A police car moving at 30 m s - 1 , chases a motorcyclist. The policeman sounds his horn at 180 Hz , while both of them move towards a stationary siren of frequency 160 Hz . If it is given that the motorcyclist does not observe any beats then, calculate the speed (in m s - 1 ) of the motorcyclist round off to two decimal places? [speed of sound = 330 m s - 1 ]

Step-by-step solution

Speed of sound v S = 330   m   s - 1 Case (i), f 1 = f 0 V s - u 0 V s - u s = f 0 330 - u 330 - 30 = 180   ( 330 - u ) 300 f 1 = 180   330 - u 300 ... (i) Case (ii), f 2 = 160   330 + u 330 ... (ii) ∵ There are no beats ∴ f 1 = f 2 180 = 330 - u 300 = 160 330 + u 330 ⇒       9 330 - u 30 = 8 330 - u 33 ⟹   9 10 330 - u = 8 11 330 + u ⟹ 32670 - 99 u = 26400 + 80 u ∴ u = 6270 179 = 35.02   m   s - 1