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 𝑥 -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 𝜋 1 2 rad. What is the displacement of the resultant of these waves at a time 𝑡 = 2 . 0 0 s and a position 𝑥 = 0 . 5 3 0 m ?

Q2:

Two sine waves travel along a string, modeled as 𝑦 ( 𝑥 , 𝑡 ) = 0 . 3 0 4 . 0 𝑥 + 3 . 0 𝑡 + 𝜋 3 1 m s i n and 𝑦 ( 𝑥 , 𝑡 ) = 0 . 6 0 ( 8 . 0 𝑥 6 . 0 𝑡 ) 2 m s i n , where 𝑥 is measured in meters and 𝑡 is measured in seconds. What is the height of the resultant wave formed by the interference of the two waves at the position 𝑥 = 1 . 0 m at the time 𝑡 = 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 𝜙 . The resultant of the waves has an amplitude of 5.00 cm. Find 𝜙 by using the fact that s i n s i n s i n c o s 𝑢 + 𝑣 = 2 𝑢 + 𝑣 2 𝑢 𝑣 2 .

Q4:

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

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