Two progressive sound waves combine to make a stationary wave. The two waves have the same amplitude, wavelength, frequency and speed. State the further condition that the two waves must satisfy for a stationary wave to be produced.
A stationary wave is set up on a string stretched between two fixed points A and B. Fig. 5.1 shows the string at time $t = 0$ when every point is at its maximum displacement. The distance AB is $0.80\,\text{m}$. The period of the stationary wave is $0.016\,\text{s}$. On Fig. 5.1, draw a solid line to show the string at time $t = 0.004\,\text{s}$ (label this line P) and at time $t = 0.024\,\text{s}$ (label this line Q).
Determine the speed of a progressive wave along the string.
A stationary wave is set up on a string stretched between two fixed points A and B. Fig. 5.1 shows the string at time $t = 0$ when every point is at its maximum displacement. The distance AB is $0.80\,\text{m}$. The period of the stationary wave is $0.016\,\text{s}$.
A beam of vertically polarised light of intensity $I_0$ is incident normally on a polarising filter whose transmission axis is at $30^{\circ}$ to the vertical, as shown in Fig. 5.2. The transmitted light from the first polarising filter has intensity $I_1$. This light then falls normally on a second polarising filter whose transmission axis is at $90^{\circ}$ to the vertical. The transmitted light from the second filter has intensity $I_2$. Calculate:
the ratio $\frac{I_1}{I_0}$
the ratio $\frac{I_2}{I_0}$