State the conditions needed for a stationary wave to be formed.
State the phase difference between any two oscillating particles in a stationary wave between two adjacent nodes.
A motorcycle is moving at $13.0\,\text{m s}^{-1}$ along a straight road. The rider spots a pedestrian standing directly in front and sounds a horn to send out a warning. The pedestrian hears the horn at a frequency of $543\,\text{Hz}$. The speed of sound in air is $334\,\text{m s}^{-1}$. Calculate the frequency, to three significant figures, of the sound emitted by the horn.
After passing the stationary pedestrian, the motorcycle continues directly away from her. While moving away, the rider sounds the horn again. The pedestrian now hears a sound with a frequency that is rising. State how, if at all, the motorcycle’s speed is changing when the horn is sounded for the second time.
A beam of vertically polarised monochromatic light is incident normally on a polarising filter, as shown in Fig. 5.1. The filter’s transmission axis is set at an angle of $20^{\circ}$ to the vertical. The incident light has intensity $I_0$ and the transmitted light has intensity $I_T$. Using the ratio $\frac{I_T}{I_0}$, calculate the ratio $$\frac{\text{amplitude of transmitted light}}{\text{amplitude of incident light}}.$$ Show your working.
The filter is now turned, about the direction of the light beam, from the starting position shown in Fig. 5.1. The rotation is in the sense that the angle of the transmission axis to the vertical first increases. Calculate the minimum angle through which the filter must be rotated so that the intensity of the transmitted light returns to the value it had when the filter was in its starting position.