# 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.

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

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?

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

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°.

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

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