(a) The equation y = \(\alpha\) sin (wt - kx) represents a plane wave travelling in a medium along the x-direction, being the displacement at the point x at time t.

(i) Given that x is in metres and t is in seconds, state the units of k and w

(ii) What physical quantity does \(\frac{W}{k}\) represent? Justify your answer

(iii) State whether the wave is travelling in the positive or negative x-direction.

 

(b)(i) What are beats?

(ii) A sonometer wire has a frequency of 259 Hz. It is sounded alongside a tuning fork of frequency 256 Hz. Calculate the beat frequency

(iii) The sonometer wire in (b)(ii) above is under a tension of 1200 N. If a metre of the wire has a mass of 0.03 kg, calculate the length l of the wire when it is vibrating in the fundamental mode.

 

(c) List two similarities between the human eye and the photographic camera.