(a) By reference to the direction of propagation of energy, explain what is meant by a longitudinal wave. (b) A car horn emits a sound wave of frequency 800 Hz. A microphone and a cathode-ray oscilloscope (c.r.o.) are used to analyse the sound wave. The waveform displayed on the c.r.o. screen is shown in Fig. 4.1. [Figure 4.1] Determine the time-base setting, in s cm⁻¹, of the c.r.o. (c) The intensity I of the sound at a distance r from the car horn in (b) is given by the expression I = k/r² where k is a constant. Fig. 4.2 shows the car in (b) on a road. [Figure 4.2] An observer stands at point O. Initially the car is parked at point X which is 120m away from point O. The car then moves directly towards the observer and stops at point Y, a distance of 30 m away from O. The car horn continuously emits sound when the car is moving between points X and Y.

1. (a)By reference to the direction of propagation of energy, explain what is meant by a longitudinal wave.[1]
2. (b)A car horn emits a sound wave of frequency 800 Hz. A microphone and a cathode-ray oscilloscope (c.r.o.) are used to analyse the sound wave. The waveform displayed on the c.r.o. screen is shown in Fig. 4.1. [Figure 4.1] Determine the time-base setting, in s cm⁻¹, of the c.r.o.[3]
3. (c)(i)The sound wave at point O has amplitude A_X when the car is at X and has amplitude A_Y when the car is at Y. Calculate the ratio A_Y / A_X.[3]
4. (c)(ii)1the minimum wavelength of the sound detected by the observer,[2]
5. (c)(ii)2the maximum speed of the car.[2]

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