Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

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:

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 π . The resultant of the waves has an amplitude of 5.00 cm. Find π by using the fact that s i n s i n s i n c o s π’ + π£ = 2 οΌ π’ + π£ 2 ο ο» π’ β π£ 2 ο .

Q4:

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.

Donβt have an account? Sign Up