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In this lesson, we will learn how to calculate 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 π₯ -direction, both having an amplitude of 7.00 cm, a wave number of 3.00 m^{β1}, an angular frequency of 2.50 s^{β1}, and a period of 6.00 s, but one has a phase shift of an angle π 1 2 rad. What is the displacement of the resultant of these waves at a time π‘ = 2 . 0 0 s and a position π₯ = 0 . 5 3 0 m ?

Q2:

Two sine waves travel along a string, modeled as π¦ ( π₯ , π‘ ) = 0 . 3 0 ο» 4 . 0 π₯ + 3 . 0 π‘ + π 3 ο 1 m s i n and π¦ ( π₯ , π‘ ) = 0 . 6 0 ( 8 . 0 π₯ β 6 . 0 π‘ ) 2 m s i n , where π₯ is measured in meters and π‘ is measured in seconds. What is the height of the resultant wave formed by the interference of the two waves at the position π₯ = 1 . 0 m at the time π‘ = 3 . 0 s ?

Q3:

What is the displacement of the resulting superposition of the three wave functions π¦ ( π₯ , π‘ ) = 0 . 0 4 0 m sin ( 4 . 0 π₯ β 2 . 0 π‘ ) , π¦ ( π₯ , π‘ ) = 0 . 0 4 0 m sin ( 2 . 0 π₯ + 4 . 0 π‘ ) , and π¦ ( π₯ , π‘ ) = 0 . 0 4 0 m sin ( 8 . 0 π₯ β 1 . 0 π‘ ) at the position π₯ = 4 . 0 0 m at the time π‘ = 8 . 0 s ? For each of the wave functions, π₯ is measured in meters and π‘ is measured in seconds.

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