# Worksheet: Wave Superposition

In this worksheet, we will practice calculating the resultant wave function of multiple wave functions occupying the same space and time as each other.

**Q1: **

Two sinusoidal waves are moving through a medium in the positive -direction,
both having an amplitude of 7.00 cm,
a wave number of 3.00 m^{−1}, an angular frequency of
2.50 s^{−1},
and a period of 6.00 s, but one has a phase shift of an angle
rad.
What is the displacement of the resultant of these waves at a time
and a position ?

**Q2: **

Two sine waves travel along a string, modeled as and , where is measured in meters and is measured in seconds. What is the height of the resultant wave formed by the interference of the two waves at the position at the time ?

**Q3: **

Two sinusoidal waves are moving through a medium in the same direction, both having an amplitude of 3.00 cm, wavelength of 5.20 m, and a period of 6.52 s, but one of the waves has a phase shift of an angle . The resultant of the waves has an amplitude of 5.00 cm. Find by using the fact that .

**Q4: **

What is the displacement of the resulting superposition of the three wave functions sin , sin , and sin at the position at the time ? For each of the wave functions, is measured in meters and is measured in seconds.