NYJC_EJC 2026 Superposition Tutorial

9814 H3 Physics (2026) Superposition Tutorial 1 H3 Superposition Tutorial 1 (a) Fig. 1.1 shows the equilibrium and actual positions at an instant in time of a series of particles forming part of a stationary sound wave. Particle M is at its maximum displacement. (i) On Fig. 1.2, sketch the variation of the displacement with distance, taking right as positive. Label your sketch with “P”. [2] (ii) On Fig. 1.2, sketch the variation of displacement with distance 1 4 period later. Label your sketch with “Q”. [1] (b) The standing wave in (a) is formed in a pipe that is closed at one end and open at the other. Sound waves from a coherent source travel parallel to the axis of the pipe. They reflect off the wall of the pipe, subsequently meet and interfere with sound waves from the same source, as shown in Fig. 1.3. Note that there is a -phase change upon reflection off the wall. (i) State the condition for the formation of a displacement antinode. (ii) Hence, determine the shortest distance x (as a multiple of the wavelength, ) from the wall of the pipe at which a displacement antinode is formed. equilibrium positions actual positions Fig. 1.1 Fig. 1.2 displacement distance M sound waves from a coherent source wave reflected off the wall incident wave wall of pipe Fig. 1.3 x

9814 H3 Physics (2026) Superposition Tutorial 2 2 (a) Fig. 2.1 shows two point-sources of waves, S1 and S2. P is a point equidistant from the two sources. Fig. 2.1 The sources radiate waves of the same wavelength. The amplitudes at P due to S1 and S2 are A1 and A2, respectively. At P, the time variation of the disturbance due to the wave from S1 may be represented by 11 cosy A t = . (i) If, at P, there is a phase angle  between the waves from the two sources, write down an expression for the disturbance y2 due to the wave from S2. (ii) By a graphical method, or otherwise, show that Ar, the amplitude of the resultant displacement at P, is given by 2 2 2 1 2 1 2 2 cosrA A A A A = + + [4] (b) Fig. 2.2 shows two vertical slits Q1 and Q2 in an opaque screen, a distance d apart. Fig. 2.2 A vertical strip-light source producing monochromatic light of wavelength 590 nm is set up at L, exactly one metre from Q1 on the normal to the screen, so that both slits are illuminated. A detector is placed at D, exactly equidistant from the slits on the other side of the screen. Readings of the light inten