(b) [3 marks]A metronome produces beeps at exactly 1 second intervals. A musician 20 metres away claps every time they hear the beep, exactly in time.(i) (2 marks)A listener standing beside the metronome hears the beep and then a slight delay before hearing the clap. How long is the delay between beeps and claps?(ii) (1 mark)A second listener is 40 m away from the metronome, in line with the musician. Will they hear the beeps and claps in sync, or with a delay? Briefly justify your answer. (c) [3 marks]A singer on a parade float is being driven down the road at a constant velocity. If the singer holds a long, constant-pitch note:(i) (2 marks)Describe what a listener hears as the singer passes them.(ii) (1 mark)Does the listener ever hear the actual note the singer is singing?

(b) (i) The speed of sound in air is approximately 343 meters per second. Therefore, the sound of the metronome's beep takes about 20/343 = 0.058 seconds (or 58 milliseconds) to reach the musician. So, the listener standing beside the metronome will hear the clap with a delay of about 58 milliseconds after the beep.

(ii) The second listener is 40 meters away from the metronome. The sound of the beep will take about 40/343 = 0.117 seconds (or 117 milliseconds) to reach them. The sound of the clap, which is 20 meters away, will take about 20/343 = 0.058 seconds (or 58 milliseconds) to reach them. Therefore, they will hear the clap about 0.117 - 0.058 = 0.059 seconds (or 59 milliseconds) after the beep. So, they will hear the beeps and claps with a delay.

(c) (i) As the singer passes the listener, the listener will hear a change in the pitch of the note due to the Doppler effect. The pitch will seem higher as the singer approaches and lower as the singer moves away.

(ii) Yes, the listener will hear the actual note the singer is singing when the singer is exactly at the listener's position. At this point, there is no relative motion between the singer and the listener, so there is no Doppler shift.