A motorcyclist riding along a straight road sounds a horn of rest frequency 700 Hz while traveling at a constant but unknown speed. A stationary observer standing beside the road records the sound. The observer notes that the recorded frequency is 770 Hz at t = –1.20 s and 630 Hz at t = +1.80 s, where t = 0 s is the instant of closest approach to the observer. The speed of sound in air is 340 m/s.
(a) Derive an expression for the motorcyclist’s speed in terms of the rest frequency, the recorded approaching frequency, the recorded receding frequency, and the speed of sound.
(b) Using the numerical data, calculate the numerical value of the motorcyclist’s speed.
(c) Determine how far from the observer the motorcyclist is at t = –1.20 s.
(d) The observer simultaneously listens to a 700 Hz reference tone. Calculate the beat frequency heard at t = –1.20 s and at t = +1.80 s.