaching motorcycle under full throttle making a 660 Hz tone and pulls the motorcycle over to give the driver a ticket. His radar gun lost the speed record but he notices the motorcycle's engine at maximum revolution makes a 560 Hz tone. (5 marks) a) Determine the speed of the motorcycle when the officer first heard it. The air temperature is 10 °C. (3 marks) b) What causes this frequency shift? Indicate with a diagram. Since this is a drawing question, feel free to put whateve you want in the blank, as we will be looking at your written work for the answer (3 marks)

Answer 1

a)

At given temperature

v = 331 + 0.6 * 10 = 337 m/s

as biker is approaching the officer,

f = f_o ( v + v_bike / v - v_officer )

as bike is receding

f' = f ( v - v_bike / v - v_officer )

so,

660 / 560 = 337 + v / 337 - v

1.1785 = 337 + v / 337 - v

397.178 - 1.1785 v = 337 + v

v = 27.62 m/s

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shift is frequency is due to Doppler effect.

As the approaching source moves closer to the observer, the wavelength shortens, hence frequency increases and pitch increases and observer hears a higher pitch than original

observer