A-level Physics (Advancing Physics)/Phasors/Worked Solutions

'''1. A sine wave with wavelength 0.1m travels through a given point on the surface of the sea. A phasor arrow representing the effect of this wave on this point rotates 1000°. How many wavelengths have gone past in the time taken for the phasor to rotate this much?'''

0.1m is irrelevant information.

$$\frac{1000}{360} = 2.78\lambda$$

'''2. A sine wave has a maximum amplitude of 500 nm. What is its amplitude when the phasor has rotated 60° from its start position?'''

$$a \sin{\theta} = 500 \times 10^{-9} \times \sin{60} \approx 433\mbox{nm} \,$$

'''3. Two waves have a phase difference of 45°. When the first wave is at its minimum amplitude of -0.3m, what is the total amplitude of the superposed waveforms?'''

The first wave has an amplitude of -0.300m. The second is at an angle of 270 - 45 = 225°.

$$a \sin{\theta} = 0.3 \times \sin{225} \approx -0.212\mbox{m} \,$$

$$-0.300 + -0.212 = -0.512\mbox{m}\,$$