A car carries a siren of unknown frequency and moves along a straight road at a constant speed. A stationary observer holds a tuning fork of 420 Hz. The observer hears 4 beats per second as the car approaches and 2 beats per second as the car recedes, the speed of the car remaining the same throughout. Taking the speed of sound in air as 340 m s⁻¹, determine
a. (a) the speed of the car,
b. (b) the frequency of the siren.